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A Study of Tellurite Glasses for

Electro-optic Optical Fibre Devices

by

Sean Manning

Supervisors:

Prof. Tanya M. Monro

Prof. Jesper Munch

A thesis submitted in fulfilment of the

degree of Doctor of Philosophy

in the

Faculty of Science

School of Chemistry & Physics

November 2011

Declaration of Authorship

I, Sean Manning, declare that this thesis titled, ‘A Study of Tellurite Glasses for Electro-

optic Optical Fibre Devices’ and the work presented in it are my own. I confirm that:

� This work contains no material which has been accepted for the award of any other

degree or diploma in any university or other tertiary institution to Sean Manning

and, to the best of my knowledge and belief, contains no material previously

published or written by another person, except where due reference has been made

in the text.

� I give consent to this copy of my thesis, when deposited in the University Library,

being made available for loan and photocopying, subject to the provisions of the

Copyright Act 1968.

� The author acknowledges that copyright of published works contained within this

thesis (as listed below) resides with the copyright holder(s) of those works.

� I also give permission for the digital version of my thesis to be made available on

the web, via the University’s digital research repository, the Library catalogue,

the Australasian Digital Theses Program (ADTP) and also through web search

engines, unless permission has been granted by the University to restrict access

for a period of time.

Signed:

Date:

iii

iv

List of Publications

1. Manning, Sean; Ebendorff-Heidepriem, Heike; Heike Monro, Tanya Mary.

Sodium Zinc Tellurite Glass: a Candidate Material for Core/Clad Fi-

bres for Electro-optic Devices.

Proceedings of the 9th Pacific Rim Conference on Ceramic and Glass Technology

(PACRIM9), held in Cairns, Queensland, Australia July 10-14 2011.

2. Manning, Sean; Monro, Tanya Mary; Munch, Jesper; Ottaway, David John.

Improved maker fringes data analysis using genetic algorithms.

Proceedings of the Australasian Conference on Optics, Lasers and Spectroscopy

and Australian Conference on Optical Fibre Technology in association with the

International Workshop on Dissipative Solitons 2009.

3. Manning, Sean; Ebendorff-Heidepriem, Heike; Monro, Tanya Mary; Munch, Jes-

per.

Tellurite glasses for photonic devices with enhanced nonlinearity.


(PACRIM8), held in Vancouver, British Columbia, Canada May 31- June 5 2009.


On the application of genetic algorithms to maker fringes analysis.

18th Australian Institute of Physics (AIP) Congress Conference, held in Adelaide,

South Australia Nov 30-Dec 5 2008..

“It doesn’t matter how beautiful your theory is, it doesn’t matter how smart you are. If

it doesn’t agree with experiment, it’s wrong.”

Richard P. Feynman

THE UNIVERSITY OF ADELAIDE

Abstract

Faculty of Science

School of Chemistry & Physics

Doctor of Philosophy

by Sean Manning

Optical fibre devices that can control light via the application of electric fields are of

enormous technological interest. These so called electro-optic devices have potential

applications in many varied places, such as data systems, pulsed lasers and sensing

technologies.

We have identified tellurium dioxide (tellurite) based glasses as being especially suit-

able for electro-optic fibre devices owing to their large nonlinear coefficients and high

crystallisation stabilities. Furthermore, tellurite glass is compatible with the extrusion

technique for producing optical fibre preforms, this being a fabrication strength of our

research group.

We developed tellurite glasses based on the general formula 10Na2O.xMO.(90−x)TeO2

with M=Magnesium, Zinc and Barium and x = 5, 10, 15 and 20. Raman spectroscopy

was utilised to determine the structure of the glasses under study, from which definite

compositional trends were observed. Further, we measured physical, thermal and optical

properties of these glasses that are critical for the design of electro-optical optical fibres.

Certain of these properties displayed compositional trends that were correlated with the

structural data, thus indicating physical origins for the properties. This information can

thus be used to guide future glass composition design.

We investigated thermal poling as a potential post processing technique for inducing

second order nonlinearities thereby enhancing the efficiency of the electro-optic effects.

The Maker fringes technique was applied to measuring the induced second order nonlin-

earities. We have made refinements to the standard way in which these measurements

are made, both in terms of the experimental technique as well as the analysis of the

data.

We developed computational models of optical fibres with internal electrodes for deter-

mining the properties, such as optical attenuation resulting from the presence of internal

electrodes. The results of these computations in combination with the measurements of

the glass properties are used to guide the design of prototype electro-optic fibres. Finally,

we developed various techniques for the fabrication of electro-optic fibre devices, such

as optical fibre preform extrusion, fibre drawing techniques and electrode insertion.

Acknowledgements

First and foremost I would like to thank my supervisors Tanya Monro and Jesper

Munch for their guidance, support and advice. Both have contributed heavily to form-

ing the physicist I have become. Additionally, much thanks and appreciation must go

to Heike Ebendorff-Heidepriem and David Ottaway who provided me with invaluable

co-supervision, if however unofficially, their experience and guidance was greatly appre-

ciated.

During my PhD I had the pleasure of working with so many great people, all of whom

helped me at some stage or other, whether directly or in spirit. People such as: Adrian

Selby, Aidan Brooks, Alastair Dowler, Blair Middlemiss, Bob Nation, David Hosken,

Eric Schartner, Herbert Fu, Ka Wu, Keiron Boyd, Kevin Kuan, Kristopher Rowland,

Matt Heintze, Matt Henderson, Michael Oermann, Mifta Ganja, Murray Hamilton,

Nikita Simakov, Peter Veitch, Shahraam Afshar, Trevor Waterhouse, Neville Wild,

Roger Moore and Tilanka Munasinghe.

I also had the fortune to travel far and wide to meet some fantastic collaborators such

as: Walter Margulis and Oleksandr Tarasenko at ACREO, Steve Madden, Barry Luther-

Davies and Khu Vu at ANU and Kathleen Richardson at Clemson University.

Finally, I would like to acknowledge my Wife and kids for their love and support. They

are the stabilising force in my life and I’d be lost without them.

Thank you.

viii

Contents

Declaration of Authorship iii

Abstract vi

Acknowledgements viii

List of Figures xiii

List of Tables xix

1 Introduction 1

1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Review of Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.1 Tellurite Glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.2 Electro-optics in Optical Fibres . . . . . . . . . . . . . . . . . . . . 7

1.3 Thesis Aims and Methodology . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.5 Statement of Original Work and Author Contribution . . . . . . . . . . . 13

1.6 List of Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2 Nonlinear Optical Theory 15

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2 Nonlinear Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3 Second Order Nonlinearities . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.1 Propagation of the Fields . . . . . . . . . . . . . . . . . . . . . . . 21

2.3.2 Derivation of the Maker Fringes Expression . . . . . . . . . . . . . 22

2.3.3 Second Order Nonlinear Effects in Thermally Poled Materials . . . 27

2.4 Third Order Nonlinearities . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.4.1 Origin of the Nonlinear Refractive Index . . . . . . . . . . . . . . . 35

2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3 Glass Theory, Design & Fabrication 39

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.2 What is a Glass? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.3 General Properties of Glasses . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.3.1 Structural Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 42

ix

Contents x

3.3.2 Relationships Between the Structure and Properties . . . . . . . . 44

3.4 The Tellurite Glass System . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.5 Designing the Glass Compositions . . . . . . . . . . . . . . . . . . . . . . 47

3.6 Procedure for Glass Production . . . . . . . . . . . . . . . . . . . . . . . . 49

3.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4 Analysis of the Microscopic Structure of Glass 55

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.2 Raman Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.2.1 Raman Spectroscopy of Tellurite . . . . . . . . . . . . . . . . . . . 58

4.2.2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.2.3 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.2.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5 Measurements of Physical and Thermal Properties 75

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.2 Density, Molecular Mass and Molar Volume . . . . . . . . . . . . . . . . . 75



5.3 Thermal Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.3.1 Differential Scanning Calorimetry . . . . . . . . . . . . . . . . . . . 81

5.3.1.1 Experimental Details . . . . . . . . . . . . . . . . . . . . 84

5.3.1.2 Results and Discussion . . . . . . . . . . . . . . . . . . . 84

5.3.2 Measurement of the Thermal Expansion Coefficient . . . . . . . . 88

5.3.2.1 Experimental Details . . . . . . . . . . . . . . . . . . . . 90

5.3.2.2 Results and Discussion . . . . . . . . . . . . . . . . . . . 90

5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

6 Measurements of the Optical Properties 97

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

6.2 UV-VIS Absorption Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . 98



6.3 Fourier Transform Infrared Absorption Spectroscopy . . . . . . . . . . . . 103



6.4 Refractive Index Measurements . . . . . . . . . . . . . . . . . . . . . . . . 108



6.5 Nonlinear Refractive Index Measurements . . . . . . . . . . . . . . . . . . 113


6.5.2 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118


6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

Contents xi

7 Thermal Poling 127

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

7.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

7.3 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

7.3.1 Experimental Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

7.3.2 Thermal Poling Apparatus and Configurations . . . . . . . . . . . 132

7.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

7.4.1 Charge Migration Thermal Poling . . . . . . . . . . . . . . . . . . 134

7.4.2 Charge Migration Thermal Poling Using a Blocking Electrode . . . 138

7.4.3 Charge Injection Thermal Poling . . . . . . . . . . . . . . . . . . . 141

7.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

8 Measurements of Second Order Nonlinearities 147

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

8.2 Maker Fringes Analysis: Background . . . . . . . . . . . . . . . . . . . . . 148

8.3 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

8.3.1 Experimental Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

8.3.2 Description of Maker Fringes Experiment . . . . . . . . . . . . . . 151

8.3.3 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

8.3.4 Calibration and Alignment . . . . . . . . . . . . . . . . . . . . . . 155

8.4 Data Fitting Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

8.4.1 Root Mean Square Error Minimisation Fitting Procedure . . . . . 161

8.4.2 Genetic Algorithm Fitting Procedure . . . . . . . . . . . . . . . . . 161

8.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

8.5.1 Quartz Reference Measurements . . . . . . . . . . . . . . . . . . . 163

8.5.2 Thermally Poled Infrasil . . . . . . . . . . . . . . . . . . . . . . . . 165

8.5.3 Thermally Poled Tellurite . . . . . . . . . . . . . . . . . . . . . . . 167

8.6 Measurement Techniques for the Thickness of the Nonlinear Region . . . 169

8.6.1 SHG Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

8.6.2 Differential Etching . . . . . . . . . . . . . . . . . . . . . . . . . . 172


8.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

9 Fibre Preliminaries 177

9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

9.2 Computational Modelling of Electro-optic Optical Fibres . . . . . . . . . . 178

9.2.1 Electric Fields Between Internal Electrodes . . . . . . . . . . . . . 179

9.2.2 Electrode Induced Optical Attenuation . . . . . . . . . . . . . . . . 186

9.2.3 Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . 191

9.3 Insertion of Electrodes into Optical Fibres . . . . . . . . . . . . . . . . . . 191

9.3.1 The Physics of Capillary Filling . . . . . . . . . . . . . . . . . . . . 192

9.3.1.1 Contact Angle Measurements . . . . . . . . . . . . . . . . 194

9.3.2 Design and Operation of the Fibre Filling Apparatus . . . . . . . . 195

9.3.2.1 Selective Filling of Optical Fibres . . . . . . . . . . . . . 197

9.4 Optical Fibre Preform Fabrication . . . . . . . . . . . . . . . . . . . . . . 201

9.4.1 Fabrication of the Electrode Jacket . . . . . . . . . . . . . . . . . . 202

9.4.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

Contents xii

9.5 Preliminary Investigations of Optical Fibre Fabrication . . . . . . . . . . . 206

9.5.1 Tellurite Step Index Fibre Fabrication Experiments . . . . . . . . . 207

9.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

10 Concluding Remarks 213

10.1 Conclusion of Thesis Findings and Results . . . . . . . . . . . . . . . . . . 213

10.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

List of Figures

1.1 An assortment of microstructured optical fibres . . . . . . . . . . . . . . . 2

1.2 Optical transmission of fused silica . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Voltage dependent wave plate as an example of an electro-optic device . . 4

1.4 Number of papers published relating to tellurite glass from 1952 to 2011 . 6

1.5 Thesis structure flow diagram . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1 Second harmonic generation energy level diagram . . . . . . . . . . . . . . 18

2.2 Diagram for second harmonic generation in a dispersive medium . . . . . 22

2.3 electro-optical response of glass before and after poling . . . . . . . . . . . 29

2.4 Illustration of the symmetry possessed by the electrical potential in ther-mally poled glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.5 Configuration for SHG in the pp-configuration . . . . . . . . . . . . . . . 32

2.6 Third harmonic generation energy level diagram . . . . . . . . . . . . . . 34

3.1 Atomic arrangements in the crystalline and glassy state . . . . . . . . . . 40

3.2 Potential cooling curves for glass and crystal formation. . . . . . . . . . . 41

3.3 The effect of network modifying ions on the atomic arrangement in a glass 43

3.4 Structural representation of Te-O subunits . . . . . . . . . . . . . . . . . . 46

3.5 Brass moulds for glass casting and the resulting billets . . . . . . . . . . . 51

4.1 Conversion between Raman shift and Frequency (blue) and Wavelengthshift (red) for input light at 514 nm . . . . . . . . . . . . . . . . . . . . . 57

4.2 Example of deconvoluted raman spectrum . . . . . . . . . . . . . . . . . . 58

4.3 Ball and stick representation of the tellurite lattice vibrations that con-tribute to the Raman A mode . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.4 Ball and stick representation of the tellurite lattice vibrations that con-tribute to the Raman B mode . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.5 Ball and stick representation of the tellurite lattice vibrations that con-tribute to the Raman C mode . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.6 Ball and stick representation of the tellurite lattice vibrations that con-tribute to the Raman D mode . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.7 Ball and stick representation of the tellurite lattice vibrations that con-tribute to the Raman E mode . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.8 Raman spectra for the TMN glass series . . . . . . . . . . . . . . . . . . . 64

4.9 Raman spectra for the TZN glass series . . . . . . . . . . . . . . . . . . . 64

4.10 Raman spectra for the TBN glass series . . . . . . . . . . . . . . . . . . . 65

4.11 Effect of modifier content on the relative intensities of the Raman A bandfor the TMN, TZN and TBN glasses . . . . . . . . . . . . . . . . . . . . . 67

4.12 Effect of modifier content on the position of the Raman A band for theTMN, TZN and TBN glasses . . . . . . . . . . . . . . . . . . . . . . . . . 67

xiii

List of Figures xiv

4.13 Effect of modifier content on the relative intensities of the Raman B bandfor the TMN, TZN and TBN glasses . . . . . . . . . . . . . . . . . . . . . 68

4.14 Effect of modifier content on the position of the Raman B band for theTMN, TZN and TBN glasses . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.15 Effect of modifier content on the relative intensities of the Raman C bandfor the TMN, TZN and TBN glasses . . . . . . . . . . . . . . . . . . . . . 70

4.16 Effect of modifier content on the position of the Raman C band for theTMN, TZN and TBN glasses . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.17 Effect of modifier content on the relative intensities of the Raman D bandfor the TMN, TZN and TBN glasses . . . . . . . . . . . . . . . . . . . . . 71

4.18 Effect of modifier content on the position of the Raman D band for theTMN, TZN and TBN glasses . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.19 Effect of modifier content on the relative intensities of the Raman E bandfor the TMN, TZN and TBN glasses . . . . . . . . . . . . . . . . . . . . . 73

4.20 Effect of modifier content on the position of the Raman E band for theTMN, TZN and TBN glasses . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.1 Experimental configuration for Archimedes Density Measurement . . . . . 77

5.2 Densities of TMN, TZN and TBN glass series . . . . . . . . . . . . . . . . 79

5.3 Molar masses of TMN, TZN and TBN glass series . . . . . . . . . . . . . 80

5.4 Molar volume of TMN, TZN and TBN glass series . . . . . . . . . . . . . 80

5.5 Schematic representation of a DSC apparatus . . . . . . . . . . . . . . . . 82

5.6 Example of DSC trace with key temperature features indicated . . . . . . 83

5.7 DSC traces for TMN, TZN and TBN glass series . . . . . . . . . . . . . . 85

5.8 Plot of ΔT=Tg−Tx for TMN, TZN and TBN glass series . . . . . . . . . 86

5.9 Plot of enthalpy of crystallisation for TMN, TZN and TBN glass series . 87

5.10 Schematic of apparatus for thermal expansion coefficient measurement . . 90

5.11 Example of thermal expansion measurement raw data for IG5 referenceglass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.12 Example of thermal expansion measurement raw data for TMN glass series 92

5.13 Example of thermal expansion measurement raw data for TZN glass series 92

5.14 Example of thermal expansion measurement raw data for TBN glass series 93

5.15 Thermal expansion coefficients for TMN, TZN and TBN glass series . . . 94

6.1 Proposed energy band diagram for tellurite glass . . . . . . . . . . . . . . 101

6.2 Examples of indirect band gap fitting procedure for the TZN series . . . . 102

6.3 Compositional dependence of indirect band gap for TMN, TZN and TBNglass series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

6.4 Infrared absorption spectrum of TMN1 and theoretical multiphonon edge 105

6.5 Compositional dependence of multiphonon onset wavelength for TMN,TZN and TBN glass series . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

6.6 Compositional dependence of attenuation due to OH− contamination . . . 107

6.7 Ray diagram for an optical fibre . . . . . . . . . . . . . . . . . . . . . . . 108

6.8 Prism coupling configuration . . . . . . . . . . . . . . . . . . . . . . . . . 109

6.9 Example trace from a prism coupler . . . . . . . . . . . . . . . . . . . . . 111

6.10 Refractive index of tellurite glasses measured at 1064 nm . . . . . . . . . 112

6.11 Simple Z scan configuration . . . . . . . . . . . . . . . . . . . . . . . . . . 114

6.12 Examples of Z scan signals for self focusing and self defocusing . . . . . . 115

List of Figures xv

6.13 Schematic of Z-scan experimental setup . . . . . . . . . . . . . . . . . . . 116

6.14 Overlap of Gaussian with truncated Bessel function . . . . . . . . . . . . . 117

6.15 Representative Z scan data set . . . . . . . . . . . . . . . . . . . . . . . . 118

6.16 Z Scan measurements at various incident intensities . . . . . . . . . . . . 119

6.17 Nonlinear refractive indices of Tellurite glasses . . . . . . . . . . . . . . . 121

6.18 Millers law plot with various representative glass types indicated alongwith TMN, TZN and TBN glasses . . . . . . . . . . . . . . . . . . . . . . 124

7.1 Schematic of the key steps in the charge migration thermal poling process 128

7.2 Schematic of the key steps in the charge injection thermal poling process . 129

7.3 Thermal poling apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

7.4 Ohms law plot for TZN2 at 250◦C . . . . . . . . . . . . . . . . . . . . . . 136

7.5 Time dependence of the current through TZN2 at 250◦C . . . . . . . . . . 136

7.6 Optical micrograph of the cathodic surface of TZN2 after thermal poling . 137

7.7 Reproduction of an optical micrograph of the chemically reduced regionat the cathodic surface of a Bismuth borate glass. . . . . . . . . . . . . . . 138

7.8 Two possible configurations for the blocking electrode thermal polingtechnique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

7.9 Time dependence of the current for TZN2 in the two blocking electrodeconfigurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

7.10 Charge injection thermal poling configuration . . . . . . . . . . . . . . . . 142

7.11 Time dependence of the current for TZN2 in the charge injection config-urations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

7.12 Schematic illustration of the electrode configuration for thermal poling ofoptical fibres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

7.13 Simulated equipotential maps and ion distributions for fibres with twoanodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

8.1 Experimental configuration for Maker et al. original Maker fringes exper-iment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

8.2 First recorded Maker fringes . . . . . . . . . . . . . . . . . . . . . . . . . . 149

8.3 Simulated Maker fringes with the inclusion of higher order interferenceand without . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

8.4 Maker fringes measurement apparatus . . . . . . . . . . . . . . . . . . . . 152

8.5 Circuit diagram for the Maker fringe data conditioning and acquisitionsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

8.6 Timing diagram for the Maker fringes experiment data acquisition system 156

8.7 Photomultiplier signal linearity plot . . . . . . . . . . . . . . . . . . . . . 157

8.8 Relative error in the Maker fringes data vs number of pulses averaged over158

8.9 Plot of SH power vs lens to sample separation . . . . . . . . . . . . . . . . 159

8.10 Optimised fit to y-cut quartz Maker fringes data . . . . . . . . . . . . . . 165

8.11 Convergence of Maker fringes fitting parameters for thermally poled Infrasil166

8.12 Optimised fit to thermally poled Infrasil Maker fringes data . . . . . . . . 168

8.13 Measured angular dependence of second harmonic power for thermallypoled TZN3 sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

8.14 Schematic of SHG microscopy sample, optical micrograph of the regionimaged in SHG micrograph and SHG micrograph . . . . . . . . . . . . . . 171

List of Figures xvi

8.15 Mean line scan of the SHG channel taken from an SHG micrograph ofthermally poled Infrasil . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

8.16 SEM of the etched depletion region of thermally poled Infrasil . . . . . . . 173

8.17 SEM of the anodic face of thermally poled infrasil . . . . . . . . . . . . . 173

8.18 Overlay of SON profile with SEM of depletion region . . . . . . . . . . . . 174

8.19 Second order nonlinear susceptibility as a function of depth under theanodic surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

9.1 Comparison between experiment and simulation for a poled SIF and themodelled electric field distribution . . . . . . . . . . . . . . . . . . . . . . 181

9.2 Modelled electric field distribution for a step index fibre with internalelectrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

9.3 Modelled electric field distribution for a hexagonal three ring MOF withinternal electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

9.4 Modelled electric field distribution for a wagon wheel MOF with internalelectrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

9.5 Core electric field strengths for three representative fibre types with in-ternal electrodes calculated over a range of electrode separations . . . . . 186

9.6 Optical fibre with internal electrodes . . . . . . . . . . . . . . . . . . . . . 187

9.7 Convergence of electrode induced loss . . . . . . . . . . . . . . . . . . . . 188

9.8 Electrode induced loss vs. electrode to core separation . . . . . . . . . . . 189

9.9 Electrode induced loss for a wagon wheel MOF calculated for variousmesh element sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

9.10 Schematic representation of pressure assisted filling of capillaries for wet-ting and nonwetting liquids . . . . . . . . . . . . . . . . . . . . . . . . . . 192

9.11 Illustration of the contact angles between a liquid on a solid substrate . . 193

9.12 Photographs of BiSn contacting silica, bismuth and tellurite substrates . . 195

9.13 Photograph of fibre filling apparatus . . . . . . . . . . . . . . . . . . . . . 196

9.14 Schematic of filling apparatus showing fibre positioning and sealing tech-nique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

9.15 Illustration of manual fibre hole blocking . . . . . . . . . . . . . . . . . . . 198

9.16 Photograph of an optical fibre with a manually blocked hole . . . . . . . . 199

9.17 Photograph of an optical fibre with pressure assisted filling of UV glue . . 199

9.18 Illustration of UV glue pressure filling set up . . . . . . . . . . . . . . . . 200

9.19 Photograph of an optical fibre prepared for selective filling demonstratingthe ideal cleave position . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

9.20 Photograph of the cross section of an optical fibre with one hole blockedfor selective filling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

9.21 Photograph of an optical fibre with a selectively filled electrode hole . . . 201

9.22 Schematic of the optical fibre preform extrusion apparatus . . . . . . . . . 202

9.23 Illustration of the extruded jacket and core for creating the preform for astep index optical fibre with internal electrodes . . . . . . . . . . . . . . . 203

9.24 Die for electrode jacket preform . . . . . . . . . . . . . . . . . . . . . . . . 203

9.25 Electrode jacket preform extrusion trials . . . . . . . . . . . . . . . . . . . 204

9.26 Linear fit to TZN refractive index data . . . . . . . . . . . . . . . . . . . . 208

9.27 Cut back measurement data showing optical attenuation of a core glassbare fibre . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

9.28 Microscopy images of tellurite step index fibre . . . . . . . . . . . . . . . . 210

List of Figures xvii

9.29 Cut back measurement data showing optical attenuation of a telluritestep index fibre . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

List of Tables

3.1 Deitzel’s Field Strength Parameters for Glass Formation . . . . . . . . . . 45

3.2 Modifier properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.3 Purity and supplier for glass raw material . . . . . . . . . . . . . . . . . . 50

3.4 Table of glass compositions investigated. . . . . . . . . . . . . . . . . . . . 52

4.1 Comparison of certain properties of Quartz and Fused Silica . . . . . . . . 56

4.2 Raman band assignment to structural subunits and nomenclature . . . . . 61

4.3 Table of Raman band relative intensities. . . . . . . . . . . . . . . . . . . 66

4.4 Table of Raman band centre positions. . . . . . . . . . . . . . . . . . . . . 66

5.1 Molar masses, Densities and molar volumes of tellurite glasses. . . . . . . 78

5.2 Thermal data for TMN, TZN and TBN glass series . . . . . . . . . . . . . 86

5.3 Measured thermal expansion coefficients for the TMN, TZN and TBNglass series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

6.1 Optical energy gaps calculated from UV-Vis spectra and correspondingwavelength cut off for optical transmission. . . . . . . . . . . . . . . . . . 103

6.2 Multiphonon onset wavelength for TMN, TZN and TBN glass series. . . . 106

6.3 Measured refractive indices . . . . . . . . . . . . . . . . . . . . . . . . . . 111

6.4 Measured nonlinear refractive indices and calculated third order suscep-tibilities for TMN, TZN and TBN glasses . . . . . . . . . . . . . . . . . . 120

7.1 Brief summary of literature reported tellurite thermal poling . . . . . . . 131

8.1 Optical parameters for quartz reference sample . . . . . . . . . . . . . . . 164

8.2 Optimised fitting parameters for y-cut quartz Maker fringes . . . . . . . . 164

8.3 Optimised fitting parameters for thermally poled Infrasil Maker fringes . . 167

9.1 Input parameters for SIF with internal electrodes electric field model . . . 180

9.2 Input parameters for hexagonal three ring MOF with internal electrodeselectric field model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

9.3 Input parameters for wagon wheel MOF with internal electrodes electricfield model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

9.4 Input parameters for electrode induced loss model . . . . . . . . . . . . . 187

9.5 Contact angle between BiSn solder and some optical glasses . . . . . . . . 194

xix

For my wife, who deserves a PhD in patience.

xxi

Chapter 1

Introduction

Photonics research has, over the last several decades, been characterised by a pro-

gressive shift from free space optical components towards fibre optical equivalents.

This shift has been driven by the desirable features of optical fibres, namely; compact-

ness, ruggedness, environmental insensitivity and, of particular importance, low cost. In

the spirit of this trend the primary focus of the work reported herein is to develop a new

class of fibre optical component to replace existing free space electro-optical devices.

This will further facilitate the advancement of optical systems towards true all-fibre

equivalents.

In the following sections we outline our motivation for undertaking this work this is given

context with a discussion of the background concepts (Section 1.1). We then provide

a review of the relevant literature pertaining to tellurite glass and electro-optical fibres

(Section 1.2). For clarity, our aims and research methodology are explained in Section

1.3 followed by an outline of the structure of this thesis in Section 1.4. This Chapter

concludes with a statement outlining those aspects of the work contained within this

thesis that were produced by the Author (Section 1.5).

1.1 Background and Motivation

Arevolution in optical fibre technology occurred in 1996 with the work of Birks et al

with the development of a new generation of optical fibres known as microstruc-

tured optical fibres1 [1, 2]. Microstructured optical fibres contain an array of small holes

that run the length of the fibre and reside in the region where the light is guided. These

holes enable the fibre to guide light via effective index guidance or photonic band gap

effects [3–5]. Additionally, size, shape and distribution of these internal holes offer fine

1Sometimes referred to as photonic crystal fibres (PCF). We restrict the use of this name to thosefibres which guide light via photonic band gap effects and instead refer generally to any fibre withinternal structure as a MOF.

1

2 Introduction

control over the guidance properties, thus providing a versatile platform for the design

of devices [6]. Figure 1.1 shows some examples of some in-house microstructured optical

fibres, in particular, these images give an indication of the diversity in micorstructures

mirroring the diversity in guiding properties2.

Figure 1.1: An assortment scanning electron microscope images of various microstruc-tured optical fibres made at The University of Adelaide. (A) Air core photonic bandgap fibre. (B) Hexagonal array effective index guiding fibre. (C) Dispersion engineeredfibre. (D) Large suspended core fibre. (E) Large mode area fibre. (F) Air core photonicband gap fibre. (G) Large suspended core fibre. (H) Exposed core wagon wheel fibre.

(I) Small core wagon wheel fibre.

To date, the vast majority of optical fibres found in commercial devices have been made

from silica (SiO2) [7]. The ubiquity of silica fibres is a result of the many desirable prop-

erties possessed by silica. For example, silica is transparent between, approximately,

200 nm and 2000 nm as shown in Figure 1.2. It should be noted that in Figure 1.2 the

reduction of the transmission which results from Fresnel reflection at the interfaces has

2Acknoledgments for these fibres is as follows: (A) Kristopher Rowland, Heike Ebendorff-Heidepriem,Roger Moore. (B) Roger Moore and Heike Ebendorff-Heidepriem and Asahi Glass Co. (for sup-plying the bismuth glass) (C) Wenqi Zhang, Heike Ebendorff-Heidepriem, Roger Moore. (D) HeikeEbendorff-Heidepriem, Roger Moore. (E) Heike Ebendorff-Heidepriem, Roger Moore. (F) KristopherRowland, Heike Ebendorff-Heidepriem, Roger Moore. (G) Heike Ebendorff-Heidepriem, Roger Moore.(H) StephenWarren-Smith, Heike Ebendorff-Heidepriem, Roger Moore. (I) Heike Ebendorff-Heidepriem,Roger Moore.

Chapter 1 3

not been removed. This transparency window makes silica an ideal transmitter of many

existing commercial laser sources. Mechanically, silica is very strong and fibres fabri-

cated from silica show exceptional resilience against tensile loads and bending. Another

factor contributing to the near ubiquity of silica fibres is the maturity of the processing

technologies surrounding their manufacture. The enormous quantities of money spent

by the telecommunications industry towards the end of the 20th century have produced

extremely well refined silica glass with optical absorptions below 0.2 dB.km−1 at 1550 nm

which is near to the theoretical limit [8, 9]. Additionally, the processing techniques for

producing the preforms, and ultimately the optical fibres themselves, have been opti-

mised.

Figure 1.2: Optical transmission of fused silica. Note: Fresenel losses are included inthe data. Reproduced from [10]

Despite its ensemble of excellent physical and optical properties, silica has limitations.

Most notably, in the context of this work, the nonlinearity of silica is inherently low

thus making it a less than ideal material for nonlinear applications such as electro-

optics. Additionally, fused silica has strong absorption features beyond approximately

2 μm (see Figure 1.2) that preclude its use for mid IR transmission. There is, therefore,

a need to develop alternative materials to circumvent the shortcomings of silica based

optical fibres.

A plethora of potential glass compositions exist that could, in principle, pave the way

for efficient, low cost electro-optic fibre devices. The search for such materials is well

documented in the literature. One of the most promising candidate materials is the

tellurium dioxide (TiO2) based family of glasses, collectively known as tellurite glasses

[11]. Tellurite glasses are amongst the most nonlinear oxide materials known, as well as

possessing optical transmission up to the mid IR region of the electromagnetic spectrum,

as high as 5 μm.

NOTE: This figure is included on page 3 of the print copy of the thesis held in the University of Adelaide Library.

4 Introduction

The class of optical device we are investigating are the so called electro-optical devices.

electro-optics is the control of the optical properties of a material via the use of external

electric fields. Typically, this involves a change in the birefringence of the material which

in turn produces a polarisation dependent phase change in the the light passing through

the material. Figure 1.3 illustrates this with a specific example of a voltage dependent

wave plate. Light linearly polarised at 45◦ to the vertical passes through a material with

a voltage applied across it. When the correct voltage is applied a relative phase difference

of π/4 is produced between the two orthogonal polarisation states, thereby generating

circularly polarised light. Such a devices are used in optical isolators, Q-switches and a

myriad other applications.

Figure 1.3: The voltage dependent wave plate as an example of an electro-optic device.Light linearly polarised at 45◦ to the vertical passing through a material with electrodesconnected to opposing faces. The strength of the applied field is sufficient to produce arelative phase difference of π/4 between the vertical and horizontal components of thelights polarisation. The light exiting from the material is now circularly polarised.

The two electro-optic effects of practical importance are the Kerr effect and the Pockels

effect. The Kerr effect involves a change in refractive index of a material that is pro-

portional to the square of an applied electric field. This is sometimes referred to as the

quadratic electro-optic effect3. The Pockels effect, or linear electro-optic effect provides

change in refractive index is linearly dependent on the applied electric field.

The Kerr effect is related to the third order nonlinear susceptibility, χ(3), of the material.

All materials have non-zero χ(3) and therefore display the Kerr effect. On the other hand,

the Pockel’s effect is determined by the second order nonlinear susceptibility, χ(2), which

3To be specific we are referring to the effects in which the applied electric field is external. As opposedto the situation when the field responsible for inducing the modifications to the refractive index is theoptical field of the light propagating through the material

Chapter 1 5

is only possessed by certain materials. For glass χ(2) = 0. It is shown in Chapter 2 that

any material with inversion symmetry (in particular glass) has this property.

It is always the case that χ(2) effects in a material will be of a larger magnitude, and

therefore more efficient, than χ(3) effects. It is for this reason that χ(2) materials are

desirable for device manufacture.

The quadratic electro-optic effect can be exploited in optical fibres, indeed, this has

been reported in the literature. To do this, however, large electric fields (in the order

of 108 V.m−1) are required to produce even modest phase changes. Devices utilising

electric fields of this magnitude are susceptible to failure via dielectric break down and

consume large amounts of electrical power.

A much better solution resides in the development of various processing techniques that

in some way or other destroy the (macroscopic) inversion symmetry of the glass. In

this thesis we focus solely on thermal poling as a means for achieving this. During the

thermal poling process the glass is heated to enhance the mobility of various ionic species

within, then under the application of strong electric fields these ions are encouraged to

migrate in one preferred direction. With the field still applied the sample is cooled to

room temperature thus leaving a nonequilibrium charge distribution which produces a

n electrostatic field within the glass. Through rectification of the intrinsic third order

nonlinearity by the electrostatic field an effective second order nonlinearity is generated.

In this situation even a modest external electric field can produce phase shifts sufficient

for any practical purpose.

1.2 Review of Literature

In the following review of literature we examine the key developments in the two

areas of research of direct relevance to the overall aims of this thesis. These areas are

tellurite glass and electroopitcal optical fibre devices. This review is based on information

obtained largely from the Scopus citation database [12].

1.2.1 Tellurite Glass

The first recorded investigation of the glass forming ability of TeO2 was made in 1834

by Berzelius [13]. Berzelius mainly looked at binary glasses of TeO2 and BaO but

not in the context of optical materials. A proper, systematic study of tellurite glasses

was not begun until the work of Stanworth in 1952 [14]. Stanworth considered the

glass forming ability of TeO2 in light of recent advances in the understanding of the

6 Introduction

factors that determine the glass forming ability of oxides. He reasoned that tellurium

oxide should behave analogously to phosphorous oxide as tellurium and phosphorus have

very similar electronegativities. This paper is significant as it was the first time that

the technological significance of tellurite glasses was noted. Stanworth discovered that

tellurites possess, relative to other glasses known at the time, large thermal expansion

coefficients, large refractive indices and low softening points. The latter two properties

are of particular relevance to the work in this thesis. These initial discoveries prompted

others to investigate this intriguing material in a technological context.

Following the work of Stanworth the research in tellurite glasses has been an extremely

active area. Figure 1.4 demonstrates this by showing the number of published papers

from 1952 to the present (mid 2011). This data was compiled using the Scopus citation

database with “tellurite glass” as the search term and searching within article title,

abstract and key words.

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 20150

25

50

75

100

125

150

Year

Num

ber o

f Pub

lishe

d Pa

pers

Figure 1.4: Chart of the number of papers published relating to tellurite glass from1952 to 2011 [12].

An important result was established in 1985 when it was confirmed that many of the

glasses reported in the literature up to then were contaminated with material from the

crucible they had been melted in, usually SiO2 (silica) or Al2O3 (alumina) [15]. These

impurities were found in concentrations as high as 6 mole% which has a large effect on

the properties of the resulting glasses. It is now common place to use gold or platinum

crucibles as these materials are much less soluble in the molten solutions.

Tellurite was first recognised as a potential material for optical fibres in 1976 in the

context of a host for lasing ions [16]. Tellurite was noted to be favourable relative to

silicate glasses for its spectroscopic parameters such as the florescence life times. In 1985

Chapter 1 7

El-Zaidia et al studied the infrared transmission of certain tellurite glasses and noted

that the low absorption in spectral region beyond 2.5 μm would make these glasses

desirable for low loss mid infrared optical fibres [17].

To date the most comprehensive review of literature is the Tellurite Glasses Handbook

Physical Properties and Data by El-Mallawany [18]. This volume contains a vast amount

of data on many tellurite glass systems as well as details relating to the measurement of

these properties. Much of the fundamental understanding of the physical mechanisms

for the origins of these properties is absent from the book and therefore the interested

reader needs to pursue the referenced papers. Since the publication of El-Mallawany’s

handbook (2002) there has been almost 1000 publications on tellurite glass, essentially

twice as many as existed at the time of publication. Since 1984 there has been over 350

patents filed relating to technologies based on tellurite glass.

1.2.2 Electro-optics in Optical Fibres

The history of electro-optical fibres begins in 1986 with the first report of the generation

of a permanent second order nonlinearity χ(2), in glass by Osterberg and Margulis [19].

At the time it was conjectured that this could be a result of the forced migration of

charged species in the glass and/or the reorientation of dipoles within the glass. Follow-

ing this discovery Myers et al deliberately caused ions to migrate under the influence

of an applied electric field using heat to increase the mobility of the ions [20]. This

processing technique was later called ‘thermal poling’ (often just ‘poling’) due to the

requirement of heat and the resulting polarity produced by the separation of charged

species. This is not to be confused with periodic poling which is a technique for quasi-

phase matching in nonlinear crystals to increase the efficiency of the interaction4.

It is now understood that the mechanisms for the poling produced by optical fields alone

(often referred to as ‘optical poling’) and those for thermal poling are subtly different

[21–23]. Regardless, the hypothesis that it was resulting from charge migration and

the subsequent experimental work lead to the discovery that permanent second order

nonlinearities can be generated in this way.

Having a technique for creating a second order nonlinearity in glass is a significant

technological achievement as it paves the way for the fabrication of low cost electro-

optical components for telecommunications, industry and science. Armed with this new

information researchers began to investigate two separate directions. One focused on

investigating the effects of this process on glasses other than silica. The other sought

4In some cases fibres have been thermally poled in a periodic manner, thus combining both techniques.

8 Introduction

to generate second order nonlinearities the region in which the light is guided within an

optical fibre.

In terms of the non-silica glass poling the breadth of the work is very large. In general,

it has been demonstrated that there is typically several ionic species that undergo mi-

gration as well as the impregnation of ionic species from the air into the glass. Further,

the conductive nature of the glass plays an integral role. That is, whether or not the

glass is a pure ionic conductor, pure electronic conductor or some combination of both

[24].

The work towards thermal poling of optical fibres has to this point been done exclusively

in silica based fibres. This is primarily due to the maturity of the fabrication technologies

surrounding silica fibres.

In 2001 a European consortium involving nine partners was established to develop and

fabricate electro-optic devices in the optical fibre and planar wave guide platforms [25].

The consortium known as GLAMOROUS (GLAss based MOdulators, ROUters and

Switches) investigated a large variety of materials and processes over the four year

duration of the project. Several techniques and devices that were not originally con-

templated by the GLAMORUS consortium were developed, such as X-ray poling and

in-fibre lithography, thus opening up many new research avenues [25].

Significantly the GLAMOROUS work resulted in the fabrication of an optical fibre

electro-optic switch. This device was constructed from silica fibre with internal electrodes

which were used first to pole the fibre then provide the modulating electric field for the

electro-optic interaction. Their work with non-silica glasses was not translated into an

optical fibre platform despite the fact that several of these glasses exhibited χ(2) values

at least an order of magnitude larger than silica. Again, it should be noted that this

is primarily due to the relative infancy of the fabrication processes required to produce

optical fibres from these materials. To date there have been no reports of such a device

being constructed from glasses other than silica.

At the conclusion of the GLAMORUS project it was noted that the fundamental limi-

tation to the efficiency of the devices was the low values of the induced χ(2) [25]. This

result provided us with the impetus for the work in this thesis, where our primary fo-

cus was to develop high efficiency electro-optical fibre devices fabricated from highly

nonlinear glasses.

Chapter 1 9

1.3 Thesis Aims and Methodology

At the outset of this work our primary objective was to develop an electro-optic fibre

device, such as a phase modulator, from a glass with a high intrinsic nonlinearity.

In Chapter 10 we present a post mortem in which the reasons for not meeting this

primary objective are discussed. Despite not producing a device there were many sub-

goals that had to be met in order to achieve the primary objective and much progress

was made in these areas. Listed below are the sub-goals that comprise this work:

1. To develop a range of tellurite glasses and characterise their properties so that in-

formed decisions can be made regarding the choice of glass. Adding to the collective

understanding of this glass system and the origin of its properties this knowledge

can be applied to the design of devices and new glasses.

2. To identify suitable tellurite glasses for nonlinear optical fibre devices.

3. To generate permanent second order nonlinearities in some of these glasses via

thermal poling, thus making possible efficient electro-optical devices for controlling

the passage of light in optical systems.

4. To design and fabricate prototype electro-optical devices from in house fabricated

optical fibres.

The way we approached the problem was to begin with a well known ternary tellurite

glass: 5Na2O.20ZnO.75TeO2 (TZN), which has been demonstrated to be suitable for

the fabrication of optical fibres [26], and explore compositional variations of this system.

We then sought to measure as many of the material properties as possible, given the

availability of equipment. Next, we looked for trends and correlations in the properties

that could shed insight into the underlying mechanisms for such properties. Further to

this, we use the observed data and trends to identify candidate compositions for optical

fibre fabrication.

Some of the more promising glasses were investigated for their suitability for post pro-

cessing. We explored the possibility of inducing permanent second order nonlinearities

via thermal poling.

In parallel to the glass development section of this work we investigated the process-

ing techniques required to produce the fibre optic devices. These include methods for

providing the fibres with internal hole for later insertion of electrodes. Techniques for

inserting the electrodes were learnt during a visit with collaborators in ACREO Swe-

den. These were generalised sufficiently to be suitable for the application of providing

microstructured optical fibres.

10 Introduction

To compliment the practical side of the fibre development we produced some compu-

tational models to guide the design and fabrication of the fibres for future optimised

devices.

1.4 Thesis Outline

To aid the reader the following is an outline of the structure of this thesis. To aid the

discussion we refer to the flow chart in Figure 1.5 which illustrates the structuring

of the Chapters and the way information flows from certain Chapters into others.

� Chapter 2

The focus of our glass making efforts is to produce suitable materials for nonlinear

fibre optic devices. We therefore discuss some important aspects of nonlinear

optical theory. We cover the general theory of second harmonic generation and then

apply it to the specific case of thermally poled glass. The Chapter concludes with

a derivation of the Maker fringes equation which used to analyse the magnitude

of the induced nonlinearities.

� Chapter 3

In this Chapter we present a detailed discussion of the main concepts underlying

the glassy state: What is a glass? How are they made and what general properties

they possess? This is followed by a discussion of family of glasses under study in

this thesis, namely tellurite glass.

Following this general discussion we then document the details concerning the

design and fabrication of the glasses that were used in this work. We describe

the process for the design of the compositions, including; the choice of chemical

components and the proportions thereof. The procedure for glass fabrication is

presented followed by the results of our trials.

� Chapter 4

In Chapter 4 we present our investigations of the structure of the glasses under

study. Specifically, we have determined the arrangement of chemical species into

molecular groupings, the type of bonding within and between these groupings

and how this varies for differing compositions is investigated. The trends that we

discovered are continuously referred to in subsequent sections as it is the structure

of the glass and the components from which it is made that largely determine these

properties.

Chapter 1 11

Figure 1.5: Flow diagram for the structure of this thesis. As indicated by the legend inthe bottom left, the chapters are split into three main sections: Introductory material,Experimental work and Concluding material. The chapter order is indicated by thickarrows. Information flowing from one chapter to another is indicated by the arrows.

12 Introduction

� Chapter 5

We have measured various physical and thermal properties of the glasses which we

then correlate to the structure via Chapter 4. The measured properties include:

Density, molar volume, the glass transition and crystallisation temperatures and

the coefficient of thermal expansion. The measured properties give us useful infor-

mation about the suitability of these glasses for the use as an optical fibre material.

� Chapter 6

Measurements of the optical properties of the glasses are presented in Chapter 6.

We have determined the transmission and absorption spectra as well as the linear

and nonlinear refractive indices. There are correlations between these properties

and the trends displayed by the structure of the glasses and the components from

which they are made. We provide a detailed discussion of the significance and

interpretation of these correlations.

� Chapter 7

In Chapter 7 we present a review of thermal poling techniques and present our

experiments to induce second order nonlinear properties in the glass samples.

� Chapter 8

The analysis of the second order nonlinearity produced in the glasses that were

thermally poled is preformed in this Chapter. The details of the experimental

apparatus that was constructed to measure these properties are set out with par-

ticular attentions to the factors that guided the design and calibration of the ap-

paratus. Data analysis of the measurements is considered in great detail, with two

methodologies presented and the pros and cons of each discussed. Also presented

are some complementary experimental techniques for determining the properties

of the thermally poled materials. The Chapter is concluded with a discussion of

the results.

� Chapter 9

This Chapter is an eclectic collection of: simulations, fabrication techniques and

design stages for future nonlinear optical fibre devices. We have performed simula-

tions in order to gain a qualitative understanding to guide the design of potential

nonlinear optical fibre devices. Several of the critical fabrication steps necessary

to produce devices have been explored and tested. The design of these steps and

preliminary results are discussed. We conclude with a summary and make some

suggestions for future work.

� Chapter 10

Finally, we make concluding remarks concerning the totality of the work presented

in this thesis and suggest the future directions.

Chapter 1 13

1.5 Statement of Original Work and Author Contribution

The following is a declaration of the aspects of this work that are, to the best of

our knowledge, original and the contributions to this work by the Author. This

discussion is broken down into Chapters:

� Chapter 2

The Author derived the Maker Fringes expression and reduced the nonlinear tensor

elements for C∞ν symmetry.

� Chapter 3

All of the composition design and glass fabrication was performed by the Author.

� Chapter 4

Analysis of the Raman spectral data and interpretation thereof was undertaken

by the Author.

� Chapter 5

All measurements and the subsequent data analysis were made by the Author

with the exception of the coefficient of thermal expansion. These measurement

were made by a student under direct supervision of the Author. The design of the

equipment and the experimental technique was performed by the Author as too

was the data analysis.

� Chapter 6

All measurements and the subsequent data analysis were made by the Author.

� Chapter 7

Equipment for thermal poling was designed and fabricated by the Author.

� Chapter 8

The Maker fringes experiment was constructed by the Author with the exception

of the electronics for the data acquisition, which was designed in consultation with

Mr. Neville Wild and Mr. Robert Nation, who also built the equipment. Mr.

Neville Wild also provided input into the construction of the LabView control

software.

� Chapter 9

The computational models for calculating the DC fields in the electrode containing

fibres was written in Matlab using the COMSOL software package by the Author.

Kristopher Rowland wrote the code upon which the electrode loss simulations were

based with additional modifications made by the Author.

14 Introduction

The design of the fibre filling apparatus was designed by the Author with close

consultation with colaborator Walter Margulis at ACREO in Stockholm. It’s fab-

rication was performed by the Author.

Fibre filling experiments were performed by the Author and an Honours student,

Hashan Tilanka Munasinghe, under his tutelage. So too was the preform fabrica-

tion.

Design of the optical fibres was performed by the Author. The author assisted in

the fabrication of these fibres.

1.6 List of Publications

1. Manning, Sean; Ebendorff-Heidepriem, Heike; Heike Monro, Tanya Mary.

Sodium Zinc Tellurite Glass: a Candidate Material for Core/Clad Fi-

bres for Electro-optic Devices.


(PACRIM9), held in Cairns, Queensland, Australia July 10-14 2011.


Improved maker fringes data analysis using genetic algorithms.

Proceedings of the Australasian Conference on Optics, Lasers and Spectroscopy

and Australian Conference on Optical Fibre Technology in association with the

International Workshop on Dissipative Solitons 2009.

3. Manning, Sean; Ebendorff-Heidepriem, Heike; Monro, Tanya Mary; Munch, Jes-

per.

Tellurite glasses for photonic devices with enhanced nonlinearity.


(PACRIM8), held in Vancouver, British Columbia, Canada May 31- June 5 2009.


On the application of genetic algorithms to maker fringes analysis.

18th Australian Institute of Physics (AIP) Congress Conference, held in Adelaide,

South Australia Nov 30-Dec 5 2008..

Chapter 2

Nonlinear Optical Theory

2.1 Introduction

As the focus of this thesis is on the the elaboration of experimental tellurite glasses

and their suitability for base materials for nonlinear optical fibres, it is pertinent

to discuss the physics of nonlinear optics. Accordingly, in the following chapter there is a

review of some key elements of the theory of nonlinear optics with particular focus on the

phenomena of nonlinear refractive index and second harmonic generation. In addition to

the review there are some derivations and calculations that infrequently appear in texts

and literature and which were performed by the author in order to properly understand

the origin of key formulae and results. Such as the specific form of the effective second

order nonlinear susceptibility matrix for thermally poled glass and the origin of the

Maker fringes expression.The information in this chapter is of direct relevance to the

material in Chapters 6 and 8.

2.2 Nonlinear Optics

The optics of our everyday experience, reflection, refraction and scattering, are linear

optical phenomena. This is because the strength of the electric field for sun light,

light bulbs and flames are weak with respect to the binding strength of electrons and

nuclei, which is ≈ 1010 V.m−1. This was, in general, the case until the invention of the

laser by Theodore Maiman [27]. Pulsed lasers can produce very strong electric fields in

the order of 107 V.m−1, in a collimated beam1. Focusing this, already intense radiation

down to a spot of approximately λ in diameter will increase the electric field strength

to around ≈ 1010 V.m−1. If this radiation is incident on a material the electric field of

1e.g a fairly typical Nd:YAG laser can produce a 1 mm diameter beam with 1 mJ Q-switched pulsesof 1 ns duration. The peak power will be 1 MW and the peak electric field strength will be 107 V.m−1

15

16 Nonlinear Optical Theory

the light is now sufficiently strong to perturb the electrons from their host nuclei and

produce new and interesting optical effects.

Unsurprisingly, shortly after the invention of the laser Peter Franken et al [28] observed

the first nonlinear optical effects and today nonlinear optics is arguably one of the most

active areas of optical research.

To understand why such high field strengths are required and specifically what is occur-

ring in materials when they are being influenced by these fields we will need to consider

the polarisation P(t), of the material in the presence of the optical field E(t). In the

linear regime we can describe the relationship between polarisation and optical field as:

P(t) = ε0χ(1)E(t), (2.1)

where ε0 is the free space permittivity and χ(1) is the linear susceptibility which, for

transparent materials, is related to the refractive index n0, by

χ(1) = n20 − 1 (2.2)

and therefore to the relative permitivity εr via

εr = 1 + χ(1) (2.3)

Therefore χ(1) determines much of the optics we experience on a day-to-day basis. We

can generalise the polarisation of the material by expressing it as a power series in E(t),

as

P(t) = ε0

(χ(1)E(t) + χ(2)E2(t) + χ(3)E3(t) + . . .

)≡ P(1)(t) + P(2)(t) + P(3)(t) + . . . .

(2.4)

We now have the additional terms χ(2), χ(3) etc which are the second, third and in

general nth order nonlinear optical susceptibilities, respectively. The strength of second

order processes is determined by the size of χ(2) just as the strength of third order

processes is determined by χ(3) and so on for higher order nonlinear processes. Typical

values for χ(2) are in the order of 10−12 m.V−1 and χ(3) is around 10−21 m2.V−2 [29].

This is why such high intensity optical fields are required for these effects to become

appreciable.

For a full and accurate description of nonlinear optical phenomena we need to use vector

quantities for the electric field and polarisation and tensors for the susceptibilities. The

Chapter 2 17

optical electric field can be represented as a discrete sum of frequency components by

E(r, t) =∑n

E(ωn)e−iωnt (2.5)

where we are summing over positive and negative frequencies (i.e. n = ±1, 2, 3 . . . ) andE(ωn) satisfies the reality condition, i.e.

E(−ωn) = E(ωn)∗. (2.6)

Using a similar notation as in Equation 2.5 we can express the nonlinear polarisation as

P(r, t) =∑n

P(ωn)e−iωnt (2.7)

We are now in a position to analyse specific nonlinear processes.

2.3 Second Order Nonlinearities

For the second order nonlinear processes we need only consider the terms in P(r, t)

which relate to the second order nonlinear susceptibility tensor χ(2)ijk(ωn+ωm, ωn, ωm).

The components of the second order susceptibility tensor are the constants of propor-

tionality which relate the amplitude of the nonlinear polarisation to the product of the

optical field amplitudes, as in:

Pi(ωn + ωm) = ε0∑jk

∑(nm)

χ(2)ijk(ωn + ωm, ωn, ωm)Ej(ωn)Ek(ωm) (2.8)

In Equation 2.8 ijk are the Cartesian components of the fields and the notation (nm)

indicates that, despite ωn and ωm being able to vary, the sum ωn +ωm is held constant.

This is necessary to conserve energy. Taking the product of the n and m electric field

components:

E(ωn)e−iωntE(ωm)e−iωmt = E(ωn)E(ωm)e−iωnte−iωmt

= E(ωn)E(ωm)e−iωnte−iωmt

= E(ωn)E(ωm)e−i(ωn+ωm)t,

we see that E(ωn)E(ωm) is associated with a time dependent product which oscillates

at ω = ωn + ωm. As this is always the case we can rewrite the argument of the second

order susceptibility tensor as χ(2)(ω3;ω2, ω1) where it is understood that ω3 = ω2 + ω1.


Thus

P(2)i (ω3) = ε0

∑jk

χ(2)ijk(ω3;ω2, ω1)Ej(ω1)Ek(ω2). (2.9)

becomes the expression for the second order nonlinear polarisation.

Consider Equation 2.9 for the situation where there is a single optical field of frequency

ω1 polarised along the x direction and that it is significantly intense for nonlinear inter-

actions to take place. Thus, we have a single optical field at frequency ω1 producing an

nonlinear polarisation at ω1 + ω1 = 2ω1 i.e.

P(2)i (2ω1) = ε0χ

(2)ixx(ω3;ω1, ω1)Ex(ω1)

2. (2.10)

This process, as illustrated in Figure 2.1, is known as second harmonic generation (SHG).

SHG involves the conversion of two input photons of frequency ω into a new photon of

frequency 2ω.

Figure 2.1: Energy level diagram describing second harmonic generation. Secondharmonic generation involves the conversion two of input photons at frequency ω intoa single output photon of frequency 2ω, i.e. ω+ω = 2ω. Note that the process is never

100% efficient consequently there is always unconverted input radiation.

We now turn our attention to χ(2)ijk which is a rank 3 tensor with 3×3×3 = 27 Cartesian

elements. For three interacting waves with frequencies ω1, ω2 and ω3 = ω1 + ω2 there

will be a nonlinear polarisation influencing each one, each with it’s own second order

nonlinear susceptibility tensor,

χ(2)ijk(ω3, ω1, ω2), χ

(2)ijk(ω3, ω2, ω1),

χ(2)ijk(ω2, ω3,−ω1), χ

(2)ijk(ω2,−ω1, ω3),

χ(2)ijk(ω1, ω3,−ω2), χ

(2)ijk(ω1,−ω2, ω3)

There are another 6 tensors for the negative frequencies and thus there are 12×27 = 324

separate elements to consider. This can be reduced to a matrix of 3× 6 = 18 elements

Chapter 2 19

by considering certain symmetries. These include the reality of the fields, intrinsic

permutation symmetry, lossless media symmetry and Kleinman symmetry [30].

After the application of these symmetries the second order nonlinear susceptibility tensor

can be written in the contracted notation as

dil =

⎡⎢⎢⎣d11 d12 d13 d14 d15 d16

d21 d22 d23 d24 d25 d26

d31 d32 d33 d34 d35 d36

⎤⎥⎥⎦ (2.11)

where the indices for dil come from the following prescription and

jk: 11 22 33 23,32 31,13 12,21l: 1 2 3 4 5 6

dijk =1

2χ(2)ijk. (2.12)

For glassy materials there is an immediate implication for the second order nonlinear

susceptibility tensor. Amorphous materials possess what is called inversion symmetry,

that is any crystal axis of the material can have its sign changed (e.g. X → −X,

Y → −Y and Z → −Z) and the material remains unchanged. Otherwise known as

centrosymmetry, this has the effect of making all of the elements of χ(2) vanish. For

example, assume that the nonlinear polarisation is given by

P(2)(t) = ε0χ(2)E2(t) (2.13)

where the optical field is give by

E(t) = E0 cosωt (2.14)

If the sign of E(t) is changed then we necessarily must change the sign of the P(2)(t), as

we have assumed that the material has inversion symmetry. Thus we obtain

− P(2)(t) = ε0χ(2)|−E(t)|2. (2.15)

Thus

− P(2)(t) = ε0χ(2)E2(t) (2.16)

which implies that

P(2)(t) = −P(2)(t) (2.17)


which can only be true if and only if

χ(2) = 0. (2.18)

Thus all materials with centrosymmetry have zero second order nonlinear coefficients.

In fact, this applies for all even ordered nonlinear coefficients as

|−E(t)|n = E(t) ∀ n even. (2.19)

Conversely, for third ordered nonlinearities we have

−P(3)(t) = ε0χ(3)|−E(t)|2(−E)

−P(3)(t) = −ε0χ(3)E3(t)

Implying that

P(3)(t) = P(3)(t), (2.20)

which provides no contradiction and thus centrosymmetric structures do possess third

order nonlinearities. Furthermore, this result is easily generalised to account for all odd

ordered nonlinearities.

Equation 2.11 allows us to express the nonlinear polarisation as a matrix equation which,

for the specific example of SHG, has the form:

⎡⎢⎢⎣Px(2ω)

Py(2ω)

Pz(2ω)

⎤⎥⎥⎦ = 2ε0

⎡⎢⎢⎣d11 d12 d13 d14 d15 d16

d21 d22 d23 d24 d25 d26

d31 d32 d33 d34 d35 d36

⎤⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

Ex(ω)2

Ey(ω)2

Ez(ω)2

2Ey(ω)Ez(ω)

2Ex(ω)Ez(ω)

2Ex(ω)Ey(ω)

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(2.21)

The precise form of the second order nonlinear susceptibility tensor will depend on the

material in question. Firstly on the symmetry properties of the material, which will

reduce the number of non-zero elements in the tensor and secondly the actual values for

these non-zero elements will be determined by the constituents of the material.

There are additional second order effects that will not be discussed in detail, however,

we can briefly summarise all of the second order processes as:

Sum frequency generation (SFG): ω1 + ω2 = ω3

Second harmonic generation (SHG): ω + ω = 2ω

Difference frequency generation (DFG): ω1 − ω2 = ω3

Chapter 2 21

The common aspect to all of these processes is that two photons are converted into a

single photon of a new frequency, with overall conservation of energy.

2.3.1 Propagation of the Fields

To understand how the fields propagate during nonlinear processes we begin with Maxwell’s

equations in a medium with no free charges or currents:

∇× E = −∂B

∂t(2.22a)

∇.D = 0 (2.22b)

∇× H =∂D

∂t(2.22c)

∇.B = 0 (2.22d)

which relate the electric and magnetic fields (E and H) to the electric displacement and

the magnetic flux density (D and B). These quantities can be further related by the

constitutive relations give by

D = ε0E+ P (2.23)

B = μ0H (2.24)

where P is given by Equation 2.4. Therefore we can write Equation 2.24 as

D = D(1) + PNL (2.25)

where we have explicitly separated the linear and nonlinear parts of D such that

D(1) = ε0E+ P(1) (2.26)

Introducing the dielectric tensor ε(1) we can thus relate D(1) and E by

D(1) = ε(1) · E (2.27)

By manipulating Maxwell’s equations and using the fore mentioned definitions we obtain

the inhomogeneous wave equation for electromagnetic radiation

−∇2E+n2

c2∂2E

∂t2= − 1

ε0c2∂2PNL

∂t2(2.28)


This is the inhomogeneous wave equation, or nonlinear wave equation, in which the

nonlinear response of the material acts as a source term for additional frequencies. In

the following section we will utilise this equation to derive the Maker fringe expression.

2.3.2 Derivation of the Maker Fringes Expression

We can now use Equation 2.28 to analyse the case of SHG from a dispersive, nonlinear

material. First, however, consider the situation in Figure 2.2.

Figure 2.2: Diagram for second harmonic generation in a dispersive medium. Ra-diation with frequency ω (fundamental) is incident at an angle θi to the surface ofa material with non-zero χ(2) and thickness L. The fundamental radiation generatesa second harmonic at 2ω. Refraction and dispersion cause the fundamental and sec-ond harmonic radiation to be transmitted at angels θtω and θt2ω respectively. Both

frequencies leave the material at the angle θi.

Monochromatic light of frequency ω is incident onto a material with non-zero second

order nonlinearity. The light is incident at an angle θi and has sufficient intensity to

generate optical harmonics. The input light therefore induces a nonlinear polarisation in

the material which generates second harmonic radiation at frequency 2ω. For the fields

to be continuous across the boundary there must be reflected and transmitted radiation

at 2ω. Due to the dispersion of the refractive index, the fundamental and SH propagate

Chapter 2 23

at angles θtω and θt2ω, respectively as determined via Snell’s Law

θtω = sin−1(sin θinω

)(2.29)

θt2ω = sin−1(sin θin2ω

). (2.30)

The wave vectors for the fundamental and SH are kω and k2ω and are directed along z

and z′. Therefore, we can write the electric fields for the fundamental and SH as

Eω(z, t) =1

2

{Aω(z)e−i(kωz−ωt) + c.c.

}(2.31)

E2ω(z′, t) =

1

2

{A2ω(z′)e−i(k2ωz′−2ωt) + c.c.

}(2.32)

where Aω\2ω is a slowly varying amplitude for the respective fields and

kω =nωω

c(2.33)

k2ω =n2ω2ω

c. (2.34)

With these expressions for the fields and 2.9 we can therefore write the nonlinear polar-

isation as

PNL(ω)i (z, t) = ε0χ

(2)ijk(2ω,−ω)A2ω

j (z′)A∗ωk (z)e−i(k2ωz′−kωz)e−iωt (2.35)

and

PNL(2ω)i (z′, t) = ε0

1

2χ(2)ijk(ω, ω)A

ωj (z)A

∗ωk (z)e−i(k2ω)z′e−i2ωt (2.36)

We can calculate the derivative terms in Equation 2.28 as

∂2

∂t2Eω

i (z, t) = −ω2Eωi (z, t) (2.37)

∂2

∂t2P

NL(ω)i (z, t) = −ω2P

NL(ω)i (z, t) (2.38)

and∂2Eω

i (z, t)

∂z2≈ −

(2ikω

dAωi (z)

dz+ k2

ωAωi (z)

)e−i(kωz−ωt) + c.c. (2.39)

With equivalent expressions for the field at 2ω. In order to simplify Equation 2.39

we have utilised the slowly varying envelope approximation which assumes that the

fractional variation of in E on the scale of the wavelength associated with the field must

be smaller than unity, i.e. ∣∣∣∣∣d2E

dz2

∣∣∣∣∣�∣∣∣∣∣kω

dE

dz

∣∣∣∣∣ (2.40)


Substituting Equations 2.37, 2.38 and 2.39 into the NL wave Equation 2.28 and dropping

the time dependence, we obtain expressions for the field amplitudes Aωi and A2ω

i , given

by

dAωi (z)

dz= −i ω2

kωc2ε0P

NL(ω)i (z)e−i(kωz) (2.41)

dA2ωi (z′)dz′

= −i 2ω2

k2ωc2ε0P

NL(2ω)i (z′)ei(k2ωz′) (2.42)

Introducing the expressions for the polarisations at ω and 2ω, given by Equations 2.35

and 2.36 and assuming that the susceptibilities are independent of frequency (i.e. Klein-

man Symmetry) we obtain:

dAωi (z)

dz= −i ω

2cnωχ(2)ijkA

2ωj (z′)Aω∗

k (z)e−i(Δk·Z) (2.43)

dA2ωi (z′)dz′

= −i ω

2cn2ωχ(2)ijkA

ωj (z)A

ω∗k (z)ei(Δk·Z) (2.44)

where nω and n2ω are the refractive indices of the nonlinear material at frequencies ω

and 2ω respectively and Δk = k2ω − kω represents the difference in the propagation

constants of the two frequencies. We have also applied a change of variable from z and

z′ to Z. This involves a projection of the propagation directions for the frequencies

at ω and 2ω onto the Z axis of the material (see Figure 2.2). This occurs under the

transformations

z → Z

cos θtω(2.45)

z′ → Z

cos θt2ω(2.46)

The justification for performing this transformation comes from the fact that the planes

of equal phase mismatch between the fundamental and second harmonic are all perpen-

dicular to the material axis Z. Accordingly, Δk · Z has the form

Δk · Z =

(k2ω

cos θt2ω− kω

cos θtω

)Z (2.47)

In nonlinear processes where the conversion efficiency is low it is customary to make the

undepleted pump approximation, which can be expressed as

dAωi (z)

dz≈ 0 (2.48)

that is the amplitude of the fundamental wave is essential unchanged under the con-

version of ω → 2ω. Further, if we introduce the effective nonlinear coefficient which

deals with the projection of the electric fields of the two waves onto the crystal axis (see

Chapter 2 25

Section 2.3.3 and specifically Equation 2.76) and complete the change of variables from

z → Z can rewrite Equation 2.44 as

dA2ω(Z)

dZ= −i ω

cn2ωdeff

[Aω(Z)]2

cos θtωei(Δk·Z) (2.49)

Having developed the expression for the spatial variation of the amplitude of the wave

at frequency 2ω in terms of one variable we can integrate Equation 2.49 with respect to

Z over the thickness of the nonlinear region (see Figure 2.2) to obtain an expression for

the amplitude of the second harmonic wave

A2ω(Z) = −i ω

cn2ω cos θtω

L∫0

deff [Aω(Z)]2 ei(Δk·Z)dZ. (2.50)

By taking the product A2ω(Z)A2ω ∗ (Z) and using the general fact that intensity is

related to the filed amplitude via

I =ε0cn

2|A|2 (2.51)

we can find an expression for the intensity of the generated SH I2ω, as a function of

incidence angle θi, give by:

I2ω(θi) =ω2I2ω

c3ε0n2ωn2ω cos2 θtω

∣∣∣∣∣∣L∫

0

deffei(Δk·Z)dZ.

∣∣∣∣∣∣2

(2.52)

It must be noted that Equation 2.53 assumes no depletion of the fundamental, i.e.

Iω =constant. This is a reasonable assumption for the low values of χ(2) observed in

most material. The dependence of Equation 2.53 is implicit and can be found explicitly

through Snell’s law.

We will assume that the effective nonlinear coefficient has no dependence on the spatial

coordinate Z and thus Equation 2.53 can be written as:

I2ω(θi) =ω2I2ω


d2eff

∣∣∣∣∣∣L∫

0

ei(Δk·Z)dZ.

∣∣∣∣∣∣2

(2.53)

Which enables us to complete the integration, yielding:

I2ω(θi) =ω2I2ω


(2πL

λ

)2

d2effsin2Ψ

Ψ2(2.54)


We have simplified the appearance result by making the replacement of

Ψ =

(2Lπ

λ

)(nω cos θtω − n2ω cos θt2ω) (2.55)

The expression in Equation 2.54 gives the angular dependence of the intensity of the

second harmonic, however, it falls short in predicting what one would observe as the

nonlinear sample is rotated with respect to the beam because it fails to take into account

the losses due Fresnel reflection at the interfaces.

The form of the Fresnel transmission coefficients depend on the polarisations of the

fundamental and second harmonic. For light incident onto an interface between materials

1 and 2 at an angle θ1 and refracted via Snell’s law to an angle θ2, for the polarisations

states s and p they are give by:

t1→2p =

2 cos θ1 sin θ2sin(θ1 + θ2) cos(θ1 − θ2)

(2.56)

t1→2s =

2 cos θ1 sin θ2sin(θ1 + θ2)

(2.57)

If the materials have refractive indices n1 and n2 for materials 1 and 2 respectively then

we can define the amplitude transmission factor as

T 1→2 =(t1→2

) n2 cos θ2n1 cos θ1

(2.58)

Given the situation illustrated in Figure 2.2 the amplitude transmission factor for the

fundamental will be given by:

T a→gω = (ta→g)

nω cos θtωcos θi

(2.59)

Further, the SH generated in the material crosses the glass/air interface as it exits the

glass at an incident angle θt2ω and thus its amplitude transmission coefficient is

T g→a2ω = (tg→a)

cos θin2ω cos θt2ω

. (2.60)

Equation 2.54 is proportional to the intensity in the second harmonic and the square of

the intensity of the fundamental, it is therefore clear that by multiplying Equation 2.54

by T g→a2ω and (T a→g

ω )2we will obtain an expression for the angular dependence of the

SH intensity.

I2ω(θi) =(T a→g

ω )2T g→a2ω ω2I2ω


(2πL

λ

)2

d2effsin2Ψ

Ψ2(2.61)

Finally, using the definition for intensity of the fundamental as the power Pω divided

Chapter 2 27

by the area of the beam A (and assuming that the fundamental and second harmonic

beams have the same area), we obtain the so called Maker fringes expression of which

more discussion will be made in Section 8.1.

P2ω(θi) =(T a→g

ω )2T g→a2ω ω2

Ac3ε0n2ωn2ω cos2 θtω

P 2ω

(2πL

λ

)2

d2effsin2Ψ

Ψ2(2.62)

2.3.3 Second Order Nonlinear Effects in Thermally Poled Materials

It is known experimentally that thermally poled glasses produce second harmonics when

exposed to intense radiation. To see how this occurs consider the first term in the

nonlinear polarisation for a centrosymmetric material (i.e. χ(2) = 0):

PNL = ε0χ(3)E3. (2.63)

When we have generated the field EDC via poling this contributes with the optical field

to the nonlinear polarisation and the total field can be written as a superposition of the

DC field and a monochromatic optical field at frequency ω, i.e. ET = E0 cosωt+EDC .

Substituting this into Equation 2.63 we obtain:

PNL =ε0χ(3)E3

T

=ε0χ(3) (E0 cosωt+EDC)

=ε0χ(3)(E0 cos

3 ωt+ 3EDCE20 cos

2 ωt+ 3E2DCE0 cosωt+E3

DC

)(2.64)

Using the trigonometric replacements: cos3 ωt = 14 cos 3ωt +

34 cosωt and cos2 ωt =

12 + 1

2 cos 2ωt

Equation 2.64 takes the from:

PNL = ε0χ(3)

(1

4E3

0 cos 3ωt+3

4E3

0 cosωt+3

2EDCE

20 +

3

2EDCE

20 cos 2ωt+ . . .

3E2DCE0 cosωt+E3

DC

)(2.65)

The fourth term in Equation 2.65 indicates that there will be radiation at frequency

2ω i.e. a second harmonic. We can thus write an effective second order nonlinear

polarisation as:

P(2)

eff=

3

2ε0χ

(3)EDCE20 (2.66)

or

P(2)

eff= χ

(2)

effE2

0 (2.67)

where we have defined the effective second order nonlinear susceptibility χ(2)

eff= 3

2ε0χ(3)EDC .


The presence of a linear electro-optic effect in thermally poled glasses can be understood

by considering Equation 2.3 for the relative permittivity and the constitutive relation

D = ε0E+P (Equation 2.24) Dividing by ε0E we obtain

D

ε0E= 1 +

P

ε0E

Combining this result with Equation 2.4 we get

D

ε0E= 1 + χ(1) + χ(2)E2 + χ(3)E3 + . . . (2.68)

Which in combination with Equation 2.3 can be expressed as

D

ε0E=εr + χ(2)E2 + χ(3)E3 + . . .

=εr +Δε

=ε′ (2.69)

where ε′ is the altered permittivity of the material under the influence of strong electric

fields. Using the relationship between permittivity and refractive index

ε′ = n2 (2.70)

and considering a small change in the refractive index of the material Δn, corresponding

to the change in permittivity produced by the electric field E we obtain

ε′ =(n+Δn)2

≈n20 + 2n0Δn. (2.71)

For glass, where χ(2) = 0 and ignoring all terms of E higher than order 2 it follows that:

Δn =ε′ − n2

0

2n0=

ε′ − εr2n0

=Δε

2n0

=1

2n0χ(3)E2 (2.72)

Consider now the case of thermally poled glass which has associated with it a frozen

in DC field EDC onto which we superpose an external electric field Eext. Then E =

EDC +Eext, which with Equation 2.72 gives:

Δn =1

2n0χ(3)

(E2

DC + 2EDCEext +E2ext

)(2.73)

The second term in 2.73 implies that for a fixed value of EDC under the influence of the

Chapter 2 29

external electric field Eext the change in refractive index (and therefore phase of light

propagating through the glass) is linear in Eext. This is the linear electro-optic effect.

The third term can be neglected because Eext � EDC [31]. If the glass has not been

poled and therefore EDC = 0 then the change in refractive index will be proportional to

E2ext i.e. a quadratic electro-optic effect .

A convenient way of visualising these two situations is shown in Figure 2.3: To begin with

the glass has an intrinsic third order nonlinearity which as we have shown can produce

a phase change that is quadratic in the applied field (red curve in Figure 2.3). After

poling this parabolic curve has shifted by an amount equal to the value of the frozen in

field EDC , such that now the phase shift is approximately linear with the applied field

(blue curve in Figure 2.3). Therefore producing a pseudo-linear electro-optic response.

Figure 2.3: electro-optical response of glass before (red parabola) and after poling(blue parabola).

Now that we have established that thermal poling does indeed produce an effective

second order nonliearity we can apply Equation 2.21 to analysing SHG from in such a

sample. But first we must first apply the symmetries of the material to the second order

nonlinear susceptibility tensor. In doing so we will be able to show that many of the

elements are equal to zero, thus simplifying the equations for the nonlinear polarisation.

Figure 2.4 is a schematic illustration of a thermally poled glass sample with the electric

field shown. By considering which transformations will leave the field in the figure un-

changed we are able to apply these to the elements of the effective nonlinear susceptibility

matrix (Equation 2.11) and determine which are the non-zero elements.

We are using the conventional capital letters notation (X,Y, Z) for crystal axis, the

laboratory frame will have lower case letters (z, y, z). However, we must stress that

the symmetries are not related to any crystal structure, instead it is the symmetry of

the electric field which has been created during poling. The field possesses rotation


Ep

-Y

X

-X

Y

Z

-Z

Ep

Figure 2.4: Illustration of the symmetry possessed by the electrical potential in ther-mally poled glass.

symmetry about the Z axis. We can rotate the figure about Z by any angle and the

field will remain unchanged. This type of symmetry is called C∞ν . Consider a clockwise

rotation by 90◦, under this operation the coordinates transform like

X → −Y ′

Y → X ′

Z → Z ′.

This can be represented by the following matrix equation

⎡⎢⎢⎣0 −1 0

1 0 0

0 0 1

⎤⎥⎥⎦⎡⎢⎢⎣X

Y

Z

⎤⎥⎥⎦ =

⎡⎢⎢⎣−Y ′X ′

Z ′

⎤⎥⎥⎦ . (2.74)

Then, using the full index notation for the dijk elements and using Equation 2.74 as a

prescription for changing the ijk’s we obtain as series of relationships between elements

of dijk. For example

d122 = −d211d211 = d122

Chapter 2 31

This produces a contradiction which can only be resolved if and only if

d122 = d211 = 0

Many similar relationships can be established via this symmetry and others which in-

clude:

� Rotation about Z by 180◦,

X → −X ′

Y → −Y ′

Z → Z ′.

� Reflection symmetry in the XZ plane,.

X → −X ′

Y → Y ′

Z → Z ′.

and in the Y Z plane

X → X ′

Y → −Y ′

Z → Z ′.

� Inversion symmetry in the X and Y axes which is equivalent to a reflection.

The final result is a nonlinear susceptibility matrix with the following form:

dil =

⎡⎢⎢⎣

0 0 0 0 d31 0

0 0 0 d31 0 0

d31 d31 d33 0 0 0

⎤⎥⎥⎦ . (2.75)

Now, if we select a specific experimental configuration, in terms of sample orientation

and input and output polarisation, we can derive an expression for the effective nonlinear


polarisation deff . The effective nonlinear polarisation is defined as [29]

deff = e2ω · dil : eω eω (2.76)

where eω is the electric field polarisation vector at frequency ω. If we consider the

following experimental configuration (Figure 2.5):

Y

Z

X

Figure 2.5: Configuration for SHG in the pp-configuration. Coordinate axes (X,Y, Z)belong to the glass and (x, y, z) are the laboratory frame.

We select the lab frame axis to coincide with those of the crystal frame for convenience.

The polarisation of the wave at frequency ω, which we will call the fundamental, lies in

the xz plane of the laboratory frame at some angle θω to the z axis. Upon entering the

glass with refractive index nω, Snell’s law,

sin θω = nω sin θ′ω. (2.77)

tells us that it will be refracted to a new angle θ′ω, where the prime indicates an angle

within the glass. Thus, in the glass the fundamental is propagating with an electric field

polarisation vector given by:

eω = (cos θ′ω, 0, sin θ′ω). (2.78)

We now assume that the fundamental wave has sufficient intensity to produce some

second harmonic (SH). Further, if we use a polariser to select the SH that has its

Chapter 2 33

polarisation in the xz plane, the polarisation vector for the SH will have the form:

e2ω = (cos θ′2ω, 0, sin θ′2ω). (2.79)

The angle θ2ω is determined by the incidence angle of the fundamental and the refractive

index of the glass at the second harmonic n2ω, by

sin θω = n2ω sin θ′2ω. (2.80)

Equation 2.76 then becomes

deff =

⎡⎢⎢⎣cos θ′2ω

0

sin θ′2ω

⎤⎥⎥⎦ ·⎡⎢⎢⎣

0 0 0 0 d31 0

0 0 0 d31 0 0

d31 d31 d33 0 0 0

⎤⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

cos2 θ′ω0

sin2 θ′ω0

0

2 sin 2θ′ω

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(2.81)

which expands to give

deff = 2d31 sin θ′ω cos θ′ω cos θ′2ω + (d31 cos

2 θ′ω + d33 sin2 θ′ω) sin θ

′2ω. (2.82)

The configuration we have considered, fundamental polarisation and SH polarisation,

is commonly called the pp-configuration. Here pp is short hand for p-polarised int-

put (fundamental) and p-polarised output (second harmonic). There is an alternative

configuration for SHG in poled glass which is the sp-configuration. Here the input is

s-polarised and the output is p-polarised. In the sp-configuration the effective nonlinear

coefficient is given by

deff = d31 sin θ′2ω. (2.83)

In general these expressions can be used to determine the angle required to maximise

the effective nonlinear coefficient for a particular experimental configuration, although

first we must square deff to obtain a value proportional to intensity. For the pp- and

sp-configuration d2eff is maximum for θω = 90◦.

We can use this specific forms of the effective second order nonlinear coefficients given in

Equation 2.82 and Equation 2.83 with then general form of the Maker fringes expression

(Equation 2.62), to derive the Makers fringe expression for thermally poled glass.


2.4 Third Order Nonlinearities

The third order order contribution to the nonliear polarisation as given by

P(3)(t) = ε0χ(3)E(t)3, (2.84)

determines the third order nonliearities of a material. If we consider a monochromatic

wave of the form

E(t) = E0 cosωt, (2.85)

substituting into Equation 2.85 into Equation 2.84 we get

P(3)(t) = ε0χ(3)E3

0 cos3 ωt. (2.86)

By appliing the trigonometric identity cos3 ωt = 14 cos 3ωt +

34 cosωt, the nonlinear po-

larisation can be expressed by

P(3)(t) = ε0

(1

4χ(3)E3

0 cos 3ωt+3

4χ(3)E3

0 cosωt

). (2.87)

The first term in Equation 2.87 predicts third hamonic generation (THG), a process

analogous to SHG, where three input photons with frequency ω, are converted into a

single photon of frequency 3ω i.e. ω + ω + ω = 3ω (see Figure 2.6).

Figure 2.6: Energy level diagram describing third harmonic generation. Third har-monic generation involves the conversion three of input photons at frequency ω into asingle output photon of frequency 3ω, i.e. ω + ω + ω = 3ω. Note that the process is

never 100% efficient consequently there is always unconverted input radiation.

There are a multitude of additional third order effects (44 in fact), far too many to

describe in detail. It suffices to say that they all involve the interaction of four photons

Chapter 2 35

and sums and differences of their frequencies. The only process of direct interest to this

thesis is that of the intensity dependent refractive index, otherwise referred to as the

nonlinear refractive index. This process is discussed in detail in the following Section.

2.4.1 Origin of the Nonlinear Refractive Index

The second term in Equation 2.87 predicts a nonlinear contribution to the polarisation at

the frequency of the incident field. This term causes the material to change its refractive

index in response to the intensity of the input beam in the form

n = n0 +n2

2I (2.88)

where n0 is the refractive index of the material and n2 is the nonlinear refractive index

which corresponds to the change in n observed with an input intensity I. The factor

of 1/2 appears in Equation 2.88 to maintain consistency with the majority of literature

reported values of n2. An alternative expression exists which originates as a result of a

different definition of the electric field and therefore intensity. This alternative differs

by a factor of 2 from the more standard definition. It is therefore not uncommon to

find reported values of the nonlinear refractive index to differ a factor of 2, thus causing

some initial confusion.

The change in refractive index described by Equation 2.88 is often called the optical

Kerr effect. This can be restated in terms of the electric field as

n = n0 + γ|E(ω)|2 (2.89)

where the intensity and the electric field are related via:

I = 2n0εoc|E(ω)|2 (2.90)

To understand how the optical Kerr effect arises from the nonlinear polarisation we

must consider the term in the nonlinear polarisation which influences the propagation

of a beam of frequency ω;

P(3)(ω) = 3ε0χ(3)(ω = ω + ω − ω)|E(ω)|2E(ω) (2.91)

here we have three photons of frequency ω combining to produce a photon at frequency

ω. To avoid the complicated tensor nature of the third order susceptibility we are

assuming the light is linearly polarised. The total polarisation, up to third order, of the


material is thus described by

P(ω) = ε0

(χ(1)E(ω) + 3χ(3)|E(ω)|2E(ω)

)(2.92)

Note that we have assumed this material to have no second order response. We can

introduce an effective susceptibility

χeff = χ(1) + 3χ(3)|E(ω)|2 (2.93)

which allows us to write Equation 2.92 as

P(ω) = ε0χeffE(ω). (2.94)

It is generally true that

n2 = 1 + χeff (2.95)

thus by substituting Equation 2.90 on the left and Equation 2.93 on the right we obtain

[n0 + γ|E(ω)|2]2 = 1 + χ(1) + χ(3)|E(ω)|2 (2.96)

and expanding gives

n20 + 4n0γ|E(ω)|2 = (1 + χ(1)) + (χ(3)|E(ω)|2)). (2.97)

We can equate the relevant terms to get relation ships for n0 and γ:

n0 = (1 + χ(1))1/2 (2.98)

γ =3χ(3)

4n0(2.99)

Finally, we note that the total refractive index must be the same regardless of description.

Thus from Equations 2.88 and 2.90 we see that

γ|E(ω)|2 = n2

2I (2.100)

and therefore the intensity dependent refractive index is related to the third order non-

linear susceptibility via:

n2 =3χ(3)

4n20ε0c

. (2.101)

Chapter 2 37

2.5 Conclusion

The essential physics describing the nonlinear processes that are of relevance to

this thesis has been outlined. Furthermore, calculations and derivations of key

relationships have been made. Notably, the form of the effective second order nonlinear

susceptibility matrix for thermally poled glass and the Maker fringes expression. These

expressions are utilised in the analysis of second harmonic generation from samples in

Chapter 8. As well as showing the relationship between the nonlinear refractive index

and the third order susceptibility. This result is employed in Chapter 6 to calculate the

third order susceptibilities from the measured nonlinear refractive indices.

Chapter 3

Glass Theory, Design &

Fabrication

3.1 Introduction

In this chapter I describe the process that was used to design the tellurite glass compo-

sitions that were the focus of my PhD research. The procedure for fabricating theses

glasses is also outlined. Finally, I summarise the results, indicating which compositions

are shown to be good glass formers and therefore become the focus of all subsequent

investigations within this thesis.

3.2 What is a Glass?

The glassy, or vitreous state, as it is sometimes called, refers to the underlying

structural arrangement of atoms in these solids. Glasses are solid materials that

are typified by a random arrangement of atoms and therefore lack long-range atomic

order (figure 3.1 right) thus resembling liquids more than crystalline solids in terms of

their atomic structure. In contrast to crystalline material, glasses do not have a precisely

defined melting point but rather soften gradually over a range of temperatures. This

range is in the order of 10◦C.

Many materials can be induced into the glassy state provided certain requirements are

met. Glass formation is really a process of rapid solidification where the rapidity is

sufficient to suppress the tendency for crystallisation. For a crystal to form, firstly it

must be nucleated and then it must have time to grow. This second step requires the

migration of atoms into the vicinity of the crystal nucleus. If either or both of theses

processes can be avoided, then a glass can be formed. Therefore, by cooling the molten

39

40 Glass Theory, Design & Fabrication

Figure 3.1: Left: Regular atomic arrangement in a crystal. Right: Irregular atomicarrangement in a glass.[32]

solution very rapidly, the mechanisms for crystallisation do not have time to occur and

a glass may be formed.

With reference to Figure 3.2, we begin with a liquid at the point ‘a’. If we cool the liquid

slowly the volume decreases at a constant rate along the line ‘ab’, until we reach the

melting temperature, Tm. For T=Tm the liquid and solid state are in equilibrium, that

is they have the same Gibbs energy1. For T �Tm a rapid and discontinuous change in

the materials volume is encountered along line ‘bc’ and a crystal is formed. Subsequent

cooling will result in a further constant decrease in volume, along ‘cd’, as the thermal

oscillations of the nuclei reduce. However for any given temperature, T < Tm, the

material has a minimum volume for that particular temperature2.

Now consider what will happen if we begin at ‘a’ but cool rapidly. The material will first

move along ‘ab’ but at T=Tm the processes required for crystallisation (nucleation and

growth) do not have time to occur. Further cooling below Tm will result in a continuous

reduction in volume and the material will move through the ‘super cooled liquid’ region

and into the ‘glass transformation range’ whereupon dV/dT decreases and the glassy

state is obtained. Further cooling serves to reduce the volume of the now formed glass

by decreasing thermal oscillations just as in the crystalline state along a line of constant

slope ‘fe’, which is called the glass cooling line.

1The Gibbs energy is a measure of the capacity of the system to do non-mechanical work. As suchit is analogous to a potential energy.

2There are some notable exceptions to this rule in an analogous way to which the volume of waterincreases upon freezing. These exceptions are curious in their own right but irrelevant to this work andwe do not lose generality by disregarding them

Chapter 3 41

Figure 3.2: Potential cooling curves for glass and crystal formation. Glass with fictivetemperature Tf , obtained with fastest cooling rate. Glass’ with fictive temperature T’f ,obtained with slower cooling rate. The approximate positions of the glass relaxationtemperatures Tg are indicated with respect to the corresponding fictive temperatures.

Crystal with melting temperature Tm, is obtained with slowest cooling rate

The intersection of the glass cooling line and the liquid cooling line is defined to be the

fictive temperature, Tf . Figure 3.2 indicates that the final volume (for a given temper-

ature) of the glass and hence Tf depends on the cooling rate. Faster cooling produces

a glass with a larger volume (lower density) and hence higher fictive temperature than

a more slowly cooled melt. The fictive temperature is closely related to the glass relax-

ation temperature3 Tg. The glass transition temperature is the temperature at which

upon heating the solid glass takes on the character of an extremely viscous liquid.

It has been demonstrated experimentally that Tg is typically slightly larger than Tf ,

however there is no simple relation between the two [33]. It is reasoned that this is

essentially due to the way in which each is determined. Tf is determined during cooling

of the melt, while Tg is determined via heating. Both Tg and Tf are indicators of the

transition from super cooled liquid to solid glass (or vice versa), however, Tg is much

easier to measure and therefore more commonly used.

3Alternatively refereed to as the glass transition temperature or glass transformation temperature.


3.3 General Properties of Glasses

The physical and optical properties of glasses will typically differ from the chemically

equivalent crystalline structures due to the amorphous nature of glasses. Further-

more, we cannot use constructs such as the unit cell and periodic boundary conditions,

as we would for a crystal, to calculate or derive the properties because of the lack of

structural periodicity. This fact makes glasses fundamentally difficult systems to model.

The following are some general properties that typify all glassy systems:

� Glasses do not cleave in any preferred direction owing to the absence of crystalline

planes.

� They will have zero-valued even-ordered nonlinear coefficients.

� The property that best typifies glass is an ill-defined melting point. Therefore a

commonly adopted convention is to define the melting point as the temperature

at which the viscosity of the glass reaches 100 dPa.s.

The properties of a glass, as with all materials, are determined by the properties of its

constituents. Because a glass is a frozen mixture of materials, stoichiometry need not be

satisfied and so there is an continuous range of possible combinations of materials that

can produce a glass.

3.3.1 Structural Properties

It is useful to think of glasses as being comprised of two different elements:

� The first is the network. This is the structure of the glass and makes up the vast

majority of the material and is the principal determinant of the properties of the

glass. The right side of Figure 3.1 represents a glass network.

� Second, there are the network modifiers which perturb the network and pro-

duce small changes to the properties of the glass. Network modifiers are present

in the form of ionic species and will alter physical and optical properties of the

glass by disrupting the network. They will reside in locations which facilitate the

neutralisation of excess charge produced by the breaking of bonds (figure 3.3).

As to which elements will be network formers, and which will be modifiers, there are

several models for predicting this behaviour. The model we will consider is Dietzel’s

Chapter 3 43

Figure 3.3: The effect of network modifying ions on the atomic arrangement in silicaglass. Reproduced from [34]

field strength criterion [35] which is well suited for glasses in which the bonds between

elements are highly polar, such as silica and tellurite. Dietzel’s model is, however, poorly

suited for highly covalent glasses like the chalcogenides where the bonding between atoms

is very weak.

Dietzel’s model for glass formation looks at the process in terms of the strength of

the oxygen−cation bonds and the cation−cation repulsion in the molten state and the

resulting battle for oxygen between two or more components. Dietzel’s Field Strength is

defined as:

FD =Zc

(rc + ro−)2=

Zc

a2. (3.1)

Where Zc is the valency of the cation and re and ro− are the ionic radii of the cation

and the oxygen ion respectively and so a = rc+ro− is the ionic bond length between the

cation and oxygen. Dietzel’s Field Strength has units of C.m−2, however FD is typically

used as a figure of merit to identify the roles various chemical components will play

during glass formation. It is therefore confusing to refer to it as a field strength. As

such we refer to FD as Dietzle’s figure of merit for glass formation, or simply Dietzle’s

figure of merit.

Dietzel defines network formers to be those cations with figures of merit with values of

1.3 � FD � 2. Network modifiers will be those cations with a figure of merit in the

range 0.1 � FD � 0.4. The intermediates will have figures of merit of 0.5 � FD � 1.1.

This is summarised in Table 3.1



To illustrate how this model predicts glass forming behaviour, consider the following

situation: Oxides of the components A and B are present in a melt. Let component

A have a figure of merit > 1.3 and B < 0.4 strength. As we cool the melt, A repels

other cations and preferentially bonds to form oxygenated complexes. Now B will have

lost the battle for oxygen and therefore do the best it can to neutralise its charge by

coordinating it’s self with oxygens already bonded to A. This situation looks very much

like Figure 3.3.

3.3.2 Relationships Between the Structure and Properties

Because there are no stoichiometric requirements for glass compositions we can produce

a continuum of compositions and we can expect that as we continuously vary the pro-

portions of the components the physical properties will also vary continuously. Many

researchers attempt to develop empirical models to predict the continuous variation in

properties of glasses, the simplest possible are the additivity relationships which predict

linear relationships between the concentration of the components and the associated

property. Additivity relations are only valid under the assumption that there are no

nonlinear interactions between the different components of the glass.

For example, a glass with N components could have an additivity relation for refractive

index (refractive index often obeys additivity relationships), in the form

n0 =N∑i

niai, (i = 1, 2, 3, . . . , N). (3.2)

Where ni are the coefficients for the refractive index n0 and ai is the proportion of the

ith component in the glass. Refractive index and density are examples of properties

that often obey additivity relations (see Sections 5.2 and 6.4) Additivity relationships,

however, do not apply in general as it is very common for the components to inter-

act in a nonlinear fashion. Thus more complicated empirical models often need to be

constructed.

3.4 The Tellurite Glass System

Pure TeO2 is not a good glass former [36], however, with the addition of network

modifying cations, TeO2 can be readily induced into the glassy state. Tellurium

oxide is therefore referred to as a conditional glass former. The structural elements

Chapter 3 45

Table3.1:Deitzel’s

Field

Stren

gth

ParametersforGlass

Formationof

VariousOxides.Rep

roducedfrom

[35].

N

OTE

:

Thi

s tab

le is

incl

uded

on

page

45

o

f the

prin

t cop

y of

the

thes

is h

eld

in

the

Uni

vers

ity o

f Ade

laid

e Li

brar

y.


present in the glassy state are known to be distorted variants of the TeO4 trigonal bi-

pyramidal (tbp), TeO3+1 polyhedron and TeO3 trigonal pyramidal (tp) sub units present

in crystalline TeO2 as illustrated in Figure 3.4.

Figure 3.4: Structural representation of Te-O subunits. Left: TeO4 trigonal bi-pyramidal (tbp). Middle: TeO3+1 distorted trigonal bi-pyramidal. Right: TeO3 trigo-

nal pyramidal (tp). Bond lengths in nm.

In tellurite glass, Te-O bond lengths for the TeO4 tbp structural subunit range from

0.185 to 0.195nm for the equatorial oxygens, and 0.205 to 0.215nm for the axial oxygens.

The elongated axial Te-O bond belonging to the TeO3+1 subunit ranges from 0.220 to

0.260nm, while the Te-O bonds in the TeO3 tp subunits lie in the range 0.185 to 0.20nm

[37]

We can calculate the glass-forming nature of tellurium oxide via Equation 3.1. Using

the mean bond length from Figure 3.4 (2 A) and the most common valency of tellurium

(Zc = 4), we obtain a figure of merit of ≈ 1. This implies that TeO2 is an intermediate

i.e. it can behave as a network former or modifier depending on the glass forming nature

of other species which may be present in the melt. For example when TeO2 is melted in

the presence of another oxide with a figure of merit much less than 1 (such as Na2O),

TeO2 readily forms a glass. It is common to refer to modifiers that induce intermediates

to become network formers as ’stabilising ions’. In isolation, however, TeO2 is prone to

crystallisation.

Some important properties of tellurite glass are:

Chapter 3 47

� TeO2 is highly polarisable (αi = 6.95/10−30 m3 i.e. 2.5×SiO2 [38]) and therefore

possesses large linear and nonlinear refractive indices. This makes it an ideal

candidate for nonlinear optical devices.

� Tellurite is optically transparent between ≈ 400 nm and 5 μm, which makes tel-

lurite an ideal candidate for visible and mid-IR applications [11].

� It has a low glass transition temperature which makes it a good glass for optical

fibre preform extrusion [11].

� It is not hygroscopic and thus does not suffer from environmental degradation

unlike the flouride glasses which are often considered for mid-IR applications [11].

3.5 Designing the Glass Compositions

The problem we have is this: How can we understand the properties and the variation

of properties observed in tellurite glasses so that predictions can be made about

which composition is most suitable for a particular application? To address this question

we fabricated a variety of tellurite glasses with systematically varied compositions to

make possible general conclusions about the way the properties of tellurite glass depend

on the additional components within them. It can be reasonably assumed that the

physical properties of a glass vary continuously with variation in the proportion of the

components within the glass. Knowing how said properties vary with the different

chemical components enables us to predict which combination of components will provide

an optimised composition for a specific purpose.

In terms of the main objective of this thesis, which is to establish the suitability of

various tellurite glasses for use as a base material for the fabrication of nonlinear optical

fibre devices, we need to consider what properties are critical to the production and

subsequent operation of such devices. Thus we make the following considerations:

1. A nonlinear device requires the use of materials that possess large nonlinear co-

efficients. Optical nonlinearities are related to the electronic polarisability (and

hyperpolarisability etc.) of the material and in particular its constituents. For

this reason it is necessary to select chemical components that will imbue the glass

with high nonlinear coefficients.

2. Any optical device must have excellent optical transmission. In particular for a

nonlinear fibre device there are two main contributing factors to the overall loss of

the device. Material absorption presents the fundamental lower limit to the devices


loss and can be minimised by selecting a material with a transmission range that

suits the desired operating wavelength or wavelengths. The purity of this material

should then be made as high as possible by starting from high purity raw materials

and using a very clean and controlled fabrication environment.

Scattering loss produced by crystals can be a major source of loss in optical fibres

and thus a glass with high resistance to crystallisation should be used. Crystalli-

sation of glass is a common problem encountered when trying to form glasses from

new or little studied glass compositions

3. We seek glasses that can be used for the fabrication of optical fibres. As such,

volume scalability is also crucial so that we may produce practical size billets for

preform production. We fabricate our optical fibres via the extrusion technique

(see Section 9.4) which requires the use of glass billets with volumes of � 20 cm3.

For a glass to be produced in volumes such as these it is critical for the glass to

possess a high degree of crystallisation stability. This is because as the volume

of the glass increases its surface area to volume ratio decreases and therefore the

ability of the cooling melt to shed heat, which it must do so rapidly to form a

glass, is reduced.

Much of the glass research reported in the literature focuses on relatively small

volumes of glass. As such the reports of what are often referred to as ’promising

candidates’ for optical fibre materials a frequently unsuitable as they cannot be

easily scaled to practical billets sizes.

To summarise our requirements; we require glasses that are highly transparent, highly

nonlinear and resistant to crystallisation to allow crystal free fibres to be fabricated.

We address the first requirement by selecting modifiers that have a variety of electronic

polarisabilities (see Table 3.2). This provides an opportunity to probe the contribution

of the modifier to the optical nonlinearity. The second requirement is met by including

10 mole% of sodium oxide (Na2O) in all the glass samples as a stabilizing ion [39].

Finally the third requirement, which is also related to the glass forming stability of the

material, is met by only studying glass compositions which have shown their ability

to be produced in large volumes. This should ensure that we can fabricate optical

fibre preforms with sufficient size so as to provide practical lengths of optical fibre.

Furthermore, glasses which can be fabricated in large volumes by default have a good

resistance to crystallisation and so will have a good chance of tolerating the fabrication

process for optical fibres.

By fabricating a series of glasses with systemically varied compositions we can determine

the compositional dependence of various properties, whilst ensuring that if a sample

Chapter 3 49

Electronic Ionic Most CommonPolarisability Electronegativity Radius Coordination

Modifier [10−23 cm3] [Pauling Scale] [A] Number

Na+ 0.41 0.93 0.95 6Zn2+ 0.8 1.65 0.83 6Ba2+ 2.5 0.89 1.43 8Mg2+ 0.09 1.31 0.78 6Sr2+ 1.6 0.95 1.27 8Pb2+ 4.9 2.33 1.32 8

TelluriteTe4+ - 2.10 1.87 3,4TeO4 6.71 - - -TeO3 5.30 - - -

Table 3.2: Potential modifiers and their electronic polarisabilities [40], ionic radii[18, 40], electronegativities, molecular masses and coordination numbers [41]. Wherepossible the properties of the tellurium ion [18] and the TeO4 and TeO3 sub units [42]

are listed.

shows particular promise for a nonlinear device it should have the necessary stability to

survive the MOF manufacturing process.

We can express the glass compositions that were investigated by the general formula:

10Na2O.xMO.(90− x)TeO2 (3.3)

Where MO is a metal oxide comprised from one of the divalent cations listed in Table

3.2.

3.6 Procedure for Glass Production

All glasses were produced using high purity raw materials as listed in Table 3.3. For

Na2O and BaO we started with the carbonates Na2CO3 and BaCO3 which readily

decompose to the oxides under the glass melting conditions. This provides higher purity

at lower cost.

The following list outlines the general procedure for producing the glass samples. The

specific details of which were developed by trial and error with some reference to pub-

lished techniques:

1. Raw materials are combined in an inert atmosphere (N2) in the appropriate pro-

portions to an accuracy of ± 0.05 mg. Combining (batching) the raw materials in


Component Purity [%] Supplier

TeO2 99.995 CERAC & Alfa AesarNa2CO3 99.99 Alfa AesarZnO 99.99 CERAC

BaCO3 99.99 CERACPbO 99.99 CERACSrO 99.99 CERAC

Table 3.3: Purity and supplier for glass raw material.

a controlled environment such as this minimises the likelihood of contamination

by dust particles and moisture from the air.

2. The combined materials are mixed by shaking in a sealed plastic container.

3. The powders are transferred to a gold crucible of either 100 mL or 300 mL volume

depending on the size of the desired billet. A lid made from gold is used in

combination with the crucible to minimise the evaporation loss while melting.

Thus we can consider the melting environment to be, approximately, a closed

system.

4. We place the crucible into a preheated furnace in open air at 500◦C and ramp the

temperature at 10◦C.min−1. This gives the volatile carbonate components time to

decompose to their oxides before the mixture has melted.

5. We hold the mixtures at a melting temperature of 900◦C for >1 h.

6. Periodically the melted solution is swirled during the melting period to ensure

homogeneity, taking care to capture any undissolved material on the inner sides

of the crucible.

7. We then cast the melt into brass moulds which were pre-heated to ≈ 250◦C. This

temperature was arrived at empirically through trial and error. If the temperature

of the mould is too low then the formed glass will possess too much internal stress

and will crack and fracture. On the other hand, for mould temperatures that are

too high the melt is wetting4 on the metal surface and consequently sticks.

8. The glass is annealed around 280◦C with the temperature decreased to ambient

at 0.3− 0.1◦C.min−1 (depending on melt volume).

9. Thermal characteristics of the glass are determined via Differential Scanning Calorime-

try (DSC) (Section 5.3.1).

4For a general discussion of wetting behaviour turn to Section 9.3.2.

Chapter 3 51

10. Finally, to eliminate any residual stresses in the glass, the samples are re-annealed

at just below Tg for > 1 h and cooled to ambient temperature at 0.3−0.1◦C.min−1

(depending on melt volume).

Typically glass melts of three different volumes were attempted for confirmation of the

scalability of the compositions; 4 cm3, 20 cm3 and 40 cm3 which, given the densities of

tellurite glasses (Section 5.2), corresponds to ≈20 g, ≈100 g and ≈200 g respectively.

Figure 3.5 shows the brass moulds used and examples of the resulting glass billets.

Figure 3.5: Brass moulds for glass casting and the resulting billets. Approximatevolumes and masses from left to right: 4 cm3/20 g, 20 cm3/100 g and 40 cm3/200 g

3.7 Results

Table 3.4 details the attempted compositions and the maximum achieved melt vol-

ume.

We stress that, although some of the attempted compositions did not form glasses, we

can not conclude that the composition is not a glass former. All that can be concluded is

that under our fabricating conditions the composition did not form a glass. This result

indicates that the failed compositions are not suitable for our optical fibre manufactur-

ing process as it stands, however after further optimisation of the melting and casting


conditions they may prove suitable. As such these compositions have been abandoned

for the purposes of this thesis.

The successful glass forming compositions all formed optically clear samples with a slight

green colouration, which is due to the position of the absorption band edge for these

materials which is around 450 nm (see Section 6.2 for more details on the band edge

and optical transmission in general).

Vol.Sample TeO2 Na2O MgO ZnO BaO PbO SrO [cm3]

TMN1 85 10 5 - - - - 4TMN2 80 10 10 - - - - 42TMN3 75 10 15 - - - - 4

TZN1 85 10 - 5 - - - 42TZN2 80 10 - 10 - - - 42TZN3 75 10 - 15 - - - 42TZN4 70 10 - 20 - - - 42∗

TZN5 65 10 - 25 - - - N/ATZN6 60 10 - 30 - - - N/A

TBN1 85 10 - - 5 - - 22TBN2 80 10 - - 10 - - 22TBN3 75 10 - - 15 - - N/ATBN4 70 10 - - 20 - - N/A

TPN1 85 10 - - - 5 - 4TPN2 80 10 - - - 10 - N/ATPN3 70 10 - - - 20 - N/A

TSN1 85 10 - - - - 5 N/A

Table 3.4: Table of glass compositions investigated. Amounts of components arein molar % and the volumes indicated are the current maximum volumes. Where astable glass was not achieved the volume is labelled as N/A. ∗ Some small crystals were

observed in the 42 cm3 billet only, thought to be undissolved ZnO.

We label the compositions of the tellurite glasses in the following way:

� The first letter in the label is ’T’, indicating tellurium oxide.

� The second letter is taken from the first letter in the chemical symbol of metal

species in the modifying oxide, e.g. zinc oxide → Z, barium oxide → B, etc.

� The third letter, which is common to all glasses is ’N’ and indicates the stabilising

compound, sodium oxide.

� We changed the molar percentages of the modifying oxides in increments of 5 molar

% for all of the attempted compositions. Accordingly we are able to represent the

modifier concentration with a single number at the end of the label. Where that

Chapter 3 53

number is the multiple of 5 mole % of the modifying oxide, i.e. 1 → 5 mol.%,

2→ 10 mol.%, 3→ 15 mol.%, etc.

3.8 Conclusion

In the preceding sections I have discussed the material requirements for fabrication of

a nonlinear fibre device. Specifically we require the glasses to have large nonlinear

coefficients, low absorption and high crystallisation stability. To meet these require-

ments we must select an appropriate material, however, in order to do so a thorough

understanding of the chosen glass system (tellurite) is required. Therefore, to address

this need we have designed a range of compositionally varied potential glasses, so that

the correlation between composition and property can be established. After experimen-

tal determination of the glass forming ability of these proposed compositions we have

arrived at three tellurite glass families; TMN, TZN and TBN, appropriately summarised

by the following formulae:

TMN: 10Na2O.xMgO.(90− x)TeO2 x = 5, 10, 15

TZN: 10Na2O.xZnO.(90− x)TeO2 x = 5, 10, 15, 20

TBN: 10Na2O.xBaO.(90− x)TeO2 x = 5, 10

⎫⎪⎪⎪⎬⎪⎪⎪⎭

(3.4)

They possess different modifying species (Mg, Zn and Ba) with a spectrum of electronic

polarisabilities (Table 3.2). Additionally, within each family of glass, the concentration

of the modifier ranges over at least 5 mol.% (Formulas 3.4). Importantly, all of these

glasses have been successfully fabricated into ≈40 cm3 (200 g) billets which provides a

preliminary indication that these glasses have a high crystallisation stability and could

then be suitable for fibre optic devices.

Chapter 4

Analysis of the Microscopic

Structure of Glass

4.1 Introduction

The properties of a material are manifest from the collective properties of the con-

stituents of that material. To understand the origins of a material’s properties

there are two things that need to be considered: what elements is the material made

from and how are they arranged?

In this chapter we seek to discover the arrangement of elements within the glasses under

study. knowing what structural elements are present will enable us to better understand

the origins of trends and changes in the physical and optical properties presented in

Chapters 4, 5 and 6.

We begin this chapter with an example that illustrates the effect of different structural

arrangements of the same elements on the properties of a material. Consider silicon

dioxide (SiO2), the elemental components of which are silicon and oxygen in the ratio 1:2.

If these elements are arranged in a regular lattice we obtain the well known crystalline

material quartz. In quartz there are well defined bond lengths between the silicon and

oxygen atoms. However, if the silicon and oxygen are arranged haphazardly the resulting

material is known as fused silica, which is a common glass. As discussed in Chapter 3

the glassy state of a material is typified by chemical bonds that are distorted from the

ideal lengths and angles. Now, these two materials are chemically identical but, owing

to their structural differences, have differing properties.

For example, in Table 4.1 we list side by side some representative properties of crystalline

quartz and fused silica.

55

56 Analysis of the Microscopic Structure of Glass

Table 4.1: Comparison of certain properties of Quartz and Fused Silica. ∗ Values ofthe ordinary (ne) and extraordinary (ne) refractive indices respectively. + Values for β

tridymite and β cristobalite respectively.

Property Quartz Fused Silica

Refractive Index [@ 627.8 nm] 1.542819 / 1.551880∗ 1.45716Density [g.cm3] 2.65 2.203

Melting / Softening Point [◦C] 1670 / 1713+ 1665

Owing to the strong dependence of properties on the structural arrangements of atoms

it is therefore critical to determine this structure to gain a proper understanding of

a material. To this end we have undertaken to determine the microscopic structural

arrangement of the tellurite glasses under study. The tool with which we achieved this is

Raman spectroscopy which, as will be seen in the following sections, can provide excellent

information regarding the arrangement of the chemical elements in these materials.

In the next sections we describe the basic principles behind Raman spectroscopy and how

they relate to the molecular structure of tellurite glass. Then we outline the experimental

technique for recording these spectra and discuss the data analysis procedure. Finally, we

present the data for the samples, accompanied by a detailed discussion of the results. In

later chapters, we present data for various properties of the tellutite glasses. We will be

referring to the structural information herein so that property-to-structure relationships

can be established.

4.2 Raman Spectroscopy

Raman spectroscopy is a measurement of the molecular rotational and vibrational

modes of a material. In solid state systems molecular rotations are impossible. We

can therefore only study the vibrational transitions. The technique relies on inelastic

scattering of monochromatic light from phonons, which essentially involve the transfer

of energy between the incident light and the vibrational modes of the material.

An incoming photon excites a vibrational mode into a virtual energy state. The state

then decays into a real vibrational state. The difference in energy between the initial

state and the final state corresponds to a change of energy, or Raman shift, of the

emitted photon. If the final state is more energetic than the initial state the emitted

photon will have a lower frequency than the incoming photon. This is called the Stokes

shift. Alternatively, if the final state is lower in energy than the initial state then the

emitted photon will have acquired some energy and therefore an increase in frequency

will be observed. This shift to higher frequency is called the Anti-Stokes shift. The

Chapter 4 57

intensity of the Anti-Stokes shifted light is much less than the Stokes shifted light and

therefore Raman spectrometers are configured to detect the Stokes shifted photons.

It is typical to measure Raman intensity with respect to wavenumber (ν [cm−1]) and

not frequency. Therefore, to maintain consistency with the literature we adopt this con-

vention. Wavenumber and frequency are proportional to one another and, importantly,

proportional to energy. In SI units the relationships between frequency, energy and

wavenumber are

ν =E

h= νc× 102. (4.1)

The measurement of the Raman shift represents a change in frequency Δν, of the input

light determined by

Δν = Δνc× 102 (4.2)

Alternatively, in terms of the change in the wavelength of the input light

Δλ = λ2Δν × 102. (4.3)

Where λ is the wavelength of the input light. Figure 4.1 is a conversion plot for the

frequency and wavelength shifts for a give Raman shift. The vales of the Raman shifts

have been chosen based on what is typically encountered in tellurite glass and Δλ’s are

calculated at 514 nm, which is the wavelength used in the measurements presented in

Section 4.2.2.

100 200 300 400 500 600 700 800 900 10000

0.5

1

1.5

2

2.5

3 x 104

Raman Shift [cm−1]

Δν [G

Hz]

5

10

15

20

25

30

35

Δλ [n

m]

Figure 4.1: Conversion between Raman shift and Frequency and Wavelength shift.Δλ calculated using λ = 514 nm (To match experiments performed within this thesis).Values of the Raman shift are taken between 100 and 1000 cm−1 which correspond to

typical Raman shifts produced in tellurite glass.


In the following analysis we will use the terms wavenumber and frequency interchange-

ably.

4.2.1 Raman Spectroscopy of Tellurite

Raman spectra of tellurite glasses, where tellurium is the only network former, have

five characteristic peaks that correspond to the inhomogeneously broadened vibrational

features found in TeO2 crystals [37, 43]. Figure 4.2 shows a typical Raman spectrum

the details of which will be discussed subsequently. In general all tellurite glasses of

this type vary in the relative intensities of these bands for different compositions of

glass [36, 37, 44, 45].Figure 4.2 shows a representative Raman spectra which has been

deconvolved into its Gaussian modes. The method for performing this deconvolution is

explained later in Section 4.2.3.

Figure 4.2: Example of a deconvoluted raman spectrum (sample: TZN2 see Section4.2.2 for experimental details). Black: Measured spectrum. Green: Gaussian vibra-tional modes. Red: Reconstructed spectrum achieved by addition of gaussians. Note:The fit is poor in the region ν < 400 cm−1. This is due to the edge filter that is usedto remove the Rayleigh scattered light therefore corrupting the spectra in this region.

The following is a summary of the assignment of the Raman bands taken from Sekiya et

al [37]. Refer to Section 3.4 for details relating to the TeO4, TeO3+1 and TeO3 polyhedra.

Chapter 4 59

The A band

Located at ≈ 450 cm−1, results from symmetrical bending and stretching modes of Te-

O-Te bonds found at corner sharing sites of TeO4, TeO3+1 and TeO3 polyhedra (see

Figure 4.3).

Figure 4.3: Ball and stick representation of the tellurite lattice vibrations that con-tribute to the Raman A mode. Tellurium = black circles. Oxygen = white circles. Fromleft to right: Corner sharing subunits: TeO3 with a NBO of the type Te=O, TeO4 andTeO3+1 with a NBO of the type Te-O−. Red arrows indicate the symmetrical bendingof Te-O-Te bonds. Blue arrows indicate the symmetrical stretching of Te-O-Te bonds.

The B band

Located at ≈ 611 cm−1, is attributed to anti-symmetric stretching of continuous net-

works of TeO4 subunits (see Figure 4.4). Accordingly the A and B bands are a measure

of the networking of the glass structure.

Figure 4.4: Ball and stick representation of the tellurite lattice vibrations that con-tribute to the Raman B mode. Tellurium = black circles. Oxygen = white circles. Redarrows indicate the anti-symmetric stretching in a continuous chain of TeO4 subunits.


The C band

Located at≈ 659 cm−1, is caused by anti-symmetric vibrations of Te-axO-eq constructed

by two unequivalent Te-O bonds (see Figure 4.5). It is often reported that this band

is related to TeO4 content, however, there are many contributing vibrations to this

band from the TeO3+1 and TeO3 subunits where the shared oxygen is bonded to a

neighbouring tellurium with unequivalent bonds, e.g. Figure 4.5 shows a TeO3 sharing

an oxygen with an axial TeO4 oxygen.

Figure 4.5: Ball and stick representation of the tellurite lattice vibrations that con-tribute to the Raman C mode. Tellurium = black circles. Oxygen = white circles. Redarrows indicate the anti-symmetric vibrations of two unequivalent Te-O bonds. In thisexample one oxygen from a TeO3 subunit with a NBO of the type Te=O is bonded to

an axial TeO4 oxygen.

The D band

Located at ≈ 716 cm−1, is due to stretching modes of Te-O− and Te=O bonds containing

non-bridging oxygens (NBO) which are formed by TeO3+1 and TeO3 polyhedra (see

Figure 4.6). As such the D band is the most unambiguous indicator of the presence of

TeO3+1 and TeO3 sub units.

Figure 4.6: Ball and stick representation of the tellurite lattice vibrations that con-tribute to the Raman D mode. Tellurium = black circles. Oxygen = white circles. Red

arrows indicate the stretching of the NBO’s both Te=O and Te-O−.

Chapter 4 61

The E band

Located at ≈ 773 cm−1, band is ascribed to stretching modes of non-bridging oxygen

atoms of the type Te-O− in TeO3+1 and TeO3 subunits (top of Figure 4.7).The Raman

E peak is a good measure of one particular type of NBO (Te-O−), which we shall denote

NBO−. There are also contributions to this band from the symmetric stretching of

continuous network of TeO4 subunits (bottom of Figure 4.7).

Figure 4.7: Ball and stick representation of the tellurite lattice vibrations that con-tribute to the Raman E mode. Tellurium = black circles. Oxygen = white circles. Top:Red arrow indicates the stretching of Te-O− type NBO. Bottom: Red arrows indicate

the symmetric stretching of a continuous chain of TeO4 subunits.

The intensities of the Raman bands are used as a measure of the glass structure as

follows in Table 4.2:

Raman Band Characteristic Structural Elements Nomenclature

A Te-O-Te bonds Network connectivityB Connectivity of TeO4 chains TeO4 connectivityC Te-axO-eq bonds TeO4 concentrationD TeO3 and TeO3+1 subunits TeO3 concentrationE Non bonding oxygens of the type Te-O− NBO− content

Table 4.2: Raman band assignment to structural subunits and nomenclature.

In addition to the five band listed above, all glasses possess a spectral feature known

as the Boson peak. This is the lowest frequency (ν < 100 cm−1) scattering feature and

can account for a large portion of the total Raman intensity. The origin of this feature

is still poorly understood and remains somewhat controversial. It is, however, believed


to be related to medium range order within the glass [46–48]. We do not attempt to

analyse the Boson peak data in our spectra because of the lack of accepted knowledge

relating to its origin. Also, during the measurement the Raman shifted light was filtered

from the Rayleigh scattered pump light with an edge filter consequently the Boson peak

was not detected for the TZN and TBN glasses and only partially detected for the TMN

glass.

4.2.2 Experimental Details

The Raman spectra presented were kindly recorded by Dr. Elizabeth Carter at the

University of Sydney1. We prepared spectroscopic samples by cutting ≈ 2 mm thick

slices from the 4 cm3 rectangular billets. These slices were then polished to optical

quality on both faces. The following experimental details were provided by Dr. Carter:

Raman spectra were recorded using a Renishaw Raman InVia Reflex Microscope. The

excitation wavelength of 514 nm was provided by an argon ion laser operating at a max-

imum power of 5.2 mW. This was attenuated using neutral density (ND) filters from 0%

to 99% depending on sample. The light is collected in the 180 ◦ configuration using a

Leica DMLM microscope equipped with 50x, 20x and 5x objectives with NA=0.75, 0.40

and 0.12 respectively. Raman signals were detected with an air cooled charge coupled

device (CCD) camera equipped with a holographic notch filter with 2400 lines.mm−1 for

removal of the Rayleigh scattered pump light. The spectrometer is regularly calibrated

using the 520.50 cm−1 Raman band of silicon to an accuracy of ±0.10 cm−1. We ob-

tained triplicate spectra for each sample from 100 cm−1 to 1000 cm−1 with a resolution

of 0.25 cm−1.

4.2.3 Data Analysis

Upon review of the literature it was noticed that there are several methods for analysing

the spectroscopic data. There appears to be a concerning lack of consistency in the

techniques and despite the frequent qualitative agreement there is a need to determine a

single and well justified approach. For example, it is common for authors to discuss the

relative intensities of the peaks in the Raman spectra. However, this is frequently done

in terms of the amplitudes of the peaks. This is an insufficient definition for intensity in

particular for the broadened peaks observed in glassy materials. There are contributions

to the peaks that are frequency shifted as a result of the distorted bond lengths in the

amorphous system. It is conceivable that changes in composition, for example, could

1As a part of the NCRIS scheme

Chapter 4 63

distort the structural element responsible for the spectral feature without changing the

number of these elements. Simply measuring the peak hight would not be sensitive to

such a change. The only way to guarantee that all of the contributions to the particular

vibrational mode are accounted for is to take the area under the peak as representing the

intensity. Another questionable technique that is used is to normalise the amplitudes

of each peak to that of the Raman C band. As we have already stated, this band is

frequently ascribed to the presence of the TeO4 subunit which is a mistake that has

propagated through the literature. We have instead chosen to normalise the intensities

of the individual Raman bands to the total intensity. That is we take the ratio of the

area under the peak to that of the total area under all peaks.

The Raman spectra within this thesis were analysed via the following procedure.

1. Spectra for each sample were recorded three times and averaged to reduce the

random error.

2. Background removal was performed by subtracting the minimum value from the

spectra (i.e. where the materials have no Raman response.)

3. Using a commercial software package (OriginPro 8�) we de-convolve the spectra

into five Gaussians centred at approximately: 450, 611, 659, 716 and 773 cm−1

[37]. No restrictions were placed on the width, amplitude or position of the peak.

4. Raman band intensities are calculated by integrating the de-convolved Gaussians.

5. We normalise to the total Raman intensity which is the total area under the

spectrum. This normalisation procedure provides relative Raman intensities which

can then be compared between samples.

6. The intensity error was estimated from the maximum standard error for the am-

plitudes.

4.2.4 Results and Discussion

Shown in Figures 4.8 to 4.10 are the recorded Raman spectral data for the three glass

series. The low frequency cut off of the TMN glasses is at approximately 100 cm−1 as

opposed to the cut off of 200 cm−1 in the case of the TZN and TBN spectra. This is

due to the inadvertent use of a different filter during the measurement. As a result the

tail of the Boson peak is observed in the spectra for the TMN glasses.

The immediate observation that can be made about all of the glass series is that as

the concentration of the modifier is increased the spectra take on more high frequency


content, around 800 cm−1, to the detriment of the lower frequency components of the

spectra near 450 cm−1. To assess the changes in the spectra more precisely, an analysis

of the deconvolved spectra is necessary.

Figure 4.8: Raman spectra for the TMN glass series. The arrows indicate generaltrends observed as the Mg2+ concentration is increased. The spectral content is trun-

cated below ≈100 cm−1 due to the use of filter in the spectrometer.

Figure 4.9: Raman spectra for the TMN glass series. The arrows indicate generaltrends observed as the Zn2+ concentration is increased. The spectral content is trun-

cated below ≈200 cm−1 due to the use of filter in the spectrometer.

The deconvoultion of the spectra was performed as per the steps outlined in Section

4.2.3. We assess the quality of the de-convolution via the correlation coefficient, R2, for

the fitted Gaussians where 0 � R2 � 1 and 1 indicates a perfect fit. In all cases for the

data obtained here R2 > 0.997.

Chapter 4 65

Figure 4.10: Raman spectra for the TMN glass series. The arrows indicate gen-eral trends observed as the Ba2+ concentration is increased. The spectral content is

truncated below ≈200 cm−1 due to the use of filter in the spectrometer.

Table 4.3 contains the relative Raman band intensities. We have indicated the position

of each band relative to the analogous band for the crystalline phase, however, we note

that in the glass phase these centre locations are shifted. Centre positions for the bands

as found in the glasses are tabulated in Table 4.4. In general, an increase in the frequency

of a Raman band indicates an increase in bond strength which is produced by shortening

of the bond length. Conversely, for a decrease in the Raman band frequency there is an

implied increase in bond length and thus an decrease in bond strength. If we refer to the

Szigeti relation [49], which relates the vibrational frequency of the stretching vibration

to the inter-atomic force F and the reduced mass, μ = m1m2/(m1 +m2), via:

ν =1

2π

√(F

μ

). (4.4)

The force F, is Coulombic which is ∝ 1/r2 (where r is the bond length). Therefore F

will increase if the bond length decreases and decrease if the bond length increases.


Table 4.3: Relative Raman band intensities for glasses under study. Values have beenmultiplied by 100 to give a %. The intensities have a maximum error of ±0.5

Raman Band

A B C D ESample (450 cm−1) (611 cm−1) (659 cm−1) (716 cm−1) (773 cm−1)

TMN1 33.0 6.8 28.9 2.3 29.1TMN2 31.6 5.5 28.0 15.8 19.2TMN3 29.7 4.1 23.9 39.8 2.5

TZN1 34.4 5.9 33.2 6.8 19.7TZN2 33.4 4.9 31.7 8.2 21.8TZN3 33.0 3.9 30.8 9.7 22.6TZN4 31.6 3.2 30.5 10.5 24.2

TBN1 30.8 4.8 37.2 12.5 14.7TBN2 26.5 5.0 26.4 37.7 4.5

Table 4.4: Table of Raman band centre positions obtained from the Gaussian decon-volution. Bands are labelled with unperturbed centre positions for reference.

Raman Band

A B C D ESample (450 cm−1) (611 cm−1) (659 cm−1) (716 cm−1) (773 cm−1)

TMN1 454 597 661 718 752TMN2 451 595 660 725 785TMN3 448 592 659 753 817

TZN1 451 596 663 721 766TZN2 447 594 663 724 770TZN3 443 592 664 728 774TZN4 438 591 667 733 778

TBN1 456 591 663 726 778TBN2 457 588 654 735 792

We summarise the observed trends in the Raman bands of the studied glass samples as:

� Raman A Band: The relative intensity of the Raman A band decreases with

increasing modifier content for the TMN, TZN and TBN glasses (Figure 4.11).

This is interpreted as representing a progressive decrease in the network connec-

tivity of the glasses by the conversion of Te−O−Te bonds into Te−O−M−O−Techains, where M represents Mg, Ba or Zn. The effect is largest for the Ba2+

containing glasses, because Ba2+ possesses the smallest electronegativity and the

highest coordination number of the three modifiers (see Table 3.2). Thus Ba2+

demands more oxygens and does so with greater strength than Mg2+ and Zn2+.

Consequently, disruption of the Te−O−Te bonds is produced, in order of degree,

by Ba2+, Mg2+ and Zn2+.

Chapter 4 67

5 10 15 2024

26

28

30

32

34

36

TMN1

TMN2

TMN3

TZN1

TZN2TZN3

TZN4TBN1

TBN2

Net

wor

k C

onne

ctiv

ity [a

rb. u

nits

]

Modifier Concentration [mol. %]

Figure 4.11: Network connectivity (Raman A band) variation with modifier content(Mg2+, Zn2+ and Ba2+) for the TMN, TZN and TBN glasses.

5 10 15 20435

440

445

450

455

460

TMN1

TMN2

TMN3

TZN1

TZN2

TZN3

TZN4

TBN1TBN2

Ram

an A

Ban

d C

entre

[cm

-1]


Figure 4.12: Position of the Raman A band variation with modifier content (Mg2+,Zn2+ for the TMN, TZN and TBN glasses.


The frequency of the Raman A band decreases with increasing modifier content

for the TMN and TZN glasses and increases for the TBN glasses (see Figure

4.12). We note that this implies an increase in the Te−O−Te bond lengths which

is associated with the modifiers (Mg2+ and Zn2+) distorting and breaking up

the network connectivity). The Ba2+ modified TBN glasses, despite displaying a

decrease in network connectivity (Figure 4.11), display an increase in Te−O−Tebond strength, implying that the bond lengths are shortening.

� Raman B Band: Figure 4.13 shows that for increasing modifier content the rel-

ative intensities of the Raman B bands decrease for the TZN and TMN glasses.

This indicates that, as Zn2+ and Mg2+ is added the connectivity of the TeO4 sub-

units is destroyed. Conversely, for increasing Ba2+ content the TeO4 connectivity

increases. This can be understood by considering the shift to higher frequencies

displayed by the Raman A peak in the TBN glasses. We interpret this to imply

that the TeO4 subunits are clustering into chains so that, whilst the overall con-

nectivity of the network decreases for increased Ba2+ (Figure 4.11), there is local

formation of TeO4 chains with less perturbed and thus shorter Te−O−Te bond

lengths.

5 10 15 202.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

TMN1

TMN2

TMN3

TZN1

TZN2

TZN3

TZN4

TBN1TBN2

TeO

4 Con

nect

ivity

[arb

. uni

ts]


Figure 4.13: TeO4 connectivity (Raman B band) variation with modifier content(Mg2+, Zn2+ and Ba2+) for the TMN, TZN and TBN glasses.

The Raman B band frequency decreased for increasing modifier content for TMN,

TZN and TBN glasses as shown in Figure 4.14. This behaviour implies that the

bond lengths for the TeO4 chains increase which is likely to be as a result of

Chapter 4 69

5 10 15 20588

590

592

594

596

598TMN1

TMN2

TMN3

TZN1

TZN2

TZN3

TZN4TBN1

TBN2

Ram

an B

Ban

d C

entre

[cm

-1]


Figure 4.14: Position of the Raman B band variation with modifier content (Mg2+,Zn2+ for the TMN, TZN and TBN glasses.

the increase in the axial Te−O bond (0.21 nm→ 0.24 nm) associated with the

conversion of TeO4 to TeO3+1 (Figure 3.4) which is common to all of the glasses

under study as shown in Figure 4.17.

� Raman C Band: The Raman C band is the most ambiguous band as its presence

is indicative of the anti-symmetric vibrations of unequivalent Te-O bonds in a Te-

O-Te linkage that can occur between TeO4, TeO3+1 and TeO3 subunits. It is

frequently claimed that this band is representative of the presence of the TeO4

subunit alone as this feature is observed in pure TeO2 crystals which are known

to be comprised exclusively of the TeO4. This is an erroneous assertion because

as has been shown the inhomogeneously broadened feature observed in glassy

tellurite systems has multiple contributing structural elements [36, 37, 44, 45].

We can, however, utilise the information from this band to determine the degree

to which the connectivity of the glass is effected by the changes in the modifier

concentration.

Figure 4.15 shows that the number of Te-axO-eqTe bonds is reduced as the con-

centration of the modifier is increased. The cause for this lays in the breaking up

of the network by the modifying species via the creation of TeO3 subunits and

NBOs.

Plotted in Figure 4.16 are the centre positions of the Raman C band for each

glass sample. It is noted that the position of the C band for the TZN series


5 10 15 2020

24

28

32

36

40

TMN1TMN2

TMN3

TZN1

TZN2TZN3 TZN4

TBN1

TBN2

Ram

an C

Ban

d R

elat

ive

Inte

nsity


Figure 4.15: Relative intensity of the Raman C band variation with modifier content(Mg2+, Zn2+ and Ba2+) for the TMN, TZN and TBN glasses.

progressively moves to higher frequencies as the amount of Zn2+ is increased.

This can be understood by considering that as TeO4→TeO3 both the axial and

equatorial bonds decrease in length thus increasing in vibrational energy. The

change to higher frequencies of this band therefore indicates an overall shortening

of the Te-axO-eq bonds which occurs as TeO4 is converted into TeO3.

Conversely, the position of the C band for the TMN and TBN series is shifting

towards lower frequencies as additional modifier is introduced. In the case of TMN

glasses it is possible that this is resulting from the presence of the intermediate

TeO3+1 subunit with its elongated axially bonded oxygen. However, this is difficult

to determine. As for the TBN glasses a strong shift towards the lower frequencies is

observed if we also consider the data for the B band we see that there is evidence to

suggest that the TeO4 subunits are taking part in the connectivity of the network,

more so that the other species.

� Raman D Band: There is an increase in the relative intensity for the Raman D

band with increasing modifier content for the TMN, TZN and TBN glasses. As

this peak is associated with the presence of TeO3+1 and TeO3 subunits we conclude

that the addition of Mg2+, Zn2+ and Ba2+ promotes the conversion of TeO4 into

TeO3 via the TeO3+1 intermediate. This behaviour is commonly seen in tellurite

glass in which an increase in modifier distorts the TeO4 subunits to produce TeO3

[44].

Chapter 4 71

5 10 15 20650

652

654

656

658

660

662

664

666

668

670

TMN1TMN2

TMN3

TZN1 TZN2TZN3

TZN4

TBN1

TBN2Ram

an C

Ban

d C

entre

[cm

-1]


Figure 4.16: Position of the Raman C band variation with modifier content (Mg2+,Zn2+ for the TMN, TZN and TBN glasses.

5 10 15 200

5

10

15

20

25

30

35

40

45

TMN1

TMN2

TMN3

TZN1TZN2

TZN3 TZN4

TBN1

TBN2

TeO

3 Con

cent

ratio

n [a

rb. u

nits

]


Figure 4.17: TeO3 concentration (Raman D band) variation with modifier content(Mg2+, Zn2+ and Ba2+) for the TMN, TZN and TBN glasses.


5 10 15 20715

720

725

730

735

740

745

750

755

TMN1

TMN2

TMN3

TZN1

TZN2

TZN3

TZN4

TBN1

TBN2

Ram

an D

Ban

d C

entre

[cm

-1]


Figure 4.18: Position of the Raman D band variation with modifier content (Mg2+,Zn2+ for the TMN, TZN and TBN glasses.

The Raman D band frequency increases for increasing modifier content for TMN,

TZN and TBN glasses (see Figure 4.18). This peak is indicative of the conversion of

TeO3+1 into TeO3 which is accompanied by a shortening of the equitorial oxygen

bonds from 0.19 nm→ 0.185 nm (Figure 3.4) and the axial oxygen bond from

0.21 nm→ 0.20 nm.

Chapter 4 73

� Raman E Band: For increasing modifier content we observe a decrease in the

intensity of the Raman E band for the TMN and TBN glasses and an increase

for the TZN glasses. This indicates that both Mg2+ and Ba2+ are inhibiting the

formation of non-bonding oxygens of the type NBO−, whereas Zn2+ is promot-

ing it. It is possible that this behaviour is somehow related to the Zn-O bonds

being the least ionic of all the modifier-oxygen bonds, as Zn2+ has the highest

electronegativity of all the modifiers (Table 3.2). We are, however, unsure of the

precise mechanism and thus leave it for future study.

5 10 15 200

5

10

15

20

25

30TMN1

TMN2

TMN3

TZN1TZN2 TZN3

TZN4

TBN1

TBN2

NB

O- C

onte

nt [a

rb. u

nits

]


Figure 4.19: NBO− concentration (Raman E band) variation with modifier content(Mg2+, Zn2+ and Ba2+) for the TMN, TZN and TBN glasses.

As shown in Figure 4.20, the Raman E band frequency increases for increasing

modifier content for TMN, TZN and TBN glasses. This band is also associated

with the conversion of TeO3+1 into TeO3 and thus by the same reasoning for the

Raman D band we expect to see an increase in the vibrational frequency.


5 10 15 20740

750

760

770

780

790

800

810

820

TMN1

TMN2

TMN3

TZN1TZN2

TZN3TZN4TBN1

TBN2

Ram

an E

Ban

d C

entre

[cm

-1]


Figure 4.20: Position of the Raman E band variation with modifier content (Mg2+,Zn2+ for the TMN, TZN and TBN glasses.

4.3 Conclusion

Through the measurements of the Raman spectra and via comparison to the pub-

lished data on analogous crystalline phases of TeO2 and similar tellurite glasses

we have been able to determine the structural units that are present in the glasses under

study. The compositionally driven trends in the relative magnitudes of the Raman bands

will be used in later Chapters to aid in the identification of the physical mechanisms

leading to other material properties, such as the linear and nonlinear refractive indices.

The results obtained are consistent with similar studies reported in the literature and

indicate that, in general, the addition of a modifying specie will promote the conversion

of TeO4 subunits into TeO3 subunits via the intermediate TeO3+1 state. Additionally,

there is a decrease in the network connectivity associated with this process which is more

pronounced for modifiers with high coordination numbers and low electronegativities.

Chapter 5

Measurements of Physical and

Thermal Properties

5.1 Introduction

In this Chapter we present measurements of a number of the physical and thermal

properties of the glasses that are important for their application in determining the

suitability of glasses for use in nonlinear devices. The measured properties include:

� Density, Section 5.2

� Molecular mass, Section 5.2

� Molar volume, Section 5.2

� Glass transition temperature and enthalpy, Section 5.3.1

� Crystallisation temperature and enthalpy, Section 5.3.1

� Thermal expansion coefficient, Section 5.3.2

Each measurement is presented with an explanation of the relevant underlying physics

followed by a detailed description of the experimental technique. We conclude each

section by presenting the data followed by a discussion of the results and correlating the

trends in these properties to the structural changes occurring in the glasses (see Chapter

3) as the relative proportions of the components are varied.

5.2 Density, Molecular Mass and Molar Volume

The density of a glass is principally determined by the chemical constituents of the

glass and how they are arranged in space. As discussed in Section 3.2 the density

75

76 Measurement of Physical and Thermal Properties

of a glass can vary depending on the rate of cooling used to form the glass from the

melt. For this reason care was taken to anneal the samples as close to Tg as possible

and cool them slowly to maximise the density (see Section 3.6 and Figure 3.2).

Molar volume is defined as the volume occupied by one mole of a substance. Thus, in

order to calculate the molar volume one requires the molecular mass and the volume,

which can in turn be obtained from the density. As glasses can be considered to be solu-

tions, the molar volume is generally considered to be a more useful parameter than the

density because it provides less ambiguous structural information. We can demonstrate

the molar volume’s ability to reveal structural information with the following generalised

example. Consider the following situation: A particular glass has some proportion of a

monovalent modifier A+ in it. We then produce an identical glass, except, we substitute

a different monovalent modifier B+ that has, for example, a larger molecular mass than

A+. In this situation the B+ containing glass will have a higher density, however, if

there is no difference in the way B+ in incorporated into the glass matrix then there

will be no change in the molar volume.

This example clearly demonstrates the superiority of the molar volume over the density

as a measure of glass structure. In the following Sections the details of the measurements

and the interpretation of the data are discussed.


Densities of the glasses were measured by using the Archimedes method [50]. Shown

in Figure 5.1 is a schematic of the density measurement experiment. The force due to

gravity on the sample with mass ms when suspended in the air is expressed as

Fs = msg (5.1)

When the sample is immersed in the liquid it displaces a volume equal to its own. This

produces a buoyancy force Fb, in the opposite direction to gravity. The net force on the

immersed sample Fi is

Fi = Fs − Fb (5.2)

Therefore

Fb = Fs − Fi (5.3)

Taking the ratio of Fs/Fb givesFs

Fb=

Fs

Fs − Fi(5.4)

Chapter 5 77

Archimedes principle tells us that the displaced volume is equal to the volume of the

sample thus Equation 5.4 can be written as

ρsVs

ρlVs=

ρsρl

= Sρ =Fs

Fs − Fi(5.5)

Where we define Sρ to be the specific gravity. We now make the replacement of Fs →Wout and Fi →Win to denote the weight of the sample out of the liquid and in the liquid

respectively, finally yielding:

Sρ =Wout

Wout −Win(5.6)

The following is a description of the procedure for measuring the density.

� With reference to Figure 5.1 we measure the mass of the suspended sample which

has been cleaned thoroughly with an organic solvent so as to remove any dirt and

oils from previous handling. Let this mass be denoted mout.

Glass sample Reference liquid

Fg

Fg

Fb

Figure 5.1: Experimental configuration for Archimedes Density Measurement. Left:Sample is weighed suspended above a beaker the force of gravity Fg acts on the sampleand is recorded as a weight on a set of scales. Right: Sample is immersed in the waterwhere the buoyancy of the sample produces an opposing force, Fb, to Fg hence reducing

the measured weight.

� The sample is then immersed in a liquid with known density and temperature.

We take care to ensure that there is no air trapped under the sample as this will

reduce the measured density.

� The mass of the immersed sample is then measured. Let this mass be denoted

min.


� Using Equations 5.5 and 5.6 with the value for waters density ρwater = 1.00 g.cm−1

(at 25 ◦C) we obtain the density of the sample.

� We repeat this process several times and take the mean value obtained for the

density. In this way we minimise the errors such as fluctuations in the measured

submerged weight, which are primarily due to vibrations of the equipment.

It should be noted that we made no corrections for the fact that the density of water

changes with temperature. All measurements were preformed at temperatures conser-

vatively estimated to be between 20◦C and 30◦. Base on literature reported values of

the density of pure water we calculate the error associated with this procedure is in the

order of 0.26% [51].


The results of the density measurements are tabulated in Table 5.1 and plotted against

modifier content in Figure 5.2. The measurement error, determined from the standard

error accumulated over five measurements per sample, is found to be no larger than the

error associated with not correcting for the temperature dependence of the density of

water, i.e. ≈ ± 0.006 g.cm−3.

Molar Mass Density Molar VolumeSample [g.mole−1] [g.cm−3] [cm3.mole−1]

TMN1 143.87 5.18 27.77TMN2 137.91 5.06 27.25TMN3 131.94 4.95 26.66

TZN1 145.93 5.23 27.90TZN2 142.02 5.18 27.42TZN3 138.11 5.15 26.82TZN4 134.20 5.13 26.15

TBN1 149.52 5.22 28.64TBN2 149.21 5.25 28.42

Table 5.1: Calculated molecular masses, Densities measured via the Archimedesmethod in pure water. Maximum measurement error of ± 0.006 g.cm−3. Molar volumes

calculated from measured densities with a maximum error of ± 0.01 cm3.mole−1.

We can calculate the molar mass of the glass from the following equation:

Mmglass =

N∑i=1

niMmi (5.7)

Chapter 5 79

5 10 15 204.9

5.0

5.1

5.2

5.3

TMN1

TMN2

TMN3

TZN1

TZN2

TZN3TZN4

TBN1

TBN2

Den

sity

[g.c

m-3

]


Figure 5.2: Densities of the TMN, TZN and TBN glass series plotted against modifiercontent.

Where ni is the molar fraction of the ith component so that

N∑i=1

ni = 1

and Mmi is the molar mass of the ith component. The molar volume is then calculated

from the density, ρ, and molar mass of the glass via:

VM =Mmglass

ρ. (5.8)

The volume occupied by one of the components of the glass is called the partial molar

volume. The partial molar volume of the ith component Vi is defined as:

Vi =

(∂VM

∂ni

)(5.9)

We have tabulated the molar masses for each glass and the corresponding molar volumes

in Table 5.1. Figures 5.3 and 5.4, respectively, are plots of the dependence of molar mass

and molar volume on the modifier content for each glass family.

In Figure 5.2 we see a clear, decreasing trend for the TZN and TMN series with increasing

modifier content. The TBN series displays an increase in density with increasing modifier

content. These results can be interpreted in the following way: As we increase the


5 10 15 20125

130

135

140

145

150

155

TMN1

TMN2

TMN3

TZN1

TZN2

TZN3

TZN4

TBN1 TBN2

Mol

ecul

ar M

ass [

g.m

ol-3

]


Figure 5.3: Calculated molar masses (Equation 5.7) for TMN, TZN and TBN glassseries plotted against modifier content.

5 10 15 2026.0

26.5

27.0

27.5

28.0

28.5

29.0

TMN1

TMN2

TMN3

TZN1

TZN2

TZN3

TZN4

TBN1TBN2

Mol

ar V

olim

e [c

m3 .m

ol-1

]


Figure 5.4: Calculated molar volumes (Equation 5.8) of TMN, TZN and TBN glassseries plotted against modifier content.

Chapter 5 81

modifier content, we are in turn decreasing the Te content. The masses for the various

elements are ordered as: Mg<Zn<Te<Ba. Therefore if we ignore volume changes due

to structural rearrangements and consider only the masses of the components, we can

see that substitution of Te with Mg, for example, will decrease the mass per unit volume

of the system and therefore decrease the density. Alternatively, when Te is substituted

by Ba the converse is true.

The variation of molar volume with modifier content is essentially linear for all considered

modifying species. Accordingly, it is straightforward to estimate and compare the partial

molar volumes simply as the gradients of the interpolated lines in Figure 5.4. In doing so

we see that the TMN and TZN series have very similar slopes and thus Mn2+ and Zn2+

must be incorporating them selves into the matrix in approximately the same manner.

On the other hand, the TBN series has a smaller gradient which leads us to conclude

that Ba2+ is producing a more tightly packed matrix. We see support for this in the

Raman spectroscopy data for the TBN glasses (Section 4.2.4) where the trend in the

Raman B peak suggests an increase in the network connectivity for increasing amounts

of barium.

5.3 Thermal Properties

Our overall aim is produce glasses which could be used for fabricating optical fibres.

We therefore require glasses with excellent thermal stability (Section 3.5). We

have determined the thermal stability for each of the glass compositions via two methods.

Firstly by observation; when we attempt to form a glass from the melt we can determine

qualitatively whether or not the composition has a good glass forming stability simply

by noting if it forms a glass. Secondly, and more quantitatively, we can measure the

temperatures at which the glass undergoes phase transitions and use this data as a

measure of glass forming stability.

5.3.1 Differential Scanning Calorimetry

Differential Scanning Calorimetry or DSC, is a measurement technique that provides us

with the necessary phase information in order to determine the glass forming stability.

Figure 5.5 is a schematic illustration of a DSC, showing all of the essential elements of

such a device.

The basic operating principle is the following: The sample under study is heated in

a sample pan simultaneously with a reference sample (empty sample pan) inside of a


Figure 5.5: Schematic representation of a DSC apparatus. The temperature of sampleand reference pans are increased at a constant rate. The control PC adjusts the heat

flow into the pans in order to achieve this.

thermally insulated container. The rate of temperature increase is kept constant for

both sample and reference by a computer controller. In order to achieve this, during

phase transitions of the sample, either more or less heat (depending on the nature of

the transition, i.e. whether it is exothermic of endothermic) will need to be put into

the sample. Thus a plot of heat flow against temperature (Figure 5.6) will reveal these

phase transitions and the temperatures at which they occur.

With reference to Figure 5.6, the important features of the graph are the:

Beginning at the left of Figure 5.6 there is a horizontal line of heat flow q W.s−1,

vs. temperature T . From this section of the data the heat capacity of the glass

can be determined by:

Cp =q/t

ΔT/t=

q

ΔT(5.10)

where ΔT/t ◦C.s−1 is the heating rate.

The next feature of interest is the glass relaxation peak otherwise known at the

glass transition temperature. We adopt the conventional definition of the onset

temperature Tg, of the glass relaxation as the intersection of the tangents to the

region of constant heat flow prior to relaxation and the region of constant rate of

change of heat flow during the relaxation. These tangents are shown in Figure 5.6.

Chapter 5 83

The glass relaxation temperature1 represents the temperature at which the atoms

and structural sub units become mobile and thus the glass takes on the nature of

an extremely viscous liquid.

� The glass relaxation peak has also associated with it an enthalpy of relaxation

ΔHg. This corresponds to the amount of energy absorbed during the transition

from glass to super cooled liquid. ΔHg is proportional to the area under the glass

relaxation peak and normalised to the sample mass to obtain units of J.g−1.

� Following the relaxation peak there is another region of approximately constant

heat flow vs. temperature. This region can be used to determine the heat capacity

of the glass in the super cooled liquid state using Equation 5.10. The heat capacity

in this region is always greater than the heat capacity in the solid region.

� The crystallisation peak has an onset temperature Tx, which is defined as the

intersection of the two tangents, indicated in Figure 5.6. In addition to the onset

temperature we also define the peak crystallisation temperature Tc.

� The enthalpy of crystallisation ΔHc is determined via integration of the crystalli-

sation peak and represents the amount of energy released during crystallisation.

Figure 5.6: Example of DSC trace, red line, (sample TZN1) with key temperature fea-tures indicated. The determination of enthalpies requires the introduction of baselines

(black) to bound the peaks for integration.

1In fact, this transition occurs over a range of temperatures due to the amorphous nature of the glass.Despite this, the convention is to specify one temperature which indicates an onset of this transition.


5.3.1.1 Experimental Details

The particular DSC instrument used was a TA Instruments DSC 29202. Calibration of

the device was performed using the following procedure:

1. We used gold sample pans and an air environment. Our reasoning is that these

conditions match exactly the melting conditions we used for producing the glass

(Section 3.6).

2. A baseline is obtained by heating two empty sample pans over a temperature range

of 100 ◦C to 550 ◦C with an isochronal heating rate of 10 ◦C.min−1.

3. The DSC’s cell constant was calibrated by recording a DSC trace for zinc which

displays a sharp, well defined melting peak at 419.53 ◦C. We chose zinc as a

calibration standard because its melting point falls within our desired measurement

range.

4. Next we calibrated for the absolute temperature scale by performing a DSC mea-

surement of the melting temperature of tin, which melts at 231.93 ◦C.

We then performed DSC on all tellurite glass samples the results of which are listed in

Table 5.2. The temperature range for the measurements was 250 ◦C to 500 ◦C with an

isochronal heating rate of 10 ◦C.min−1. This heating rate is commonly used for DSC

studies of glasses [52].

Initially, we used ≈ 20 mg samples which were ground to a fine powder in an agar

mortar and pestle. This produced DSC traces with very noisy crystallisation peaks. We

interpreted this to be due to individual particles of glass crystallising, but due to their

small size the crystal growth halts quickly. We then turned to using single ≈ 20 mg

chips of glass produced by smashing the edges off of large glass samples with a mortar

and pestle. We collected the fragments which had approximately the right mass for

use in the DSC. The DSC traces acquired in this way did not present the same noise

in the crystallisation peaks as once the crystal growth has been seeded it can progress

unencumbered through out the entire sample. The DSC traces are shown in Figure 5.7.

5.3.1.2 Results and Discussion

Figure 5.7 shows the DSC traces for all glass samples and the temperatures and en-

thalpies measured are listed in Table 5.2. It is interesting to note that the position of

2Kindly provided for our use by Milena Ginic-Markovic and Rachel Pillar at Flinders University

Chapter 5 85

Tg does not change significantly for increasing modifier content in the TZN and TBN

series, however, for the TMN series there is a near linear increase in Tg with increasing

Mg content of ≈ 2.2 ◦C.mol−1. With the exception of TZN3, all of the crystallisation

peaks were easily determined.

Figure 5.7: DSC traces for TMN (magenta), TZN (red) and TBN (blue) glass series.The vertical scale is in W.g−1 with an arbitrary vertical offset introduced to separate

the traces. The trends in Tg have been indicated by the dashed lines.

For all glass series, the amount of modifier has a significant effect on the position and

enthalpy of crystallisation which has ramifications for the glass forming stability [53].

We can estimate the glass crystallisation stability via [18]:

ΔT = Tg − Tx. (5.11)

Where values of ΔT > 100 ◦C are generally considered to represent glasses with high

crystallisation stability [53]. Glasses with ΔT > 100 ◦C will require a reasonably large

amount of heat energy to activate the crystallisation processes (i.e. � 150 J.g−1 [18]) and

are therefore considered stable. A ΔT ≈ 100 ◦C also provides us with a large working


range for processes such as optical fibre preform extrusion, where we are required to

heat the glass beyond Tg and force it through a die (see Section 9.4). Glasses with

a ΔT > 100 ◦C can comfortably be heated above Tg and softened without inducing

crystallisation. Note in Table 5.2 that all glasses under study have ΔT > 100 ◦C which

is to be expected as we selected these glasses from the investigated compositions for

their ability to be produced in large volumes (Section 3.7).

Tg Tx Tc ΔT ΔHg ΔHc

Sample [◦C] [◦C] [◦C] [◦C] [J.g−1] [J.g−1]

TMN1 295 436 446 141 7.49 73.7TMN2 307 435 497 128 8.24 69.6TMN3 317 453 478 136 6.72 105

TZN1 291 405 423 114 7.63 37.0TZN2 292 421 455 129 7.49 25.2TZN3 293 464 484 171 8.44 ≈1.2TZN4 293 465 482 172 8.60 17.6

TBN1 287 454 475 167 3.72 15.8TBN2 288 410 436 122 5.78 17.2

Table 5.2: Thermal data for TMN, TZN and TBN glass series. Temperatures areaccurate to ±2 ◦C and enthalpies are accurate to approximately 1%.

5 10 15 20100

110

120

130

140

150

160

170

180

TMN1

TMN2

TMN3

TZN1

TZN2

TZN3 TZN4

TBN1

TBN2

ΔT [o C

]


Figure 5.8: Plotted values of ΔT=Tg−Tx for TMN, TZN and TBN glass series. Thisis a measure of crystallisation stability where ΔT > 100 indicates a stable glass.

Chapter 5 87

5 10 15 200

20

40

60

80

100

120

TMN1TMN2

TMN3

TZN1

TZN2

TZN3

TZN4

TBN1 TBN2

ΔHc [J

.g-1

]


Figure 5.9: Plot of enthalpy of crystallisation ΔHc for TMN, TZN and TBN glassseries.

Our criterion for a stable glass is ΔT > 100◦C. Both TZN3 and TZN4 have the largest

value for ΔT and therefore represents the most stable glasses. However, during the glass

production stage it was noted that the 42 cm3 TZN4 billet showed a small amount of

crystallisation. We believe this to be an issue of reaching the solubility limit of ZnO

in TeO2 and not glass forming stability. The ΔT > 100◦C criterion has its limitations

and, in fact, is much more related to the workability of the glass at temperatures above

Tg and less so to the formation of the glass from the melt. There is another parameter

suggested by Hruby and Stourac [52], the so called Hruby parameter, which is calculated

as

Kg =Tc − Tg

Tm − Tc(5.12)

where Tm is the melting temperature. The only sample for which melting was observed

was TMN1, where a distinct endothermic peak was observed at ≈ 480◦C (see Figure

5.7).

Tellurite glasses have been shown to obey the classical two-third rule which is an empir-

ical relationship between the transition temperature and the melting temperature, i.e.

Tg/Tm = 2/3 (in absolute temperature units) [54]. Using the two-third rule we esti-

mate the melting temperatures of the glasses to be in the range 570◦C→610◦C which is


outside of the range of the DSC that was used and therefore helps to explain why they

were not observed, except in the case of TMN1. The TMN1 glass only weekly obeys the

two-third rule, as the ratio of Tg to Tm is 0.75.

Some authors use the two-thirds rule to calculate the melting temperature from incom-

plete DSC data and then use this value to calculate the Hruby parameter. This is a

reasonable method provided the glass is known to obey the two-third rule, however,

based on TMN1 not showing close agreement with the rule we do not adopt this prac-

tise and instead simply use the crystallisation stability criterion expressed by Equation

5.11.

In addition to the temperature data obtained from the DSC, the crystallisation enthalpy

can also be used as a measure of crystallisation stability [55]. At every temperature,

the glass attempts to minimise its internal energy through the motion of its atomic con-

stituents. A low crystallisation enthalpy implies that the glass is, structurally speaking,

already in a reasonably stable state. Thus a low value for crystallisation enthalpy im-

plies a stable glassy state and therefore that particular glass will have a low tendency

to crystallise.

Based on this criterion for crystallisation stability we can see in Figure 5.9 that TZN3 has

the lowest enthalpy of crystallisation and therefore the highest crystallisation stability.

5.3.2 Measurement of the Thermal Expansion Coefficient

Of particular importance for the fabrication of core/clad optical fibres is good knowledge

of the thermal expansion coefficients for the core and cladding materials. To achieve the

refractive index contrast for optical guidance we must necessarily use different materials

for the core and the cladding. There will inevitably be a difference between the thermal

expansion coefficients for two materials which will result in axial mechanical stresses

being produced when the fibre is drawn [56]. The stress in the fibre will effect both

its optical and mechanical properties, often detrimentally. In particular, if the internal

stresses are comparable to the failure strength of the material, which is approximately

equal to the Young’s modulus of the material (50 to 70 GPa for glass) the manufacture

of a mechanically stable fibre is not possible.

It is possible to calculate the axial stress σ, via [57]:

σ =(α1 − α2)(T − Tg1)E

(R/r)2(1− μ)+

(α∗1 − α2)(Tg2 − Tg1)

(1− (R/r)2)/3K∗1 − 1/3K2

. (5.13)

The first term in Equation 5.13 applies to the situation where the core and cladding

are both solid. The subscripts 1 and 2 represent the core and cladding respectively

Chapter 5 89

and α is the coefficient of thermal expansion, T is the room temperature, Tg the glass

transition temperature, E is Young’s modulus, R the radius of the cladding, r the core

radius, μ is Poisson’s ratio. The second term provides the hydrostatic stress i.e. when

the core is liquid and the cladding solid. In this term a superscript of ∗ denotes values

of parameters just above the transition temperature and K is the bulk modulus.

It is clear that to minimise σ we should find materials with α1 ≈ α2 and Tg2 ≈ Tg1. We

note that the TZN glasses satisfy this second condition (refer to Section 5.3.1.2). Further,

it has been noted in the literature that acceptable Δα = α1 − α2 is approximately

50× 10−7 ◦C−1 [58].

We have measured the thermal expansion coefficients for all of the glasses under study

so that, through careful choice of composition, we can minimise the stress in an optical

fibre produced from them.

The thermal expansion of a material is simply a change in length for a given change in

temperature. For most materials this relationship is linear in the region of interest and

can be expressed as

l2 = l1(1 + αT ) (5.14)

where l2 is the length at temperature T ◦C, l1 is the length at 0◦C and α is the ther-

mal expansion coefficient. Thus to measure the thermal expansion coefficient we simply

measure the length of the sample over a range of temperatures and use the linear rela-

tionship to find α. Note that the amount by which the material increases in length is

in direct proportion to the value l1. Accordingly, the changes become easier to measure

the larger the sample.

The key material property that determines the thermal expansion coefficient is bond

strength. That is, as we put energy in the form of heat into the material the oscillation

amplitude of the atoms increases. This has the effect of increasing the mean separation

of the atoms and therefore the size of the material. A bond with a high strength requires

more energy to produce an equivalent oscillation amplitude than does a weak bond.

It is therefore reasonable to assume that compositional trends in the thermal expansion

coefficient will be explainable in terms of the reported compositionally driven structural

changes (see Section 4.2.4).

In the following sections we describe a simple experimental technique for determining

the thermal expansion coefficients and present the data for the glasses under study.

Attempts to correlate the observed trends in the thermal expansion coefficients with the

structural information presented in Chapter 3 are made


5.3.2.1 Experimental Details

In general tellurite glass has a large thermal expansion coefficient, typically of the order

10−5 ◦C−1 [18]. Compare this with silica which is 5.5×10−7 ◦C−1. It is therefore possibleto measure the expansion of a relatively small sample of telluite which, conveniently,

corresponds to the size of the spectroscopic samples described in Section 6.2.1. These

samples measure about 15 mm across their longest dimension, which is a distance that

can be determined mechanically using a micrometer.

The measurement apparatus consisted of the following (see Figure 5.10): A hot plate

with a controllable temperature range of ambient→300◦C had mounted on it a specifi-

cally designed metal sample holder with a clamp both machined from aluminium. The

sample holder was designed to maximise the thermal contact between it and the glass,

leaving ≈ 0.2 mm of over hanging sample with which to contact the micrometer to in

order to make a measurement of the sample length3.

Figure 5.10: Schematic of apparatus for thermal expansion coefficient measurement.The glass sample is held in an aluminium clamp to ensure even heating. Measurement

of the sample length is made as shown.

5.3.2.2 Results and Discussion

To establish the accuracy of the measurements we used a sample of commercial glass

with a thermal expansion coefficient of similar size to that expected for tellurite. We

chose a chalcogenide glass produced by Schott Glass Co. known as IG5 with a reported

thermal expansion coefficient of α = 14× 10−6 ◦C−1 [59].

3All measurements were performed by an undergraduate student, Matthew Mielczarek, who wasunder my supervision

Chapter 5 91

We recorded the length of the sample for temperatures between ambient and ≈ 180◦C.

Equation 5.14 can be rearranged to give

l2 − L1

l1= αT (5.15)

The acquired data is plotted as l2−L1l1

vs T in Figure 5.11 along with a linear fit. The

slope of the linear fit is equal to α as per Equation 5.15. Via this analysis we obtain

a value for α = 14 ± 0.12 × 10−6 ◦C−1, in good agreement with the reported value.

From this test we can conclude that this technique for measuring the thermal expansion

coefficient is accurate to about 1%.

25 50 75 100 125 150

0.0000

0.0005

0.0010

0.0015

0.0020

(l 2-l 1)/l1

Temperature [oC]

Figure 5.11: Plot of l2−L1

l1vs T for IG5. The slope of line of best fit equal to α.

Using the same technique, we measured the thermal expansion of the TMN, TZN and

TBN. Figures 5.12, 5.13 and 5.14 show the data plotted as l2−L1l1

vs T . From the slopes

of the lines of best fit we obtain the thermal expansion coefficients for each glass, the

results of which are tabulated in Table 5.3 and plotted in Figure 5.15.

It can be seen in Figure 5.15 that the addition of Zn to the TZN glasses causes the

value of the thermal expansion coefficient to decrease. Conversely, the addition of Mg

and Ba into the TMN and TBN glasses, produces an increase of the thermal expansion

coefficient.


0 50 100 150 200 250

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030 TMN1 TMN2 TMN3

(l 2-l 1)/l1

Temperature [oC]


l1vs T for the TMN glass series. The slopes of the lines of

best fit are equal to α for each glass.

0 50 100 150 200 250

0.000

0.001

0.002

0.003

0.004 TZN1 TZN2 TZN3 TZN4

(l 2-l 1)/l1

Temperature [oC]


l1vs T for the TZN glass series. The slopes of the lines of


Chapter 5 93

0 50 100 150 200 250-0.0002

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0.0018

TBN1 TBN2

(l 2-l 1)/l1

Temperature [oC]


l1vs T for the TBN glass series. The slopes of the lines of


αSample [10−6 ◦C]

TMN1 7.57TMN2 1.98TMN3 1.88

TZN1 19.8TZN2 19.8TZN3 18.8TZN4 17.4

TBN1 3.21TBN2 8.79

IG5 14.1

Table 5.3: Measured values of the thermal expansion coefficient for TMN, TZN andTBN glass series. Accuracy of measurements ≈ 1% determined from a reference stan-

dard chalcogenide glass (IG5 Schott).

To understand the trends observed in Figure 5.15, we consider the electronegativities of

the modifying cations, which are listed in Table 3.2. The relative electronegativities of

elements determines the strength of the chemical bonds between them. As such, when

discussing a substitution of one element for another in a glass matrix the electronega-

tivities of the elements being exchanged are directly related to the bond strengths. Of

the modifying species barium has the lowest electronegativity and thus the highest bond


5 10 15 200

5

10

15

20

αx10

-6 [o C

-1]


Figure 5.15: Thermal expansion coefficients α, for TMN, TZN and TBN glass series.

strength. Magnesium has the next lowest electronegativity and then zinc. Accordingly

the values for the thermal expansion coefficient for the TBN glasses are the lowest.

Followed closely by the TMN series and then the TZN series.

Within the individual glass series the trends are explained in terms of the conversion

of TeO3 →TeO3+1 →TeO3. With reference to Figure 3.4 we can see that during this

conversion the equatorial bond lengths are decreasing from 0.19 nm to 0.185 nm. Mean-

while one of the axial bonds has its length increased from 0.21 nm to 0.24 nm. Now,

the shortening of a bond is associated with an increase in bond strength and vice versa.

From the Raman spectroscopy data presented in Chapter 3, and in particular Figures

4.17 and 4.19 it can been seen that, for the TMN and TBN glass series, there is a rapid

conversion of TeO4 to TeO3 with increasing modifier content as indicated by the slopes

of the graphs. This conversion is associated with the intermediate TeO3+1 state which

possesses a elongated axial bond and further, because the elongation of this bond is sig-

nificant with respect to the shortening of the equatorial bond lengths (i.e. 10× greater),

the increase in thermal expansion coefficient can be understood in terms of the decrease

in bond energy associated with the creation of TeO3+1 subunits.

Conversely, the TZN series displays a very low tendency for the conversion of TeO4 to

TeO3 (Figure 4.17) and so the change in thermal expansion coefficient across the series

Chapter 5 95

is small. Further, we are substituting the Te4+ ion with an electronegativity of 2.10

for Zn2+ ion which has an electronegativity of 1.65 (Table 3.2). This substitution has

the effect of increasing the average bond strength and therefore decreasing the thermal

expansion coefficient. The effect of substitution appears to not dominate for the TMN

and TBN glasses.

In terms of suitable materials for an optical fibre, it is generally recognised that for a

core/clad fibre if the thermal expansion coefficient cannot be matched exactly then the

next best scenario is for the core to have a slightly higher thermal expansion coefficient

that the cladding to ensure that the core is under compression [60]. Additionally, the

Δα should be no greater than 50× 10−7 ◦C−1 [58].

If we consider the data in Figure 5.15 we can see that the TZN series for Zn content

greater than approximately 10 mol.% satisfies this first criterion. Furthermore, the total

variation of α over the entire composition range is ≈ 25×10−7 ◦C−1, thus satisfying the

second criterion. Later, in Chapter 7, we will revisit this data in terms of designing a

core clad fibre.

5.4 Conclusion

Wemeasured the densities of the glasses, from which molar volumes were calculated.

The compositional dependence of the molar volumes are indicative of how the

modifying ions are incorporated into the glass network. Zinc and magnesium display

similar rates of change in molar volumes with modifier concentration (i.e. partial molar

volumes). This we attribute to the similarity of the coordination numbers for the Zn2+

and Mg2+ ions ( coordination number of 6, see Table 3.2). Barium, on the other hand

possesses a larger coordination number and therefore perturbs the glass network to a

higher degree. This is observed as a larger partial molar volume.

We have determined the thermal properties of the tellurite glasses including the transi-

tion and crystallisation temperatures and enthalpies (Table 5.2) as well as the coefficient

of thermal expansion (Table 5.3). Using the criterion for crystallisation stability we have

determined the most stable compositions within each family and overall. The most sta-

ble compositions are listed below:

� TMN1: Within the TMN series TMN1 has the highest ΔT and very close to the

lowest ΔHc (Table 5.2). Thus making it the most stable TMN composition.


� TZN3: The TZN series is in general a much more stable series than the TMN

series. The optimal composition is TZN3 which one of the highest ΔT values and

by far the lowest ΔHc (Table 5.2).

� TBN1: For both TBN compositions the ΔHc varies very little. However, TBN1

has the highest ΔT and therefore represents the most stable glass in this series

(Table 5.2).

In addition to the thermal stability of the glasses studied we measured the thermal

expansion coefficients (Table 5.2). We find that the size of the thermal expansion coeffi-

cient is determined by composition as well as the microscopic structure of the glass. For

glasses with a strong tendency to convert into a matrix of TeO3 subunits, with the addi-

tion of modifier, the changes in the thermal expansion coefficient are largely determined

by the elongation of the axial Te-O bond typified by the intermediate TeO3+1 state.

Glasses that display a low tendency for this conversion, such as the TZN glasses, have

thermal expansion coefficients that appear to be determined by the electronegativities

of the components.

Of all the studied glass compositions TZN3 has the highest crystallisation stability.

Additionally, the TZN glass series displays the lowest variation of α. We therefore

conclude that glasses in the compositional vicinity of TZN3, that is glasses with zinc

concentrations around 15 ± 2 mol.%, are ideal for fabricating core/clad optical fibres.

This is further evidenced by the fact that other researchers have also chosen this glass

from which to make optical fibres [61, 62]. As such much of the subsequent work on

thermal poling (Chapter 7) and optical fibre design and fabrication (Chapter 9) will

focus on this composition range.

Chapter 6

Measurements of the Optical

Properties

6.1 Introduction

It is essential to measure the optical properties of the tellurite glasses so that an

optimal choice for a particular nonlinear optical device can be made. Furthermore,

it is also desirable to build an understanding of the physics determining these properties

so that, through control of the composition of the glasses, the optical properties can be

optimised.

The following sections describe the various characterisation techniques that were used

to analyse the glass samples. They include:

� Ultra violet and visible light spectroscopy, Section 6.2.

� Infrared spectroscopy, Section 6.3.

� Refractive index measurement, Section 6.4.

� Nonlinear refractive index and third order susceptibility, Section 6.5.

We begin each section by describing the information we intend to obtain from the mea-

surements and how that information fits into the context of this thesis. Next, the physics

required to understand and interpret the measurement are discussed. Once we are armed

with the requisite understanding the specific experimental details are outlined along with

the data analysis techniques employed. Finally, we present the data accompanied by a

detailed discussion of the results, including correlations between the measured properties

and the composition and structure of the glasses.

97

98 Measurements of the Optical Properties

6.2 UV-VIS Absorption Spectra

From the measurement of a materials absorption spectra in the ultra violet and visible

regions of the spectrum we can determine several things about that material. Most

fundamentally, we determine the wavelengths over which the material is transparent.

This is an obvious necessity for determining the suitability of a material for an optical

device. At the short wavelength end of the transmission window of the glass is the UV

edge or band edge. This feature of the transmission spectrum originates from electronic

transitions in the material, which are determined by the constituents of the material and

their spatial arrangement. Thus certain correlations can be made between the structure

of the glass and the position of the band edge, in particular, how the position of the

edge depends on the proportions of the elements in the glass.

Glasses fall into the family of materials known as dielectrics. Typical to dielectric ma-

terials is the existence of forbidden electron energies which result in the well known

electronic band structure of these materials. The phenomenon of the band structure

of crystalline dielectrics is well understood in terms of resonant scattering of electrons

from the periodic potential presented by the regular arrangement of nuclei in the crys-

tal, so called Bragg scattering. The consequence of this is that photons with energies

which correspond to energies less than the band gap cannot be absorbed by electrons

in the material and thus the material is said to be transparent in that range of photon

wavelengths.

As for amorphous materials, such as glass, the regular ordering of the atoms is not

present and the band theory based on periodic potentials breaks down. Despite the

lack of ordering glasses do possess electronic bands. These are much more complicated

than those exhibited by crystalline systems. Indeed, it is common instead to explain the

optical absorption of glasses in terms of molecular orbital theory [41]. In this picture the

electronic structure of the structural subunits present in the glass determine the band

gap. The presences of modifying ions and polymerised chains of these subunits serve

to perturb the energies hence leading to a shift of the band edge [63]. For example; ab

initio calculations of the molecular orbitals of the subunits found in tellurite glass have

determined the energy gaps between highest occupied molecular orbital (HOMO) and

the lowest unoccupied molecular orbital (LUMO) to be 4.4 eV for the TeO4 subunit

and 5.5 eV for the TeO3 [42]. Indicating that pure tellurite glass should have an optical

absorption edge in the vicinity of 280 nm. In reality, pure tellurite glass has its absorption

edge at ≈ 330 nm and other multi-component tellurite glasses have absorption edges in

the range of to 350 - 600 nm because of distortions of the subunits and the influence of

modifying species and polymerised chains of subunits on the electronic structure of the

structural subunits [18, 63].

Chapter 6 99


We prepared the spectroscopic samples by cutting 10×10×2 mm thick slices from the

4 cm3 blocks. Then they were ground and polished to optical quality. Absorption spectra

were recorded with a Cary UV-Vis-NIR spectrophotometer1 between 200−3300 nm with

a 1 nm resolution.


The acquired data is in the form of absorbance A, which is defined in terms of the input

and output intensities, I0 and I, as:

A = − log

(I

I0

). (6.1)

We can combine this with the Beer-Lambert law for optical absorption over a distance

z in a material,

I = I0e−αz (6.2)

to obtain the absorption coefficient α, by2

A = − log(e−αz

)=

1

ln(10)αz.

Therefore,

α(ω) = A(ω)ln(10)

z(6.3)

where z is the sample thickness (in cm) and we have made the frequency dependence of

the optical density and optical absorption coefficient explicit. The absorption coefficient

consequently has units of cm−1.

Losses due to Fresnel reflection and scattering from surface imperfections are removed

by subtracting the minimum absorption value from the entire spectrum. In doing so

we are assuming that at some wavelength there is zero loss. This assumption is not

strictly correct, however, it does provide a means of eliminating the effects of reflection

and surface scatter to allow relative comparisons between the samples. To perform this

analysis without this assumption would require the measurement of the refractive indices

of each glass at every wavelength within the spectral region of interest, or at least enough

1Kindly provided by the Defence Science Technology Organisation (DSTO), Edinburgh, SA2Using the relation loga N =

logb Nlogb a


wavelengths such that an interpolating function (e.g. Cauchy or Sellmeire equation [64])

could be fitted to the data . Both of these options are outside of our present capabilities.

In Chapter 9 measurement of the attenuation in an optical fibre made from TZN glass

with the composition 10Na2O.12ZnO.73TeO2 is presented (Figure 9.27). The attenua-

tion measured at 1550 nm is 2.8±0.09 dB.m−1 or 6.4±0.2× 10−3cm−1. Assuming that

the absorption of the glasses under study are roughly equal in their transparency regions,

the absolute value of the absorption is, in principle, in error of at least this magnitude.

All glass samples showed excellent transmission from �370 nm, below which there is

strong optical absorption due to electronic transitions, and �2800 nm whereupon ab-

sorption due to the presence of water begins to dominate.

We have analysed the band edge using the theory of Davis and Mott [65] to obtain

values for the optical energy gaps. Davis and Mott found empirically that Equation 6.4

provides an accurate representation for the shape of the band edge [65].

α(ω) = A(�ω − Eopt)

r

�ω. (6.4)

Here α(ω) is the frequency dependent optical absorption coefficient, A is a fitting con-

stant, � is the reduced Plank constant, Eopt is the optical energy gap and r is an

empirically derived index which can take the values of 2, 3, 1/2 and 3/2 depending on

the nature of the electronic transition. It has been established [66–70] that for glass

and amorphous materials in general, r = 2 best represents the experimental data, this

further implies that the band edge is dominated by indirect transitions. We illustrate

this situation with the hypothetical band map, Figure 6.1, which shows how an indirect

transition Eind, can have a lower energy than a direct transition Edir. For the direct

transition, electrons in the valence band acquire energy from an incoming photon with

energy Edir, and move into the conduction band (blue arrow). The indirect transition

involves a valence electron acquiring energy from an incoming photon Eind (red arrow)

and momentum from a phonon (yellow arrow). The net result is that the valence elec-

trons are elevated into the conduction band and therefore radiation with energy equal to

Eind is absorbed. In this scheme Eind <Edir and therefore Eind marks the fundamental

absorption edge of the material .

Using r = 2 in Equation 6.4 we can obtain the following relation:

(α�ω)1/2 =√A(�ω − Eopt). (6.5)

Chapter 6 101

Figure 6.1: Proposed energy band diagram for tellurite glass (Electron energy (E)vs. wavevector (k)). For the direct transition, electrons in the valence band acquireenergy from an incoming photon with energy Edir, and move into the conduction band(blue arrow). The indirect transition involves a valence electron acquiring energy froman incoming photon Eind (red arrow) and momentum from a phonon (yellow arrow).

As implied by Equation 6.5, a plot of (α�ω)1/2 vs. �ω will produce a straight line in the

vicinity of the band edge. Furthermore, the x−intercept of this line will be the value of

Eopt.

Figure 6.2 shows the absorption spectra for the TZN series plotted as (α�ω)1/2 vs. �ω.

One can clearly see the linear regions in the high photon energy region of the figure. We

have fitted straight lines to the data for all glass series in this region and obtained the

values for Eopt which are tabulated in Table 6.1 and plotted against modifier content in

Figure 6.3. The data were analysed to determine if the indirect gap is in fact dominant.

By setting r = 1/2 and following an analogous procedure we determined that all of the

direct transitions occurred at photon energies approximately 0.15 eV higher than the

indirect transitions. Thus confirming that the indirect transition determine the band

edge for these glasses.

It can be seen in Figure 6.3 that the band edge moves towards shorter wavelengths (blue

shifted) for increasing Zn2+ and Mg2+ content and shifts towards longer wavelengths

(red shifted) for increasing Ba2+ content. The trends observed for the TZN and TBN

glasses are consistent with results for similar tellurite glasses reported in the literature

[71, 72].


Figure 6.2: (α�ω)−1/2 as a function of photon energy for the TZN series. The inter-section of the linear fits with the horizontal axis provide the band gap energies, Eopt

(see Equation 6.5.

5 10 15 203.250

3.275

3.300

3.325

3.350

3.375

3.400

TMN1

TMN2

TMN3

TZN1

TZN2

TZN3

TZN4

TBN1

TBN2

E opt [e

V]


Figure 6.3: Compositional dependence of indirect band gap for TMN, TZN and TBNglass series.

Chapter 6 103

Eopt λcutoff

Sample [eV] [nm]

TMN1 3.310 375TMN2 3.335 372TMN3 3.376 368

TZN1 3.267 380TZN2 3.293 377TZN3 3.332 373TZN4 3.359 370

TBN1 3.299 376TBN2 3.253 382

Table 6.1: Optical energy gaps calculated from UV-Vis spectra, maximum error of±0.005 eV, and corresponding wavelength cut off for optical transmission ±1 nm.

It is generally noted in the literature that tellurite glasses experience a blue shift of

the band edge for decreasing amounts of TeO2 [18]. As exemplified by the TZN and

TMN glasses. One possible explanation for this is the conversion of TeO4 → TeO3 as

the modifier concentration is increased. As previously mentioned, the energy gaps for

the individual TeO4 and TeO3 subunits have been calculated to be 4.4 eV and 5.5 eV

respectively [42]. These energy gaps corresponds to wavelengths of 283 nm and 226 nm

and so as the relative proportions of TeO4 and TeO3 shift to favour the TeO3 species

the band edge should shift to shorter wavelengths.

In specific cases, such as with the TBN glasses, additional mechanisms take precedence.

We hypothesise that the disordering of the glass network structure induced by Ba2+ has

produced defect states in the band gap thus decreasing the energy required to bridge

this gap. We can see from Figure 4.11 that the TBN glasses posses the least network

connectivity and so there is tentative evidence that disordering of the network structure

could be producing the observed narrowing of the band gap.

Additional analysis of the band edge trends will be made in Section 6.4, where compar-

isons with compositional trends in the refractive index can be analysed.

6.3 Fourier Transform Infrared Absorption Spectroscopy

Fourier Transform Infrared (FTIR) Absorption Spectroscopy is a complementary

spectroscopic technique to Raman spectroscopy. Both techniques probe the low

frequency vibrations of a solid, however, in contrast to Raman, the interaction of the

light with the material is elastic. Pure TeO2 crystalline Tellurite is known to have


characteristic IR absorption bands at 780 cm−1, 714 cm−1, 675 cm−1 and 635 cm−1

[73].

Furthermore, there are some reported IR spectra for various crystalline binary tellurite

oxides which include MgTe2O5, ZnTeO3, Zn2Te3O8 and BaTeO3. These crystalline

compounds have IR spectral features that fall in the range 620 cm−1 → 790 cm−1

[73]. Based on the crystalline vibrational features glasses comprised from these elements

will have resonances at similar frequencies, however, these will be inhomogeneously

broadened due to the amorphous structure.

The samples we used for this measurement are much too thick (1 mm) to resolve these

features. As such we are only able to determine the onset of the multiphonon edge

which results from harmonics and overtones of the fundamental IR absorption bands.

We do, however, make inferences as to the behaviour of the fundamental IR absorption

bands by noting the changes in the position of the multiphonon onset wavelength and

by comparison to the Raman spectra.


We recorded inferred absorption spectra using a Bruker Vertex 70 FTIR spectrometer3,

for wavelengths from 2 μm to 10 μm with a resolution of 1.55 nm. These spectra

were recorded using the same glass samples that were described in Section 6.2.1 in

transmission. We have concentrated on determining the location of the multiphonon

edge and the vibrational spectra of impurities, in particular hydroxide groups.


The raw data from the spectrometer is measured as absorbance K, which is related to

the transmission through the material via:

K = log

(1

T

). (6.6)

This is converted to absorption units of dB.m−1 via Equation 6.7, which is a convenient

unit for assessing materials for their potential use in optical fibres. Just as in Section

6.2.2, just as for the UV-VIS data we eliminate the effect of Fresnel reflection and surface

scattering by subtracting the minimum loss value from the entire spectrum.

αdB.m−1 = Kln(10)

L(6.7)

3Kindly provided by the Defence Science Technology Organisation (DSTO), Edinburgh, SA

Chapter 6 105

For the samples described here, we melt the tellurite glass in an open atmosphere furnace

and thus in the presence of atmospheric water. Accordingly there is a strong presence

of water in the glasses which can be easily seen in the infrared absorption spectra (see

Figure 6.4) by the presence of characteristic vibrations of the OH− groups at ≈ 3.5 μm

and ≈ 4.5 μm.

Figure 6.4: Infrared absorption spectrum of TMN1 (Red) and theoretical multi-phonon edge (Blue).

Figure 6.4 also shows a sharp increase in absorption at the mulitphonon edge where

combinations and overtones of the fundamental lattice vibrations occur. We can estimate

the position of the multiphonon edge by fitting an exponential of the form:

L = Ae−(Bλ). (6.8)

Where L is the loss in dB.m−1 and A and B are fitting constants with units of dB.m−1

and μm respectively. Equation 6.8 predicts the location of the multiphonon edge for the

tellurite glasses without the contribution from water. Therefore this is a theoretical fea-

ture. We define the multiphonon onset wavelength as the point at which the absorption

exceeds 1 dB.m−1. Listed in Table 6.2 are the multiphonon onset wavelengths for the

tellurite glass samples with the associated fitting parameters A and B.

Note that all of the glasses show similar multiphonon onset wavelengths. The multi-

phonon onset wavelengths are plotted for each glass sample in Figure 6.5, which shows a

general trend of increasing multiphonon edge wavelength for increasing modifier content.

This result is indicative of an increase in the mean bond length possibly related to the


Multiphonon onset A BSample wavelength [μm] [dB.m−1] [μm]

TMN1 4.27 1.5×1012 120TMN2 4.29 2.7×1012 123TMN3 4.39 1.4×1013 133TZN1 4.56 9.0×1013 146TZN2 4.54 6.7×1013 145TZN3 4.57 1.4×1014 149TZN4 4.66 7.6×1014 160TBN1 4.52 7.9×1013 145TBN2 4.76 1.1×1016 176

Table 6.2: Multiphonon onset wavelength for TMN, TZN and TBN glass series..

5 10 15 204.2

4.3

4.4

4.5

4.6

4.7

4.8

TMN1TMN2

TMN3

TZN1 TZN2TZN3

TZN4

TBN1

TBN2

Mul

tipho

non

Ons

et [μ

m]


Figure 6.5: Compositional dependence of multiphonon onset wavelength for TMN,TZN and TBN glass series.

general loss of network connectivity displayed by the glasses as the amount of modifier

is increased.

Perhaps the most significant result from the FTIR data is the high absorption from

≈ 2 μm onwards, due to the presence of hydroxyl (OH−) groups in the glass. In Figure

6.6 we have plotted the attenuation in dB.m−1 at the peak of the OH− absorption which

Chapter 6 107

is at ≈ 3.4 μm. The magnitude of the absorption is a direct measure of the concentration

of OH− in the glass and therefore Figure 6.6 can also be read as the dependence of the

OH− concentration on modifier concentration [74]. What we observe is that the amount

of OH− contamination decreases with increasing modifier content. One exception to that

conclusion is the data point for TZN3. It is suspected that this is an outlier, possibly

due to surface contamination of atmospheric H2O, alternatively, contamination could

have occurred during fabrication of the glass. There is strong evidence to suggest that

TZN3 is indeed an outlier based on the consistent linear trend displayed by the TMN

series and the other TZN glasses.

5 10 15 201200

1400

1600

1800

2000

2200

TMN1

TMN2 TMN3TZN1

TZN2

TZN3

TZN4

TBN1

TBN2

Abs

orpt

ion

@ 3

.4 μ

m [d

B.m

-1]


Figure 6.6: Compositional dependence of attenuation due to OH− contamination.

The observed reduction in OH− content can be explained by considering the way in which

the modifier species incorporate themselves into the glass structure. These charged

entities preferentially locate themselves in the regions of NBOs to fill in voids in the

structure. These are precisely the same locations that the hydroxyl groups would form.

As such, the increase of modifier concentration displaces the OH− from the glass.

Absorption due to hydroxyl groups is deleterious to the operation of optical fibre devices

that are intended to operate in the near to mid infrared region of the spectrum, i.e.

≈ 2 → 5 μm. For these glasses to be considered for use in the mid infrared it will


be necessary to reduce the water content (dehydroxylation) to a point where the loss

is below 1 dB.m−1. The reduction achieved via increase in modifier concentration are

inadequate for this purpose. It is possible to reduce the water induce loss by fabricating

in a dry atmosphere of N2. Alternatively, the addition of fluorinated compounds such as

NaF can reduce the OH− contamination via the reaction: OH−+F− →HF+O2−. These

dehydroxylation methods are left for future work.

6.4 Refractive Index Measurements

One of the most fundamental properties of an optical material is the refractive index.

The refractive index determines the speed of light in that particular medium v,

as per the relation:

v =c

n(6.9)

where c is the speed of light in vacuum and n is the refractive index. Besides simply

determining the speed of light in the material, the refractive index also dictates the

angle of refraction as light moves from one material to another via Snell’s law. This is of

consequence to optical fibres as it determines whether or not light can be guided within

a fibre. In the simplest picture of an optical fibre we have a cylindrically symmetric

interface between two material of differing refractive index as per Figure 6.7. The central

region, the core, has a slightly higher refractive index than the outer region or cladding.

The ray picture of light in combination with Snell’s law predicts that certain rays incident

onto the core/cladding interface will be totally internally reflected at every point along

the fibre and thus confined to the core.

Figure 6.7: Ray diagram for an optical fibre. Ray 1 is incident onto the core/claddinginterface at an angle less than the critical angle for TIR and it transmitted out of thefibre. Ray 2 is incident onto the core/cladding interface at an angle greater than the

critical angle and is thus transmitted along the fibre.

For the design of an optical fibre it is essential to know the refractive indices of the

material or materials being used as these will determine the operation of the fibre.

Chapter 6 109

Further, typical index contrasts between core and cladding are in the order of Δn ≈ 0.01

therefore necessitating accurate measurements of the indices of refraction, at least as

accurate as 1/10th of the desired index contrast.

We measured the refractive indices using a prism coupler. This method is superior to

most alternative techniques such as the method of minimum deviation [75] as it requires

relatively little sample preparation. The measurements were made at two wavelengths,

1064 nm and 532 nm. These wavelengths were chosen to facilitate the Maker fringes

analysis in Chapter 8.

A prism coupler works by measuring the angle at which total internal reflection (TIR)

ceases at the interface between a prism of know refractive index and the sample under

study. From Figure 6.8 it is clear that for certain incidence angles θ at the prism/sample

interface, θ will be larger than the critical angle for total internal reflection θc. In this

case a signal will be recorded at the photo diode. However, as θ is decreased the point

at which θ < θc TIR no longer occurs. This will be recorded at the photo diode as a

sharp decrease recorded signal at θ = θc (see Figure 6.9).

Figure 6.8: Schematic diagram of the internal configuration of the Metricon prismcoupler. Laser light is directed via two mirrors, M1 and M2, onto the interface betweenthe sample and a reference prism. The polariser P, selects the polarisation state ofthe light (this is only relevant for birefringent materials). The light reflected fromthe interface is detected with a photodiode PD1. The sample, prism and detector aremounted on a rotation stage. Mirror M2 is partially transmitting, allowing the reflectedlight from the prism to pass through the aperture A, and onto the photodiode PD2.This reflected beam is used to calibrate the angular position of the rotation stage.



We used a prism coupler (Metricon4) which has been retrofitted to include an additional

laser wavelength. The schematic representation of this equipment is shown in Figure

6.8. The measurements were made at 1046 nm and 532 nm using a rutile (TiO2) prism.

The absolute accuracy of the measurement was determined by first measuring the index

of a commercial glass SF57 (SCHOTT Glass Co.) It was found that at 532 nm the

measured index was in agreement with the value reported by SCHOTT to 0.08 % and

0.05 % at 1064 nm. The main source of this error is likely to stem from uncertainty

in the refractive index of the reference prism which is quoted to be ±1.5 × 10−1 [76].

Clearly, from the results at hand, this is a conservative estimate.


Shown in Figure 6.9 is a representative data set from the prism coupler in which the

position of the knee is indicated, and a line intersection method is used to find the

critical angle from which the refractive index is calculated. Using Snells law for a prism

refractive index np, and sample index ns and setting the transmitted angle to 90◦ we

obtain the following equation

ns = np sin θc. (6.10)

Software which accompanies the prism coupler performs this data analysis automatically

provided a distinct knee is recorded. The absence of a distinct knee results when the

contact between the prism and sample is not conformal. In these cases the sample was

removed and, using adhesive tape, dust was removed from the sample and prism surfaces

that make contact.

Table 6.3 contains the measured refractive index values and plotted in Figure 6.10 are

the refractive index values measured at 1064 nm for each composition. We note that,

for increasing modifier content, the TMN, TZN and TBN glasses display a decrease in

refractive index.

These compositional trends in refractive index can be explained by considering the rel-

ative contributions to the electronic polarisability by the individual components of the

glasses. The linear susceptibility can be related to the electronic polarisability of an

ensemble of n identical entities through:

χ(1) =n

Vα (6.11)

4Prism Coupler was kindly provided by S. Madden and B. L. Davies at The Australian NationalUniversity (ANU)

Chapter 6 111

Figure 6.9: Example trace from a prism coupler.

Sample n532 n1064

TMN1 2.09568 2.02124TMN2 2.06038 1.99058TMN3 2.02314 1.95850TZN1 2.10540 2.02636TZN2 2.07768 2.00218TZN3 2.05680 1.98418TZN4 2.02854 1.96012TBN1 2.09494 2.01668TBN2 2.06268 1.98926

SF57 1.85996 1.81272

Table 6.3: Measured refractive indices at 532 nm and 1064 nm. Absolute measurementerror 0.08 % at 532 nm and 0.05 % at 1064 nm

where V is volume of material and n/V , the atomic number density can be expressed

as N = n/v. Thus by Equation 2.98 we can relate the electronic polarisability to the

linear refractive index by

n0 = (1 + 4πNα)1/2. (6.12)

To relate the changes in polarisabilty and hence refractive index to the composition of

the glasses we consider the individual electronic polarisabilities of the modifiers (Mg2+,

Zn2+ and Ba2+) and the TeO4 and TeO3 subunits (Table 3.2). Sodium need not be

considered as it is in equal portions in all glass samples. The behaviour is similar for all

glass families (TMN, TZN and TBN) and so we can generalise the discussion by referring

to a general modifier M2+ (where M2+ = Mg2+, Zn2+ or Ba2+). As we increase the


5 10 15 201.95

1.96

1.97

1.98

1.99

2.00

2.01

2.02

2.03

2.04

TMN1

TMN2

TMN3

TZN1

TZN2

TZN3

TZN4

TBN1

TBN2

n (1

064n

m)


Figure 6.10: Refractive index of tellurite glasses measured at 1064 nm.

amount of M2+ we are decreasing the amount of Te4+ as a result there are fewer TeO4

and TeO3 subunits present in the glass. We are therefore substituting components with

electronic polarisabilities of ≈ 6 × 10−23 cm3 (approximate electronic polarisibility of

TeO2) with components with electronic polarisabilities of � 2.5× 10−23 cm3 (Ba2+ has

an electronic polarisability of 2.5×10−23 cm3 which is the highest of the three modifiers)

and so we should expect a decrease in polarisability. Any decrease in polarisability will

be accompanied by a corresponding decrease in refractive index as predicted by by

Equation 6.12.

Furthermore, the Raman spectra in Section 4.2.4 indicate that as we increase the amount

of M2+ in the glass there is a tendency for the TeO4 subunits to convert into TeO3

subunits. As the electronic polarisability of the TeO4 subunit is ≈ 20% greater than the

TeO3 subunit [42] the progression to lower refractive index with increasing M2+ is also

mediated by the conversion of TeO4 to TeO3.

The progression to lower polarisability with increasing modifier content, as indicated by

the trends in refractive index, leads us to an interesting apparent contradiction. With

reference to the data for the band edges of the glasses in Section 6.2.2 the band edge

is blue shifted for the TMN and TZN glass series as we increase the modifier content.

Typically, a decrease in polarisability will be associated with a blue shift in the band

Chapter 6 113

edge. This behaviour is exhibited by the TMN and TZN glasses. However, the TBN glass

displays a red shifted band edge with increasing Ba2+ content despite the poarisability

decreasing which we have hypothesised to be resultant from progressive and extreme

disordering of the TeO2 network by Ba2+ (Section 6.2.2). This disordering leads to

longer band tailing and, subsequently, a red shifted band edge.

6.5 Nonlinear Refractive Index Measurements

There are several experimental techniques for measuring χ(3) including degenerate

four wave mixing [77], electric field induced second harmonic generation [78] and

third harmonic maker fringes [79] to name a few of the more common. The technique we

used is the Z-Scan technique which used the phenomenon of Kerr focusing to determines

the value of the intensity dependent refractive index n2 as given in Equation 2.88.

In the Chapter 2.4.1, for simplicity, we did not consider the imaginary parts of the

nonlinear susceptibilities. The imaginary part of χ(3) mediates an effect known as two

photon absorption and can be thought of as a nonlinear loss mechanism. For two photon

absorption to occur the energy of the conduction band of the material must be less than

twice the energy of the photons. This can be negated by choosing a probe wavelength

for which the second harmonic is below the UV cut off [80]. The following sections

describe the theory and experimental details, followed by the results for the studied

glass samples.

As shown in Section 2.4, there is a component of the refractive index that scales with

the intensity of the transmitted light. If we have light with a plane phase front and

a Gaussian transverse intensity distribution incident onto a nonlinear medium then by

Equation 2.88 the modified refractive index of the material in the vicinity of the beam

can be written as

n = n0 +n2

2I0 exp

(−2r2w2

). (6.13)

In Equation 6.13 I0 is the on axis intensity, r is the transverse spatial coordinate and w

is the radius of the incident beam. In the pariaxial approximation we can expand the

exponential to lowest order and obtain:

n ≈ n0

(1− n2I0r

2

n0w2

). (6.14)

It is straight forward to show that when a material has a parabolic index profile as

described by Equation 6.14 it will cause plane waves to be focused. Provided the material

with thickness L is thin and the paraxial approximation holds the focal length of the


induced lens is given by

f =n0w

2

2n2I0L. (6.15)

Now if the input wave does not have a flat phase front, then the expressions become

more complex. However, we can gain a qualitative understanding of the Z scan by

keeping these approximations. Consider then experimental configuration as shown in

Figure 6.11.

Figure 6.11: A Simple Z scan configuration. Top: Sample positioned before the un-perturbed focal point causes less light to reach the detector. Bottom: Sample positioned

after the unperturbed focal point causes more light to reach the detector.

A collimated beam with a Gaussian intensity profile is focused to a point some distance

form an aperture. We then translate a thin sample along the propagation direction.

Assume that the beam has sufficient intensity to generate a change in the refractive

index of the sample of the form in Equation 6.14. The diagram at the top of Figure 6.11

shows the additional focusing from the sample causing the actual focal point to move

away from the aperture. The spreading out of the beam results in less light reaching

the detector. At the bottom of Figure 6.11 the sample is now closer to the aperture and

therefore the focusing of the beam results in more light passing through the aperture

and this being detected. An example of a Z scan signal is shown in Figure 6.12

This simplified version of the Z scan illustrates that as the sample is translated along

the beam and through the waist the signal detected after the aperture first decreases

then increases. The analysis for a curved wave front, which is in fact the case due to the

lens, is more complicated and is expressed, not in terms of a focal length but, instead,

in terms of the on axis phase change caused by the material. The analysis performed

Chapter 6 115

Figure 6.12: Examples of Z scans. Red: Self focusing produced by a positive phaseshift for a material with n2 > 0. Black: Self defocusing produced by a negative phase

shift for a material with n2 < 0. Reproduced from [81]

by Shiek-Bahae et al [82] derives a useful approximation for the on axis phase shift,

provided that the material is thin (i.e. L << z0) and the beam has a Gaussian intensity

profile. Under these conditions the on axis phase shift is given by

|ΔΦ0| = ΔTpv

0.406(1− S)0.27(6.16)

where ΔTpv is the difference between the peak and the valley of the normalised trans-

mittance and S is the fraction of the beam transmitted through the aperture (before

the self focusing). The nonlinear refractive index is related to ΔΦ0 via

n2 =

(λ

2π

)ΔΦ0

I0Leff. (6.17)

Combining Equations 6.16 and 6.17 we obtain

n2 =

(λ

2π

)ΔTpv

I0Leff

1

0.406(1− S)0.27(6.18)


The experimental Z-scan setup for measuring the nonlinear refractive indices is illus-

trated in Figure 6.13.



��

��

�� !��

�"�#

�"��

�"��

��

��

�#

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$��

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%"�

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&

Figure 6.13: Schematic of Z-scan experimental setup. Optical paths red dotted lines,electrical paths grey lines. M1-3; Mirrors, F; IR filter, LP; Linear Polariser, A1-3;Apertures, ND1-2; Neutral density filter wheels, BS1-2; Beam splitters, L1-2; Lenses,

LS; Linear translation stage, PD1-3; Photo diodes

The mode locked output from a Clark-MXR CPA-2001 Ti-Sapphire laser is injected

into a Quantronix TOPAS OPA. Via nonlinear processes the 788 μJ 775 nm pulses are

converted into 120 μJ 1500 nm pulses. As per the UV-VIS spectroscopy results in

Section 6.2 the band edge is at ≈ 3.3 eV for all glasses under study. For this reason

we chose a probe wavelength of 1500 nm, for which the two photon energy is ≈ 1.7 eV.

Therefore making two photon absorption negligible.

The duration of the frequency converted pulses is approximately 150 fs (full width half

maximum), thus providing a peak power of ≈752 MW. Several wavelengths are emitted

from the TOPAS; there is the 1500 nm signal accompanied by the 1603.4 nm idler.

Additionally there are doubled signal and idler at around 750 nm and 800 nm respec-

tively and there is also some sum frequency radiation resulting from the addition of the

pump and idler which is at 525 nm. All of the spurious wavelengths are filtered by an

appropriate filter (F).

The intensity incident on the sample is controlled by the ND1 and ND2 filter wheels

by between 3 % and 0.3 % of maximum. The beam is passed through an aperture

Chapter 6 117

(A1) to produce diffraction such that at aperture A2 there is an airy disc. By carefully

adjusting the size of A2 we are able to select the central peak of the airy disc and

generate a near Gaussian beam with an approximate diameter of 2 mm. Figure 6.14

illustrates the validity of the Gaussian approximation for a truncated Airy disc. We

define the percentage overlap between the two functions as:

%Overlap =

⎛⎜⎜⎜⎜⎜⎜⎜⎝1−

∣∣∣∣∣∣a∫

−aB(x)2dx−

∞∫−∞

G(x)dx

∣∣∣∣∣∣∞∫

−∞G(x)dx

⎞⎟⎟⎟⎟⎟⎟⎟⎠× 100 (6.19)

The functions B(x) and G(x) are Bessel and Gaussian functions, respectively, which

provide a simple 2D method for evaluating the overlap. The integration limit a, is the

position of the first root of the Bessel function which corresponds to the position of the

aperture. Under these conditions the degree of overlap is ≈ 96% which therefore shows

that the Gaussian approximation is valid.

Figure 6.14: Illustration of overlap between a truncated airy disc (red) and a Gaussian(green).

A small fraction of the beam is directed into a photo diode (PD1) by a glass microscope

slide (BS1). The signal from PD1 is used for normalising the intensity fluctuations in the

laser beam. Next the beam is focused by lens L1 which has a focal length of 17 cm. This

produces a beam diameter at the focal plane of 20 μm and a Reighlegh range of ≈7 mm

and so the 2-3 mm thick samples we are using meet the criterion for being thin i.e.

L < z0. LS, the computer controlled linear translation stage has a full range of 90 mm

and is used to move the sample along the beam. At BS 2, which is also a microscope

slide, the signal is split into the open aperture channel recorded at PD 3 and the closed


aperture channel recorded at PD 2. The aperture in the closed aperture channel, A3,

has its diameter set to ≈3 mm. This diameter is adjusted iteratively to give the best

Z-scan signal by viewing the closed aperture signal on an oscilloscope as the sample is

manually translated through the beam focus. We have an optimised aperture diameter

when the signal on the oscilloscope is symmetric about the focal point.

6.5.2 Data Analysis

The raw data from the Z scan analysis is analysed in the following way:

1. For each glass sample we have Z scan traces for a variety of laser powers. The

signal from PD1 is averaged over the entire scan. This value is proportional to

the mean intensity I0, at the sample over the duration of the experiment which is

used later to calculate the relative nonlinear refractive index (see Equations 6.18

and 6.21).

2. The data from the closed aperture channel is divided by the open aperture channel.

This serves two functions. Firstly, it normalises the power fluctuations in the

signal. Secondly, if there is any two photon absorption the power loss in the closed

aperture channel that results from this loss is recovered.

Figure 6.15: Representative Z scan data set: Closed aperture signal, red, open aper-ture signal, blue and ΔTpv indicated. This particular Z scan is for TZN3.

3. We determine ΔTpv and the mean value of the open aperture channel at each laser

power and plot this against the averaged PD1 signal. Figure 6.16 shows the data

Chapter 6 119

for the TZN3 glass. As expected, the signals are proportional to the intensity. The

slope of the ΔTpv vs intensity is obtained for each glass sample and is equal to

ΔTpv/I0.

1.4 1.5 1.6 1.7 1.8 1.90.24

0.28

0.32

0.36

0.40

ΔTpv

Mean Laser Power [arb. units]

1.6

2.0

2.4

2.8

3.2

Mea

n O

pen

Cha

nnel

Sgn

al [V

]

Figure 6.16: Z Scan measurements at various incident intensities. Red: Peak totrough value of the normalised transmission at various incident intensities. Blue: Mean

open aperture signal at various incident intensities.

4. We also perform the Z scan on a reference sample with a well known nonlinear

refractive index. A commercial lead silicate glass (SF57, SCHOTT) was used.

Silica is a commonly used reference material [77], however, it is desirable to use

a reference that possesses a nonlinear refractive index more closely matched to

the sample under study as this eliminates the problem of detector dynamic range.

Silica, for example, requires approximately 10× the incident intensity to achieve

a phase shift comparable to tellurite. SF57, on the other hand, has a nonlinear

refractive index within a factor of 2 of tellurite. Thus we can use the dynamic

range of the detector more efficiently without the need for beam attenuation as

would be required is silica was used as the reference.

5. If we apply Equation 6.18 to the reference sample:

nr2 =

(λ

2π

)ΔT r

pv

Ir0Lreff

.1

0.406(1− S)0.27(6.20)


and the sample under study (Equation 6.18) and take the ratio,(assuming that S

is held the same, i.e. the aperture is not adjusted in between measurements.), we

obtain an expression for the relative nonlinear refractive index:

n2 =1

nr2

ΔTpv

ΔT rpv

Ir0Lreff

I0Leff. (6.21)

where a superscript of r indicates a reference quantity. The ratios ΔTpv/I0 and

ΔT rpv/I

r0 have been calculated from the Z scan data (as described above), the

sample lengths (Leff and Lreff are known as is the reference nonlinear refractive

index nr2. We can therefore calculate the value of the nonlinear refractive index of

the samples under study, these are presented in Section 6.5.3.


The results of the Z-scan measurements are displayed in Table 6.4 where we also quote

the reported nonlinear refractive index for SF57. Further, we have used Equation 2.101

to estimate the values of χ(3) for each sample, also listed in Table 6.4. The validity

of this estimation is based on the assumption that the value of the refractive index

at 1064 nm is approximately equal to that at 1500 nm, i.e. the wavelength at which

the n2 measurements were made. The refractive index at these two wavelenght was

kindly measured for the TZN3 sample by Jeremy VanDerslice at J.A. Woolam on an

spectroscopic ellipsometer. The difference in the values at 1064 nm and 1500 nm is

determined to be approximately 6% giving an error of approximately 12% for χ(3), as

χ(3) ∝ n20 (Equation 2.101).

n2 χ(3)

Sample [10−19m2.W−1] [10−21m2.V−2]

TMN1 5.89 8.52TMN2 4.49 6.30TMN3 3.49 4.74TZN1 5.76 8.37TZN2 5.55 7.88TZN3 4.86 6.77TZN4 4.82 6.56TBN1 5.41 7.79TBN2 5.08 7.12

SF57 4.10 5.02

Table 6.4: Measured nonlinear refractive indices and calculated third order suscepti-bilities (Equation 2.101) for TMN, TZN and TBN glasses at 1500 nm. Reference value

of SF57 is quoted [83]

Chapter 6 121

The values of the nonlinear indices are plotted in Figure 6.17 vs the concentration of

the various modifier.

5 10 15 20

3.5

4.0

4.5

5.0

5.5

6.0TMN1

TMN2

TMN3

TZN1TZN2

TZN3 TZN4

TBN1

TBN2

n 2 [10-1

9 m2 .W

-1]


Figure 6.17: Nonlinear refractive indices of Tellurite glasses.

At the incident power levels used we observed no two photon absorption, this is largely

because of our choice of probe wavelength and the lack of material absorption at the

two photon energy. Figure 6.15 shows the Z scan data for TZN3 with the highest

input power, ≈ 25 MW peak. The open aperture signal (blue) is essentially constant

with position. Two photon absorption would appear as a sharp downwards peak in the

centre of the data no such features were observed in any of the data.

Observe that for all glass series the nonlinear refractive index is decreasing with increas-

ing modifier. An understanding of why this occurs is necessary if we wish to discover

alternative glass compositions with larger nonlinear susceptibilities. Larger nonlinear

susceptibilities will enable more efficient nonlinear devices and are therefore of techno-

logical interest. To a first approximation, we can understand the progressive decrease in

terms of the substitution of the highly polarisable tellurium ions for the less polarisable

modifying ions (see Table 3.2). If this were the only mechanism we would expect the

slopes in Figure 6.17 to have be ranked in the order TMN<TZN<TBN. This is because


the polarisabilities of the ions Mn2+, Zn2+ and Ba2+ follow that ordering. What is ob-

served is that the slope of the TMN glasses is the lowest but the TBN and TZN glasses

have approximately equal slopes. As the polarisability of the Ba2+ ion is greater than

2× that of the Zn2+ ion this requires further analysis.

We therefore draw attention to the Raman spectroscopy data in Chapter 3. In particular

the trend in the Raman D bands (as shown in Figure 4.17) which can be used as a

measure of the concentration of the TeO3 subunits. Notice that the increase in the

TeO3 concentration with increasing modifier content is more pronounced for the TBN

series than for the TZN series. It is known from quantum chemical ab initio models that

the polarisability of the TeO3 subunit is ≈ 80% of the TeO4 subunit [42]. Therefore, as

the amount of TeO3 increases the nonlinear refractive index is expected to decrease. As

this trend is much more pronounced for TBN glasses than for TZN glasses the tendency

towards lower nonlinear refractive index, based on TeO3 content alone is less for the

TZN glass series.

With these two mechanisms in action we can summarise the trends in nonlinear refractive

index as follows:

� TMN: The Mg2+ ion has a polarisability that is approximately 2 orders of mag-

nitude lower than tellurium (Table 3.2). This substitution thus decreases the net

polarisability. Additionally, there is a pronounced conversion of TeO4 →TeO3 as

the concentration of Mg2+ is increased (Figure 4.17). Together these two trends

contribute to produce the steepest slope in the n2 vs. modifier content graph in

Figure 6.17.

� TZN: Zn2+ ions have a polarisability that is ≈ 10× less than tellurium (Table

3.2) therefore when tellurium us substituted for zinc there is a decrease in the

polarisability. However, the progression of TeO4 →TeO3 is relatively slow (Figure

4.17) and so the dominant effect for the lowering of the nonlinear refractive index

is simply related to the substitution of lower polarisabilty ions.

� TBN: The polarisability of the Ba2+ ion is of the same order as tellurium, however,

slightly lower (Table 3.2). Consequently, as we substitute tellurium for barium the

change in polarisabilty is small. In particular with respect to the changes observed

in the TMN and TZN glasses. On the other hand, the increase in the concentration

of TeO3 subunits as Ba2+ is added is large (Figure 4.17). Therefore the decrease

in nonlinear refractive index observed in the TBN glass series is dominated by the

conversion of TeO4 →TeO3.

Chapter 6 123

In 1964 Miller analysed the relationship between the linear and nonlinear susceptibility

for a large range of crystals [84]. An empirical relationship was observed, later named

Miller’s rule, that showed that the ratio

χ(2)(ω1 + ω2, ω1, ω2)

χ(1)(ω1 + ω2)χ(1)(ω1)χ(1)(ω2)(6.22)

was essentially constant for all materials with non-zero second order nonlinear suscepti-

bilities. It has since been shown that this ratio is related through

χ(2)(ω1 + ω2, ω1, ω2)

χ(1)(ω1 + ω2)χ(1)(ω1)χ(1)(ω2)=

maε20N2e3

(6.23)

where m is the mass of the electron, e is the electrons electronic charge, N is the atomic

number density and a is a constant that is related to the strength of the nonlinearity

[30]. N is of the order 1022 cm−3 for nearly all solid materials. Furthermore, a can be

shown to be roughly constant for all materials [30]. It is therefore clear that the ratio

in Equation 6.22 should be approximately constant for most materials.

This relationship can be further generalised to show that there exists a similar scaling

law for the higher order susceptibilities as was done in the work of Wang [85]. Wang

derived an empirical relationship for the first and third order susceptibilities given by:

χ(3) =g′

Nf�ω0

(χ(1)

)2(6.24)

where f is the oscillator strength, ω0 is an average transition frequency and g′ is a

dimensionless parameter ≈ 1 that is assumed to be constant for all materials [30]. This

generalisation of Miller’s law has been shown to be accurate for many materials including

glass.

With reference to the data for nonlinear refractive index and the measurements of linear

refractive index in Section 6.4 we notice when the refractive index decreases the nonlinear

refractive index also decreases. This trend is consistent with the scaling law of Wang,

however, despite the fact that Wang developed the relation between χ(3) and χ(1) (and

therefore n2 and n) this scaling law is referred to as Miller’s law in the literature.

Figure 6.18 (adapted from [6]) is a plot of Millers law with various glass families indicated

(circles) along with the glasses under study in this thesis (squares). As can be seen the

results correlate well with Millers prediction.

We note that the nonlinear refractive index of silica, the current material of choice for

electro-optic fibres is 2.7 × 10−20 m2.W−1. This is some 20× smaller that the values


Figure 6.18: Millers law plot with various representative glass types indicated alongwith TMN, TZN and TBN glasses. Adapted from [6]

measured for the studied tellurite glasses. Indicating the superiority of tellurite as a

material for electro-optical fibres.

6.6 Conclusion

In conclusion, the tellurite glasses under study have optical transmission from ≈370 nmto ≈4500 μm. While the edges of this transmission window are largely determined

by the properties of TeO2, there are some small changes in the positions that are subtly

effected by the modifiers. The infrared transmission of the glasses is dominated by

absorption due to the presence of water (OH−) in the glass in the spectral region ≈2 → 5 μm. For progress in the area of mid IR glasses this will have to be reduced or

eliminated via dehydroxylation processes.

Refractive indices display a clear linear decrease for increasing modifier which results

from an overall decrease in the net polarisability as the proportion of the most polarisable

component, TeO2, is decreased. The addition of modifier forces the conversion from a

more polarisable subunit (TeO4) into a less polarisable subunit (TeO3). These two

processes in combination produce the measured decrease in index. Furthermore, the

nonlinear refractive index displays close correlation to the compositional trends observed

for the refractive index. We claim that these trends are also related to the substitution


Chapter 6 125

of lower polarisability modifiers in place of the highly polarisable tellurite sub groups, as

well as the progressive conversion of the more polarisable TeO4 into the less polarisable

TeO3 subunits.

In terms of identifying suitable glasses from which to fabricate electro-optic fibres devices

we note the following:

� All of the studied glasses possess approximately the same transmission windows

from 350 nm to 4.5 μm. However, the presence of hydroxyl ions limits the usable

portion of this this transmission window up to approximately 2 μm after which

the absorption is prohibitively high (i.e. > 10 dB.m−1).

� We observe near linear variation in the refractive index with modifier concentration

for each of the glass series. This offers the possibility of tuning the index with subtle

alterations in composition so as to achieve the necessary refractive index contrasts

for step index fibres.

� The measured nonlinear refractive indices and calculated third order susceptibili-

ties are in excess of one order of magnitude larger than those of silica. As such, all

of the studied glasses offer increased electro-optic efficiency as compared to silica.

In Chapter 5 the TZN glasses with zinc concentrations in the vicinity of 15 ± 2 mol.%

were identified as being the most stable. Taking this into consideration we note that

the refractive index variation in the TZN system over this range of compositions is

Δn ≈ 0.02. This is sufficient for producing a large range of refractive index contrasts

necessary for step index optical fibres.

Chapter 7

Thermal Poling

7.1 Introduction

There are several processing techniques for glass that can generate a non-zero χ(2)

by producing an anisotropy in the electrostatic field. Generally speaking they all

involve the displacement of charged species to create a DC electric field inside of the

glass. In this thesis we have studied thermal poling as a possible method for creating

nonzero χ(2) glasses.

The work presented in this Chapter documents efforts to create permanent second order

nonlinearities in the glasses under study. The results obtained elucidate some subtleties

relating to the thermal poling of tellurite glass. This information will be invaluable for

future research in this area.

7.2 Background

We have identified that there are two, essentially different, glass thermal poling

techniques that are often not sufficiently differentiated from one another in the

literature. Both involve the forced migration of charged species under the application of

heat and high electric fields and both have been applied to the thermal poling of tellurite

glass.

We shall distinguish the two thermal poling techniques in the following way:

� Charge migration thermal poling

This, the most common style of thermal poling, relies on the temperature activated

mobility of charged species within the glass being poled. The mobile species are

usually sodium ions due to their presence as impurities in many raw materials and

the high mobility of such small ions. The poling configuration for this technique

127

128 Thermal Poling

employs electrically conductive electrodes, usually stainless steel or doped silicon

wafers, which are put in physical contact with the glass to be poled (Figure 7.1

(A))

Figure 7.1: Schematic of the key steps in the charge migration thermal poling process.(A) The glass to be poled in sandwiched between two electrodes. Initially there isa homogeneous distribution of positive and negative charge. (B) Heat and a strongelectric field is applied. This causes the mobile positive charges to migrate away fromthe positive electrode, producing a region depleted of positive charge. (C) The glasscooled and the field removed. Positive charges from the air are attracted to the highlynegative depletion region. (D) The negative charges at the surface have been neutralisedby the positive charges from the air. Leaving a thin buried layer of negative charge in

the glass.

Under the application of heat and a strong electric field, cations migrate away

from the anode producing a region depleted of positive charge (Figure 7.1 (B)).

After the sample is cooled and the field is removed, there is a high negative surface

charge on the anodic side of the glass. Positive ions from the air, namely H+ and

H3O+, move in to neutralise the charge (Figure 7.1 (C)), however, as they have

limited mobility in the glass at room temperature they are only able to neutralise

a thin layer at the surface. This leaves behind a thin region of negative charge

buried under the anodic surface of the glass (Figure 7.1 (D)).

Silica is poled in this way as are many other glasses such as borosilicates [86],

borophosphates [87, 88] lead borates [89] and chalcogenides [90]. Tellurite glass

has also been poled in this manner, however, a borosilicate glass microscope cover

Chapter 7 129

slip is often used at the cathode as a blocking electrode to prevent electrons from

flowing into the glass and reducing the tellurite [91].

� Charge injection thermal poling

This technique involves supplying the glass to be poled with a source of mobile

ions. A typical configuration for this type of poling consists of sandwiching the

glass between the electrodes with a commercial borosilicate microscope cover slip

on the anodic side of the glass (Figure 7.2 (A)).

Figure 7.2: Schematic of the key steps in the charge injection thermal poling process.(A) The glass to be poled in sandwiched between two electrodes with an additionalglass with a high cation content at the anodic side. Initially there is a homogeneousdistribution of positive and negative charge in both glasses. (B) Heat and a strongelectric field is applied. This causes the mobile positive charges in the anodic glassto migrate away from the positive electrode and jump the gap into the glass sample,producing a region of excess positive charge. (C) The glass cooled and the field removed.Negative charges from the air are attracted to the highly positive region. (D) Thepositive charges at the surface have been neutralised by the negative charges from the

air. Leaving a thin buried layer of positive charge in the glass.

The cover slips are a rich source of sodium ions which are mobile above ≈ 150 C◦.

Provided there is conformal contact between the glass to be poled and the cover

slips, which can be ensured by polishing the glass surface and providing some addi-

tional pressure from the electrodes, the ions can jump from one glass to the other.

At the anodic side of the glass sodium ions move from the cover slip and impreg-

nate them selves into the glass forming a positively charged layer ≈ 10 μm thick

(Figure 7.2 (B)). After the sample has been cooled and the field removed, negative

130 Thermal Poling

ions, most likely O− and OH− from the environment will neutralise the high sur-

face charge (Figure 7.2 (C)). However, because the mobility of these negative ions

is small, due to the temperature being low, they cannot completely neutralise the

entire charged layer. Thus, a thin buried positive layer exists in the glass (Figure

7.2 (D)). It is the interaction between the DC electric field and the third order

nonlinear coefficient that then produces an effective second order nonlinearity (see

Section 2.3.3).

Table 7.1 summarises reported tellurite thermal poling results for a wide variety of

tellurite compositions. Where possible the significant poling conditions have been noted.

In particular the poling temperature Tp, poling voltage Vp, poling time tp and the

measured χ(2) a presented. Importantly, we indicate the method that was used to pole

the glasses, either charge migration CM, or charge injection CI. Further, if the poling

was performed under vacuum, we indicate this with a -V in the method column. We

note that this list is not exhaustive, but does provide a picture for the range of glass

compositions and conditions that have been successfully used to produce second order

nonlinearities in the tellurite glass system.

Also in Table 7.1 are some reported poling conditions and measured χ(2) values for

Infrasil 301 (Heraeus Holding GmbH) [92]. This commercial glass has been studied

extensively for thermal poling and was used by us to test and calibrate our apparatus,

measurements and data analysis techniques.

7.3 Experimental Details

7.3.1 Experimental Plan

Prior to beginning the experimental poling work an experimental plan was developed.

This plan, described below, was intended to provide us with samples poled under a range

of conditions such that optimal conditions could be determined.

1. First, a sample of commercial silica glass is poled under conditions that will pro-

duce a small second order nonlinear coefficient. We used Infrasil 301 (Schott Glass

Co.), which is a well studied material in the area of thermal poling and thus pro-

vides predictable outcomes.

This step is preformed to provide us with a means of: 1) Testing the performance

of the poling apparatus. 2) Determining the limitations of the characterisation

experiment as described in Chapter 8.

Chapter 7 131

Tp Vp tp χ(2)

Glass [◦C] [kV] [min] [pm.V−1] Method Ref.

Li2O.Nb2O5.TeO2 250 4.0 30 * CM [91]30ZnO.70TeO2 250 4.0 30 0.44 CI [93]

10MgO.20ZnO.70TeO2 260-300 4.0 20 0.24 CI [93]15MgO.15ZnO.70TeO2 260-300 4.0 20 0.26 CI [93]

20B2O3.80TeO2 260-300 4.0 20 0.22 CI [93]25B2O3.75TeO2 260-300 4.0 20 0.02 CI [93]30NaO1/2.70TeO2 225 3.0 20 0.16 CI [94]

10NaO1/2.20ZnO.70TeO2 260 3.0 20 0.46 CI [94]

30ZnO.70TeO2 280 3.0 20 0.9 CI [94]15Nb2O5.85TeO2 * 3.0 15 * CI [95]

15Nb2O5.85TeO2 + Na+ * 3.0 15 * CI [95]5Sb2O3.25Pb(PO3)2.70TeO2 200 4.0 60 0.4 CM-V [96]

” 225 4.0 60 0.58 CM-V [96]” 250 4.0 60 0.33 CM-V [96]

70TeO2.15Bi2O3.15ZnO 280 5.0 60 1.2 CI-V [97]” 300 5.0 60 0.26 CM-V [97]” 300 3.0 60 0.22 CM-V [97]

90TeO2.5Bi2O3.5ZnO 300 3.0 60 0.36 CM-V [97]

Infrasil 301 290 4.0 90 0.20 CM [98]” 300 4.0 60 0.01 CM [87]” 325 4.0 60 0.08 CM [87]” 350 4.0 60 0.06 CM [87]

Table 7.1: A summary of some reported thermal poling experiments performed onvarious tellurite glass systems. When possible the poling conditions such as polingtemperature Tp, voltage Vp and time tp as well as the measured χ(2) are stated. Thepoling method has been indicated where: CM, charge migration. CI, charge injectionand -V indicates that the poling was performed under vacuum. An * indicates that the

value was not explicitly reported in the cited reference.

2. Using the results in Chapter 5 regarding the crystallistion stability of the glasses

we narrowed our focus onto the TZN2 and TZN3 compositions. These glasses rep-

resented the most promising candidates for optical fibre materials, as they possess

the largest crystallisation stabilities.

3. Results in the literature (see Table 7.1 indicate that most tellurite glasses have

optimal poling temperatures in the region of Tg − 50◦C. This temperature is thus

used as a starting point for our investigations. The resistivity of the samples is

measured at this temperature by recording the current vs. voltage. During these

measurements we note the voltage at which the sample undergoes dielectric break-

down. This then represents the maximum voltage permissible, at this temperature.

We are able to discuss the dielectric breakdown in terms of voltage rather than

electric field because all of the samples under study were prepared with the same

132 Thermal Poling

thickness (1 mm). For the poling experiments the poling voltage will be chosen to

be ≈ 500 V lower than the breakdown voltage.

4. The poling program for each glass type involves first poling for a duration sufficient

to reach a sate wherein the current is zero. This situation is understood to represent

the case where the resistivity of the poled region is high enough to negate the

applied voltage, thus indicating the cessation of poling.

5. Following this, several samples will be poled for times less than the steady state

time.

6. Steps 4 and 5 are then repeated for several temperatures either side of the initial

Tg − 50◦C.

Following the initial poling investigations it became apparent that the proposed exper-

imental plan was not adequate. Specifically, after each experiment the samples were

destroyed. Further to this, initial characterisation experiments revealed that no measur-

able second harmonic generation was observed in the sample fragments. This resulted

in a series of experiments designed to determine the issues identified with the initial

approach.

7.3.2 Thermal Poling Apparatus and Configurations

We constructed an apparatus for thermally poling glass. Shown in Figure 7.3 is the

apparatus which is placed in an oven during the poling process. Stainless steel electrodes

are held in ceramic (Macor, Corning Inc.) blocks to electrically insulate them from the

support frame and oven. The cathode is mounted on a spring, as indicated schematically

in Figure 7.3. The anode is fixed to a plate, the vertical position of which can be adjusted.

The electrical connections are made with glass fibre insulated high voltage cables with a

stainless steel braid over-jacket. These cables are capable of supporting >10 kV at over

500◦C.

The final design was achieved through trial and error. It was discovered that it is critical

to have no sharp edges on the poling electrodes as this often results in dielectric break

down due to the high electric fields that form at these edges. We also found that spring

loading one of the electrodes enables one to ensure good physical contact between the

sample and the electrodes, the force of which is kept fairly constant during the periods

of thermal expansion and contraction during heating and cooling of the sample as well

as from experiment to experiment.

Chapter 7 133

Figure 7.3: Thermal poling apparatus with the electrical configuration indicatedschematically. Stainless steel electrodes contained within ceramic insulating blocks arefixed to metal plates, one of which has vertical adjustment. The lower electrode, chosento be the ground is spring loaded to ensure good physical contact between the electrode

and the sample. The entire assembly can be placed in an oven.

134 Thermal Poling

7.4 Results and Discussion

Based on the crystallisation stability results in Section 5.3.1, where it was determined

that TZN2 and TZN3 represented promising base glasses for optical fibres due to

the large ΔT values and, in the case of TZN3, very small enthalpy of crystallisation,

we decided to focus the efforts to create a second order nonlinearity in these glasses.

Furthermore, we had many more TZN2 glass samples than any other composition and

as the process of thermal poling, as will be discussed, is often destructive most of the

poling results are for TZN2.

In the following sections the two poling techniques are discussed separately and the

results for each are presented in each respective section. The successful generation of a

second order nonlineariry is determined by exposing the poled sample to the output of a

Q-Switched Nd:YAG laser operating at 1064 nm, and 10 Hz. The SH signal is detected

with a photomultiplier tube and an oscilloscope. This measurement provides a yes/no

answer to weather or not a second order response has been generated. Subsequent to

this measurement, a precise determination of the vale of χ(2) is made via the Maker

fringes experiment (Section 8.1).

7.4.1 Charge Migration Thermal Poling

Thermal Poling of Infrasil

As a test of the performance of the thermal poling apparatus and the Makers fringes

experiment, that was constructed for determining the value of the induced nonlinear

coefficient (see Section 8.1), we commenced this work by thermally poling a commercial

fused silica glass, Infrasil 301. There are many reports of the successfully poling of

this material [98–102], additionally, many analytical techniques have been developed

for studying the depletion region that is formed [98, 101–104] and finally, an excellent

theoretical model that describes the charge migration dynamics has been established

[105]. This being such a well studied material it makes an ideal test material for our

experiments and procedures.

The poling conditions for the Infrasil sample were chosen intentionally to produce a

sample with a low χ(2), as a means of testing the limitations of the characterisation

experiment described in Chapter 8. From the work of Triques et al. it is known that

the observed second harmonic signal is smallest for samples poled for long times, i.e.

greater than 90 min at 280◦C [99]. Therefore we used the following poling conditions:

A 1 mm thick Infrasil disc was thermally poled between two stainless steel electrodes

at 290◦C for 90 min with an applied potential of 4 kV. No attempt was made to record

Chapter 7 135

the current during the poling, however, it was noted to be approximately 18 μA at the

commencement of the poling and ≈ 0 at its completion.

We recorded a non zero second order response from this sample using the Maker fringes

experiment. In Section 8.1 there is a detailed discussion relating to the measurement of

the induced nonlinearity.

Thermal Poling of Tellurite

Using the TZN2 glass we assessed the possibility of charge migration thermal poling using

doped silicon electrodes in physical contact with the glass sample. The temperature was

set to 250◦C and the applied voltage was increased from 0→2.5 kV at a rate of 100 V

every 10 s. This enabled the current to stabilise between each voltage step also helping

to avoid thermal run away and dielectric breakdown [106]. It was determined that, at

the elevated temperature of 250◦, for voltages above ≈2.5 kV the sample underwent

dielectric breakdown. The current through the sample was recorded at each voltage,

this relationship is plotted in Figure 7.4. The axis of Figure 7.4 have been chosen such

that a linear fit to the data provides us with the resistance via Ohm’s Law, V = IR.

We find the resistance of the TZN2 glass at 250◦C to be 6×107 Ω. With a sample

thickness of ≈ 1 mm and an electrode surface area of ≈ 1.27 cm2 the corresponding

resistivity ρ is equal to 7.3×108 Ω.cm. For comparison the resistivity of fused silica is

1011 Ω.cm [107] at 250◦C.

The next step in the process is to hold the voltage constant for some period of time to

allow the migration of charge and the formation of a depletion region. The formation of

a depletion region will be observable as an increase in resistivity and therefore a decrease

in the poling current. The explanation of this assertion is based on the fact that as we

form the depletion region the number of charge carriers decreases which means that the

conductivity of that thin region of glass decreases. Thus, the resistivity increases and

the voltage drop across the depletion region increases via Ohm’s Law. This effect has

been reported for glasses that pole via charge migration [106].

In Figure 7.5 are the data taken over 1 h of constant voltage for the TZN2 sample. Note

that the current in fact increases over this time period, indicating that no depletion

region was formed. A possible explanation for this observation is that at this temperature

and in this poling configuration the sample is conducting electrons from the cathode to

the anode. These electrons can then in turn alter the oxidation state of the cations within

the glass and thus change the conductivity. In particular if the redox state of Te4+ or

were to change to produce elemental metallic Te then we would naturally expect the

conductivity to increase. We see evidence for this in Figure 7.6 which shows an optical

micrograph of the cathodic surface of the glass sample in question. There is evidence

136 Thermal Poling

0.0 1.0x10-5 2.0x10-5 3.0x10-5 4.0x10-5 5.0x10-50

500

1000

1500

2000

2500

3000

3500

DATA Linear Fit

Vol

tage

[V]

Current [A]

Figure 7.4: Ohms law plot for TZN2 at 250◦C. Blue squares: Data for TZN2 andlinear fit in red.

Figure 7.5: Time dependence of the current through TZN2 at 250◦C.

Chapter 7 137

of chemical reduction of Te4+ →Te in the region of contact between the cathode and

the glass at the left of Figure 7.6. The dark spots are thought to be evidence of this

reduction. The part of the sample that was in the vicinity of the edge of the silicon

electrode has a higher concentration of these dark regions, which is consistent with the

higher field strengths encountered at the edges of a conductor.

Figure 7.6: Optical micrograph of the cathodic surface of TZN2 after thermal poling.The region to the left was in contact with the Si electrode.

The phenomenon of chemical reduction at the cathode has been reported for certain

tellurites [91] as well as other non-silica glasses [24]. In particular Deparis et al published

a photograph of the cathodic surface of a bismuth borate glass that experienced chemical

reduction (reproduced in Figure 7.7) the appearance of which closely matches what is

observed in the TZN2 glass. Deparis et al analysed the sample with x-ray photoelectron

spectroscopy (XPS) and found that the proportion of oxygenated bismuth is significantly

reduced in the dark features. Thus indicating that the bismuth was indeed reduced into

metallic bismuth. We observe similar features in the thermally poled TZN2 sample.

Another possible cause for the increase in conductivity would be the establishment of

microscopic cracks in the sample. Such a crack can conduct electrons on the surface of

the material instead of through the volume. Surface conductivities are, in general, higher

than volume conductivities which would match with the observed change in current. The

microscopic inspection of the sample did not show unequivocal evidence for micro cracks,

however, higher spatial resolution may be required.

Following the period of constant voltage and temperature, we decreased the temperature

to ambient in two steps: First, from 250→200◦C at 5◦C.min−1 then from 200→30◦C at

a cooling rate of 3◦C.min−1. We used such a slow cooling rate to avoid breaking the

138 Thermal Poling

Figure 7.7: Reproduction of the chemically reduced region at the cathodic surface ofa Bismuth borate glass. Inset scanning electron micrographs of the individual particles.

(Reproduced from [24]).

tellurite, as it was observed to be an extremely fragile material that would often break

upon cooling.

Notice, that in Figure 7.5, after the initiation of the cooling period the current initially

decreases from ≈ 7.5 μA to ≈ 6.5 μA and then remains constant. We stopped recording

when the sample had reached 150◦ because it was noticed that the sample had cracked

and was discharging through this crack.

The sample did produce light at 532 nm when exposed to the output of a Q-switched

Nd:YAG laser. However, further investigations revealed that this was, in fact, due to

ablation of the surface caused by the strong optical absorption of the black particles

on the cathodic face. The ablation produced white light the 532 nm component of the

white light made it to the PMT and was incorrectly recorded as a SH event. Therefore,

we cannot state definitively whether or not a second order response was induced.

7.4.2 Charge Migration Thermal Poling Using a Blocking Electrode

In an effort to pole the tellurite glass via charge migration while avoiding chemical

reduction at the cathode we trailed two blocking electrode configurations as shown in

Figure 7.8.

Chapter 7 139

Figure 7.8: Two possible configurations for the blocking electrode thermal polingtechnique (anodic sides towards the top). (A) A borosilicate blocking electrode is inphysical contact with the glass to be poled. The poling electrodes are n-type siliconfor the anode and stainless steel (s.s.) at the cathode. (B) The borosilicate blockingelectrode is separated from the glass to be poled by a p-type silicon wafer. The poling

electrodes are the same as for (A).

Tellurite Sample A

The configuration shown in Figure 7.8 (A) has a doped silicon anode and a stainless steel

cathode, of which the anode is in physical contact with the tellurite (TZN2), blocking

the flow of electrons from the cathode is a 0.15 mm thick borosilicate microscope cover

slip. Borosilicate is a good choice for a blocking electrode as it has a relatively high

ionic conductivity at elevated temperatures as well as a very low electron conductivity.

It is thus able to prevent the flow of electrons from the stainless steel cathode with out

reducing the field across the sample.

We equilibrated the temperature of the assembly to 250 ◦C then increased the voltage

across the electrodes from 0→3.0 kV at 100 V every 10 s. The voltage was then held at

3.0 kV for 1 h.

Plotted in Figure 7.9 (blue squares) are the data for this experiment. Note that once

the voltage is held constant that the current steadily decays then, during the cooling

phase the current further decreases to zero.

A current profile such as this is consistent with the formation of a depletion region. As

the decrease in current is associated with an increase in the resistivity of the ion depleted

layer. After the sample was removed from the oven and inspected, three things were

observed. First, the tellurite sample was stuck to the borosilicate cover slip. Second,

the tellurite was severely cracked and third there was a white precipitate on the cathode

From these observations we conclude the following: Charge migration occurred in the

borosilicate glass whereupon Na2+ left the glass and deposited itself on the cathode. The

Na2+ combined with atmospheric oxygen to produce oxides of sodium. The migration

140 Thermal Poling

Figure 7.9: Time dependence of the current for TZN2 in the two blocking electrodeconfigurations as shown in Figure 7.8. Blue squares: Data for configuration (A). Red

circles: Data for configuration (B).

of positive charges away from the anodic side of the borosilicate produced a strong elec-

trostatic attraction between the cover slip and the tellurite. Upon cooling, the difference

in thermal expansion coefficients between tellurite and borosilicate induced stress in the

tellurite which ultimately cracked under the compressive forces. This produced irregular

glass fragments with dimensions of ≈ 2× 2 mm.

We were unable to determine if a second order nonliearity was induced in the sample,

due to the difficulties in mounting such small, irregular samples and directing the probe

laser beam through them at angles sufficient to observe second harmonic generation

(θ ≈ 60◦, for details of this experiment see Chapter 8).

Tellurite Sample B

Following this we repeated the experiment, instead using the configuration (B) in Figure

7.8. The same temperature, voltage and times as were used for the configuration A were

applied here. As shown in Figure 7.9 (red circles) the dynamics of the process are

subtly different. The key differences are that the maximum achieved current is slightly

smaller. Secondly, the decay of the current during the constant voltage and temperature

phase of the experiment essentially halts after ≈ 15 min then remains constant until the

temperature is decreased. The first observation can be explained by the added resistance

Chapter 7 141

introduced by the p-type silicon, which has quoted resistivity range of 1-20 Ω.cm, as well

as the resistance of the interfaces, the value of which is difficult to estimate. As for the

constant current during the period of constant voltage, we believe that a surface current

was established during this period thus corrupting the data. Supporting this claim is the

visual observation of arcing across the surface immediately prior to the cooling period.

After the sample had cooled it was inspected and the following observations were made.

The tellurite sample had a dark area where the p-type silicon had been in contact with

it just as did the sample poled between two silicon electrodes (see Section 7.4.1). As

the flow of electrons should, in principal, be blocked by the borosilicate then the p-type

silicon must have acted as a source of electrons which caused chemical reduction of the

tellurium ions. It was also noted that there was a white precipitate on the cathode, most

likely Na2O. Therefore, there was a reasonably high electric field across the borosilicate

and so there must have been conduction of charge through or across the tellurite.

Sample B displayed the same tendency to ablate at the cathodic surface as did the TZN2

sample poled in between two silicon electrodes with no blocking electrode.

7.4.3 Charge Injection Thermal Poling

The charge injection method is by far the most common approach towards poling tellurite

glass. Of particular relevance is the work done by Narazaki et al where sodium zinc

tellurites were studied [94]. They report a maximum d33 of 0.23 pm.V−1 for sodium

containing zinc tellurites with an optimised poling temperature that depends on the Tg

with the following linear relationship:

Tp = 0.72× Tg + 45 (7.1)

Using Equation 7.1 to predict an optimal poling temperature for TZN2 and TZN3 we

obtain Tp ≈ 250◦C.

Using this poling temperature we attempted to thermally pole TZN2 and TZN3 glass

samples of 1 mm thickness sandwiched between two commercial borosilicate microscope

cover slips1. The poling configuration is illustrated schematically in Figure 7.10,

where the electrodes are made from stainless steel and the blocking electrode is a borosil-

icate microscope cover slip. Following is the descriptions of the TZN2 and TZN3 exper-

iments covered separately:

1Frequently in the cited references these are referred to as ’microscope slides’. This is an unfortunatemisuse of the language. Microscope slides are ≈ 1 mm thick, the electric fields that result when thisthickness of glass is used are insufficient for poling.

142 Thermal Poling

Figure 7.10: Charge injection thermal poling configuration (anodic sides towards thetop). The glass to be poled is sandwiched in between two commercial borosilicatemicroscope coverslips which are sandwiched in between two stainless steel electrodes.

TZN2 Charge Injection Thermal Poling

We sandwiched a 1 mm thick sample of TZN2 in between two borosilicate microscope

cover slips as per Figure 7.10. This in turn was placed between two stainless steel

electrodes and placed in an oven. Once the temperature of the assembly had equilibrated

at 250◦C for approximately 1 h the voltage across the electrodes was steadily increased

in 100 V steps up to 3.0 kV. We then held this voltage and temperature for 60 min

before decreasing the temperature to ambient with the voltage held constant.

Figure 7.11 shows the time dependence of the current through the poling circuit. As

can be seen, the increase in current is linear during the initial stage of the experiment

while the voltage was being increased linearly with time. Subsequent to this there is an

observed decay in the current during the phase of constant voltage. This is produced by

the migration of charge and the associated increase in resistivity due to the depletion of

charge carriers.

After the sample had cooled, it was dismantled and inspected. The TZN2 sample cracked

into small pieces, and physically stuck to the borosilicate cover slip at the cathodic

side. As with the experiment in Section 7.4.2 we believe that these two observations

can be explained by the electrostatic attraction between the TZN2 sample and the ion

depleted anodic surface of the cover slip. This sticking produces a stress on the glasses

during thermal contraction. We made visual inspections of the sample at several stages

during the poling process and this cracking only began to appear during the temperature

decrease phase of the experiments.

The size of the fragments was approximately 2× 2 mm, consequently we were unable to

measure the induced nonlinearity.

TZN3 Charge Injection Thermal Poling

The experiment above was repeated using a sample of TZN3 and a slightly lower poling

Chapter 7 143

Figure 7.11: Time dependence of the current for TZN2 in the charge injection con-figurations.

temperature of 230◦C. We used this new poling temperature to see if there was any

effect on the sample destruction that always accompanied the use of a borosilicate cover

slip as a blocking electrode. With reference to the data presented in Section 5.3.2, the

coefficient of thermal expansion of TZN3 is similar to TZN2.

The time dependence of the current was not recorded in for this experiment, however,

it was noted that the current did follow approximately the same profile as for the TZN2

charge injection thermal poling experiment above. i.e. there was an initial linear in-

crease of current during the voltage ramping phase, an exponential-like decay during

the constant temperature and constant voltage phase, followed by a more rapid decay

during the temperature decrease phase.

The observations made after the sample had cooled were consistent with the TZN2

experiment. The average size of the fragments was ≈ 4× the size of the TZN2 fragments.

By chance one fragment was just large enough to use for a SHG measurement, which is

described in the following Section 8.1.

144 Thermal Poling

SHG was detected coming from the TZN3 sample. Further measurements were made of

its angular dependence and are shown in Section 8.1.

7.5 Conclusion

Thermal poling experiments were performed on the TZN2, TZN3 and Infrasil 301

samples. Both poling configurations were explored for the tellurite glasses.

In the charge migration configuration we observed, relative to Infrasil, high conductiv-

ities as well as probable chemical reduction of the tellurium ions. We were unable to

determine if a second order nonlinearity had been produced because the formation of

black particles on the surface which ablated when exposed to the pulsed laser radiation.

The high conductivities can be attributed to the tellurite glass possessing a relatively

high proportion of sodium ions. For comparison, Infrasil has approximately 1 ppm of

sodium where as the tellurite glass has approximately 100,000 ppm. We note that there

was not a 5 order of magnitude difference between the observed conductivities of the

Infrasil and tellurite and thus there are necessarily other factors to consider. Factors

such as; different mobilities of the sodium ions in the two glasses and the reduction of

the tellurium could also contribute.

Tellurite glass poled via the charge injection method developed a white precipitate,

most likely an oxide of sodium. Additionally, the structural integrity of the glass in

compromised when poled in this manner. Thus resulting in significant cracking of the

sample. Second harmonic generation was observed from charge injection thermally poled

tellurite glass.

In terms of future work, the development of thermally poling tellurite based optical fibres

is likely to be challenging. The charge injection method, which was shown to produce

a non zero χ(2), is not feasible in the fibre format. The electrodes must be positioned

near the core of the fibre (see Figure 7.12) and thus are internal to the fibre and, given

current knowledge, it is not possible to have a ion source in between the anode and the

tellurite glass. The charge migration method, may or may not produce a non zero χ(2),

however it is now known that significant chemical changes occur in the region of contact

between the glass and the electrode. In a fibre this will compromise the strength of the

fibre as well as its optical absorption.

The problem of chemical reduction at the cathode could also be detrimental for a ther-

mally poled fibre, however, a very encouraging result from Margulis et al shows that a

fibre may be poled in the charge migration configuration with both internal electrodes

acting as the anode [108]. In this case the cathode, or ground potential is provided by

Chapter 7 145

Figure 7.12: Schematic illustration of the electrode configuration for thermal polingof optical fibres. This cross section of the fibre shows the core positioned bewteen the

two internal electrodes which are provided via the technique in Section 9.3.

ionisation of the air surrounding the fibre and so the exterior surface behaves as the

ground. After charges begin to migrate from near the anodes towards the surface of

the fibre the resistivity of the glass immediately next to the electrodes increases causing

the potential at the fibre core to decrease. As this process progresses, the potential

difference between electrodes and core increases, pushing the depletion region towards

the core and thus poling the fibre. Fibres poled via this method have shown a factor of

2 increase in the achieved χ(2) [108].

Figure 7.13: Simulated equipotential maps prior to (a) and during (b) poling withtwo anodes. (c) Initially Na+ ions are evenly distributed the voltage drop is mainlybetween the electrodes and the surface of the fibre. (d) After charges have migratedthe resistivity of the glass around the electrodes increases and the voltage drop acrossthe core increases. distributions for fibres with two anodes. Reproduced from [108].

This result offers a promising solution to the problem of chemical reduction at the cath-

ode for thermally poled tellurite fibres, as it takes the reducing electrode (the cathode)


146 Thermal Poling

out of the vicinity of the fibre core. It is also probable that the enhanced χ(2) observed

in silica fibres will also be seen in tellurite fibres.

It is our conclusion that the only potentially feasible way to thermally pole an optical

fibre made from the tellurite glasses under study is the dual anode poling as reported

by Margulis et al [108]. As this will avoid the precipitation of metallic tellurium in the

vicinity of the core.

Chapter 8

Measurements of Second Order

Nonlinearities

8.1 Introduction

At the outset of this work our goal was to thermally pole the glass compositions

deemed most suitable for optical fibre fabrication under various conditions of tem-

perature, voltage and poling time. These samples would then have their second order

nonlinear properties measured so as to determine optimal compositions and poling con-

ditions which could then be investigated in the fibre format eventually leading to χ(2)

fibre devices. The complexities of thermally poling these glasses was not anticipated,

primarily due to the lack of definitive information in the literature. That being so, the

anticipated requirement of characterising the thermally poled glasses necessitated the

development of an experimental apparatus for measuring χ(2) as well as various compli-

mentary characterisation techniques whereby the spatial extent of the poled region in

the glasses could be investigated. This work progressed in parallel to the thermal poling

program during which much progress was made in the understanding of the experimental

techniques and data analysis.

There are several techniques for measuring the second order nonlinear properties of

materials such as parametric florescence, difference frequency generation and second

harmonic generation techniques such as Maker fringes [109]. Based on a review of the

literature it was determined that the Maker fringes technique was the most suited for

measuring the nonlinear properties of thermally poled glass samples. The nonlinear

region in these samples is typically very thin, ≈ 10 μm, thereby ruling out parametric

florescence and difference frequency generation which require long sample lengths in

order to increase signal to noise levels [109].

The following sections describe the Maker fringes technique, including a qualitative

description of the origin of the fringes (a derivation of the Maker fringes can be found

147

148 Measurements of Second Order Nonlinearities

in Section 2.3.2), the design and characterisation of the experimental apparatus as well

as the data analysis techniques. Measurements of the second order nonlinear properties

of a quartz reference sample, thermally poled Infrasil and tellurite glass are presented

in Sections 8.5.1, 8.5.2 and 8.5.3 respectively.

We explored two methods for determining independently the spatial extent of the nonlin-

ear region. The impetus for this stems from the reliance on the accuracy of the measured

χ(2) values on the accurate knowledge of the size of the thermally poled region. The

Maker fringes analysis does provide a measure of this region, however, in order to be

certain of the results we obtained independent measurements. Two techniques were iden-

tified in the literature as being suitable, namely: Second harmonic microscopy (Section

8.6.1) and differential etching (Section 8.6.2) [86, 101, 110].

8.2 Maker Fringes Analysis: Background

The predominate technique for determining the strength of the second order nonlin-

ear susceptibilities of a material is the Maker fringes analysis. Maker fringes were

first discovered by Maker et al [111] in 1962, shortly after the the invention of the laser

and the advent of nonlinear optical research. Maker’s experiment (Figure 8.1) involved

exposing a quartz plate to the output of a ruby laser, the transmitted light was filtered

to remove the red light and the blue SHG light was detected. The quartz sample was

rotated about its crystalline Z axis and the change in power of the blue light signal was

recorded as a function of incidence angle (Figure 8.2).

Ti:Sapphire �Detector

Blue Filter

Quartz plate

Figure 8.1: Experimental configuration for Maker et al. original Maker fringes exper-iment. The high intensity light from a Ti:Sapphire laser in passed through a sample ofquartz. The quartz is rotated with respect to the incident beam by an angle θ. A filter

removes the red light from the beam and the generated blue SH is detected.

A theoretical description of the Maker fringes was first put forth in a paper by Jer-

phagnon and Kurtz (JK) [112] in 1970. In Section 2.3.2, we have derived a version of

the Maker fringes expression that closely resembles that of Jerphangnon and Kurtz.

Jerphagnon and Kurtz made certain assumptions when deriving the expression, such as

no reflection of the SH at the material/air interface, no wavelength dispersion in the

Chapter 8 149

Figure 8.2: Maker fringes for quartz first measured by Maker et al. Reproduced from[111].

refractive index (i.e. nω = n2ω) and no absorption of the fundamental or SH waves. In

1995 Herman and Hayden (HH) published an extended theory of MF that accommodated

for these additional effects. The HH Maker fringes expression is applicable for materials

that have high refractive index, thus making the reflection at the material/air interface

appreciable, high dispersion, or materials that are absorbing at either of the frequencies.

To demonstrate the difference between the JK Maker fringe and those of HH we have

plotted the theoretical fringes for a y-cut quartz with a thickness of 2 mm as shown in

Figure 8.3.

With reference to the two sets of fringes in Figure 8.3 the observed detail can be explained

by braking it down into four separate contributions:

� Maker fringes are characterised by a small scale modulation seen on the order

of 10’s of degrees (Figure 8.2). This occurs because the effective thickness of the

material changes with angle. The effective thickness increases as t cos θω, where t is

the actual thickness of the material and θω is the incidence angle. As this thickness

increases the optical path difference between the fundamental, bound SH and free

SH waves changes. Thus the fringes in the pattern are in fact interference fringes

produced by the interaction between the three propagating waves.

� On a very small angular scale (Δθ � 1◦) there is a high frequency interference

pattern that results from SH interfering with reflected SH in the nonlinear material.

JK’s analysis did not predict this because they assumed that the reflection of the



Figure 8.3: Simulated Maker fringes with the inclusion of higher order interference(red line) and without (blue line).

SH is negligible. They are predicted by the analysis of Herman and Hayden [113],

however, researchers rarely use an angular resolution sufficiently small to resolve

them. The red line in Figure 8.3 shows the simulated Maker fringes for y-cut quartz

with the higher order interference included. The HH Maker fringes expression is

derived assuming that the light is composed of infinite plane waves. Therefore, this

high order interference is observed for all incidence angle. In reality a laser is used

to probe the Maker fringes. Laser beams have finite widths thus at larger angles

the reflected beam does not overlap well with the transmitted beam. Therefore

this interference will only be observed at incidence angles near to normal incidence.

� The envelope of the fringes is determined by the effective nonlinear coefficient deff

(Equation 2.76) which, depending on the material, generally has a period of the

order of 45 �◦ θ � 90◦, and the Fresnel reflection and transmission coefficients at

the fundamental and SH.

Subsequent to their initial Maker fringes paper, Jerphagnon and Kurtz applied the

measurement of Maker fringes to characterising relative nonlinear susceptibilities for

several materials [114]. This was the beginning of Maker fringes analysis and today it

is the most common technique for determining second order nonlinear coefficients.

Chapter 8 151

8.3 Experimental Details

8.3.1 Experimental Plan

The experimental plan for the determination of the second order nonlinear coefficients

for the thermally poled samples was developed under the following considerations:

� There is no way to know in advance the magnitude of the nonlinearities that could

be induced in the samples. Therefore we were guided by results in the literature to

give an indication of what to expect. As per the information collated in Table 7.1

tellurite glasses have been observed to possess χ(2) in the order of 1 to 0.1 pm.V−1.

Accordingly, it was deemed necessary for the Maker fringes apparatus to be capable

of measuring nonlinearities at least one order of magnitude lower than the lowest

value reported in the literature, i.e. 0.01 pm.V−1.

� It is always possible to measure a low nonlinear coefficient by using higher intensity

laser pulses to produce a measurable amount of SHG. Provided, that is, that

the laser pulse is not sufficiently intense as to ablate or damage the material

under study. The problem we face is that tellurite glasses have low laser damage

thresholds. Literature reported results indicate that tellurites have surface damage

thresholds in the order of 10 GW.cm−2 which, for comparison, are three orders

of magnitude lower than silica (7 × 103 GW.cm−2) [60]. We therefore sought to

design a Maker fringes experiment that had high SHG detector sensitivity and

high signal to noise rather than high laser intensity.

These considerations and the overall design of the Maker fringe experiment are addressed

in the following Section 8.3.2.

8.3.2 Description of Maker Fringes Experiment

We constructed a Maker fringes measurement system (see Figure 8.4) described as fol-

lows:

The fundamental excitation source was provided by a modified Spectra Physics Quan-

taRay GCR-16 that produces p-polarised, 10 ns, Q-switched pulses at 1064 nm with

a pulse repetition rate of 10 Hz. We introduced an intra-cavity aperture of ≈ 3 mm

diameter to force the laser to run in a Gaussian-like transverse mode.

First the output of the laser is passed through an edge filter with > 99.9% attenuation

below 550 nm. This element was critical as it eliminated the flash lamp light from


Nd:YAG1064nm

PM

T1

�/2 L1

L3

L2

F532

ND

P2

DAQ

PC

Power Reference(Quartz)

Sample

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50:50

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PD

PM

T2

DM

SP

F532P3

Oscilloscope

Figure 8.4: Configuration for the Maker fringes experiment. Red dotted lines: Op-tical path for the fundamental beam. Green dotted line: Optical path for the secondharmonic beam. LP: Long pass (> 550 nm) filter. W: Glass wedge. λ/2: Halfwaveplate. P1-3: Polariser. M: Mirror. L1-3: Lens. ND: Neutral density filter. DM:Dichroic mirror. SP: Short pass (< 600 nm) filter. F532: 532 nm laser line filter. PD:

Photodiode. PMT1-2: Photomultiplier tube. Grey lines: Electrical connections.

the beam path which contained a significant amount of light at the SH (532 nm). To

maintain intensities sufficiently low to ensure that the samples are not damaged we

attenuated the output via reflection from a glass wedge (W). This provided a nominal

pulse energy of 200 μJ as determined by the calibrated photodiode (PD).

The light passed through the wedge is directed into a beam dump (BD). Additional

control of the pulse energy was achieved with a half wave plate (λ/2) and polariser (P1)

combination.

The beam is then directed through a second λ/2 plate to allow control of the polarisation.

The beam is focused with a 20 cm focal length lens (L1) through a 50:50 non-polarising

beam splitter, provides us with two focused fundamental beams with pulse energies of

100 μJ each. We calculate the intensity at the focus to be in the order of 10 MW.cm−2,

i.e. three orders of magnitude below the reported damage threshold of tellurite glass

[60].

One of the beams was directed onto the sample under study, which is mounted on a

computer controlled rotation stage. The SHG that is produced in the sample, as it

Chapter 8 153

is rotated about the input beam, is collected by the lens L3. We attenuate the SH

signal with a calibrated neutral density filter (ND) the strength of which depends on

the sample being used and is chosen to reduce the signal to coincide optimally with the

dynamic range of the detector electronics. Residual fundamental radiation is filtered

from the signal by two dichroic mirrors (DM), with approximately 70% transmission at

1064 nm, a short pass filter (SP) and a 532 nm laser line band pass filter (F532) which

is mounted directly onto a photomultiplier tube (PMT1). This combination of filters

provides approximately 83 dB suppression of the fundamental wavelength.

Prior to detection a polariser (P2) is used to select a specific polarisation state the nature

of which depends on the material under study and the form of its nonlinear susceptibility

tensor.

The other focused fundamental beam is passed through a reference sample of y-cut

quartz which is held at a fixed angle to the beam. The signal is conditioned in the

same was as for the sample and detected with a photomultiplier tube (PMT2). The

second harmonic radiation generated from this sample was used as a reference channel

to normalise the power fluctuations in the sample under study. Normalising to the SHG

signal is preferable to normalising to the laser output power as the SHG is sensitive

to the square of the laser power and thus provides a more sensitive measure of the

fluctuations in that power. In order to minimise stray light signals from the room the

entire apparatus is contained within a light tight box.

8.3.3 Data Acquisition

We designed a built the data collection system for the MF experiment. The system is

comprised of a pulse conditioning and sampling system in combination with a 16 bit

dynamic range National Instruments data acquisition (DAQ) module (USB-6210) and a

PC running LabView1.The electronic circuit diagram for this system is shown in Figure

8.5.

The following list details the sequence of events that take place during the data acqui-

sition:

1. The flash lamp synchronised trigger signal is sent to the system which initiates the

sample and hold (S/H) timing.

1The Author specified the requirements of the system which was then designed and built by Mr.Neville Wild and Mr. Bob Nation.


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UT

39R

Figure 8.5: Circuit diagram for the Maker fringe data conditioning and acquisitionsystem. Pulse conditioning circuitry for one input channel shown on left. This is dupli-cated in the device for the additional input channel. The pulse conditioning circuitryis powered from an external DC supply (shown bottom right of Figure). The pulsesampling circuitry (shown in the centre of the Figure) is utilised for both inputs. All

other power is supplied by the USB-6210, internal circuitry not shown.

Chapter 8 155

2. Shortly after, a pulse from each of the PMTs enters a charge sensitive amplifier.

This integrates the voltage pulse producing a signal the peak of which is propor-

tional to the total charge in the pulse, which is in turn proportional to the power

in the optical pulse.

3. We shape the short, asymmetric output from the charge sensitive amplifier by

using low pass filters to produce a ≈ 100 μs long symmetric pulse with a peak

voltage which is still proportional to the optical power.

4. We then use a sample and hold circuit to sample the peak of the shaped pulse.

5. The output of the sample and hold is acquired by the DAQ and sent to the PC.

The LabView program that controls this process is also responsible for controlling the

angular position of the sample rotation stage and dividing the sample signal by the

reference signal.

8.3.4 Calibration and Alignment

The linearity of the detectors was investigated to identify the optimal operating condi-

tions. For PMT bias voltages of 1500 V and 2000 V we used a series of calibrated neutral

density filters to attenuate the signal generated from a y-cut quartz sample which was

oriented at an angle, ≈ 10◦, to the incident beam that maximised the SHG signal (see

Figure 8.10). The plots in Figure 8.7 show that the detector has a linear response up

to approximately 4.5 V independent of PMT bias voltage. As such, we ensured that all

acquired signals were appropriately attenuated to ensure that the signal fell below this

value.

We determined the number of pulses needed to ensure a measurement error below 1%

buy collecting data on the signal (CH1), reference (CH2) and the normalised signal

(CH1/CH2) channels. Using the LabView program we collected the standard error,

represented as a percentage and plotted this data as a function of the number of pulses.

Figure 8.8 shows this data. When the number of pulses exceeds ≈ 150 the relative

error is < 1% in the normalised signal thus ensuring an accuracy in calculated nonlinear

coefficients of approximately the same order.

It is important that the focal point of the beam coincide with the rotation axis of the

sample otherwise, as the sample rotates, the sample will either move away from or

towards the focal point thus altering the intensity at the sample.This makes the Maker

fringe appear asymmetric thus increasing the error in the nonlinear coefficient. For

the alignment transverse to the beam a 0.1 mm diameter aperture was mounted in the


Figure 8.6: Timing diagram for the Maker fringes experiment data acquisition system.

sample holder which was translated on a micrometer driven stage orthogonal to the

beam to maximise the optical throughput.

The position of the sample relative to the focus of the beam is also critical for an

accurate measurement of the Maker fringes. It was shown by Jerphagnon and Kurtz

that the minima of the fringes are influenced by the divergence of the beam [112] which

must be minimised. The optimal position for the sample is therefore at the focal point.

Also, the Rayleigh range should be made to be large compared to the sample thickness

to minimise the divergence at the sample.

Chapter 8 157

y = 25.045x + 0.08R² = 0.9966

y = 424.35x + 0.3287R² = 0.9607

0

1

2

3

4

5

6

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

PMT

Sign

al [V

]

Transmission

1500V2000VLinear (1500V)Linear (2000V)

Figure 8.7: Photomultiplier tube output signal vs. fractional transmitted intensityfrom the y-cut quartz reference oriented at 10◦ to the beam to ensure maximal SHG(see Figure 8.10) Red triangles: Data for 1500 V bias with linear fit. Blue squares:

Data for 2000 V bias with linear fit.

To ensure that the sample is correctly positioned longitudinally, with respect to the

focus, we mounted the focusing lens on a translation stage and recorded the SH signal

generated from a thermally poled Infrasil sample, which has its nonlinear region at the

surface, at various lens-to-sample separations. We have plotted the second harmonic

power P2ω, vs the micrometer reading on the lens translating stage in Figure 8.9 (Red

circles). It is clear from the data that the micrometer reading of 10.5 mm corresponds

to the maximum SHG signal and thus the position at which the sample is at the focal

point. This is because the second harmonic power is proportional to the intensity of the

fundamental to the second power and thus P2ω ∝ 1/w4 where w is the beam radius.

Interestingly, if we plot P−1/42ω vs position we have a parameter that is proportional to

the beams radius and its dependence on position. From the theory of Gaussian beams

[115] the expression for the beam radius as a function of the propagation coordinate is

w(z) = w0

[1 +

(z

z0

)2]1/2

(8.1)

where w0 is the beam radius at the focus and z0 is the Rayleigh range given by

z0 =πw2

0

λ(8.2)


0 100 200 300 400 500 600 700 8000

1

2

3

4

5

6

7

8R

elat

ive

Erro

r [%

]

Number of Pulses

CH1 CH2 CH1/CH2

Figure 8.8: Relative error in the Maker fringes data vs number of pulses averagedover.

By first fitting a function of the form

w(z) = a

[b

(1 +

((z − c)λ

bπ

)2)]1/2

(8.3)

we are able to find the constants a, b and c where a is the scaling constant to turn the

arbitrary units from the measurement into beam radius in mm. The constant c is the

horizontal shift required to put the waist at z = 0 and b = w20. In so doing we find that

a = 7.72, w0 = 0.096 mm and c = 10.5 mm. Using this information and Equation 8.2

we calculate the Rayleigh range to be z0 = 27 mm.

We stress that this measurement has limited accuracy due the measurements being made

close to the waist and, in particular, no far field measurements being made. Neverthe-

less, this measurement indicates that, to a reasonable approximation, the beam can be

considered Gaussian and therefore the standard expressions for the Maker fringes can

be applied. Furthermore, the Rayleigh range is > 10× the thickness of the reference

quartz sample and so the divergence problem is avoided.

Chapter 8 159

-5 0 5 10 15 20 252.0

2.5

3.0

3.5

4.0

P2ω

P 2ω [a

rb. u

nits

]

Position [mm]

0.72

0.74

0.76

0.78

0.80

0.82

0.84

0.86

P2ω

-1/4

Gaussian Fit

P 2ω-1

/4 [a

rb. u

nits

]

Figure 8.9: Red: Plot of SH power vs lens to sample separation. Blue: P−1/42ω vs lens

to sample separation and Gaussian beam fit to data.

8.4 Data Fitting Techniques

In general, determining the value of the second order nonlinear coefficient for a material

involves; first recording the Maker fringe for a material with a known second order

nonlinear coefficient, fitting the theoretical Maker fringes expression (Equation 2.62) to

the data then under identical conditions (i.e. laser power, beam spot size, etc) recording

the Maker fringes for the sample under study and fitting Equation 2.62 to the data.

The fitted equations can then be compared to provide a relative measure for the second

order coefficient of the sample.

The fitting and subsequent calculation of the nonlinear coefficient is what we refer to as

‘Analysis’. The following is a discussion of the steps required to preform this analysis.

The expression for the Maker fringes is given by Equation 2.62, which, for convenience,

is reproduced below:

P2ω(θi) =(T a→g

ω )2T g→a2ω ω2

Ac3ε0n2ωn2ω cos2 θtω

P 2ω

(2πL

λ

)2

d2effsin2Ψ

Ψ2


The Makers fringes expression can be written simply as a function of incidence angle,

θi by applying Snell’s law. We make the replacement θi → θ and collect the constants

into a single constant, α, in order to simplify the expressions. We can therefore write

Equation 2.62 as:

P2ω = αL2T (θ)d(θ)2Ψ(θ) (8.4)

where we have summarised the contributions to the expression in terms of the inter-

ference term Ψ(θ) = sin2Ψ/Ψ2, the transmission term T (θ), and the angular part of

the effective nonlinear coefficient d(θ) which depends on the material in question, its

orientation and the input and output polarisation. Note that we are making a relative

measurement and will thus be interested in a ratio of the constant α for the two mate-

rials. We can therefore neglect the common constants such as c and ε0. Furthermore,

the power measurements are normalised and so Pω is equal to unity. By making these

considerations we obtain

α = d2 (8.5)

where d2 = d2ij which is simply the square of the particular element of the second order

nonlinear susceptibility tensor under study.

If we acquire the Maker fringes data for a reference sample and fit Equation 8.4 to the

data we obtain a reference value of α = αr. We then record the Maker fringes for the

sample under study, making sure that the same experimental conditions are used, i.e.

laser power and beam area. After fitting Equation 8.4 to this data we have the sample

value of α = αs. The ratio of αs/αr can be used to calculate the value of the nonlinear

coefficient for the sample by:αs

αr=

(dsdr

)2

(8.6)

Thus

ds = dr

√αs

αr(8.7)

It is occasionally the case that the SH signals exceed the dynamic range of the PMTs, in

particular for the reference material. In this case it is necessary to attenuate the signals.

Equation 8.7 is modified to yield

ds = dr

√αs

αr.10(NDs−NDr)/2 (8.8)

which accounts for attenuation of the sample and reference signals with neutral density

filters with values of NDs/r, respectively. χ(2) is then calculated via the relationship in

Equation 2.12, i.e. χ(2) = 2ds.

In the following sections we describe two techniques for fitting Equation 2.62 to exper-

imental data. We quote the nonlinear coefficients in terms of elements of the reduced

Chapter 8 161

nonlinear susceptibility tensor suing the contracted notation, i.e. the dil coefficients

(See Section 2.3), as these are what is measured. In this context χ(2) is a less useful

parameter, but can be easily calculated from d if necessary.

8.4.1 Root Mean Square Error Minimisation Fitting Procedure

This data fitting technique considers the Maker fringes expression to be a function of

two parameters, α and L. Using the condensed version of the Maker fringes Equation

8.4 we can write it as:

P2ω(θ : α,L) = αL2T (θ)d(θ)2Ψ(θ) (8.9)

Which indicates that Equation 8.9 is a function of the angle θ and the fitting parameters

α and L.

Maker fringes data will inevitably have some small angular offset which arises from the

difficulty in perfectly aligning the sample with respect to the beam. We denote this

offset as Δθ. Maker fringes data is always symmetric about the zero degrees, or normal

incidence angle and so in order to remove the angular offset from the data we need to

find the centre of the data and the difference between it and the zero angle position. We

do this prior to the following data fitting procedure.

The fitting procedure begins with the generation of an array of pairs of α and L, where

the parameters are allowed to vary over some physically meaningful range. This range

is determined by the sample at hand. From each of these pairs of α and L a theoretical

Maker fringes pattern is generated. We then find the root mean square error (RMSE)

between the function and the data. The minimum of this array and the parameters

corresponding to that minimum provides us with the best fitting parameters.

8.4.2 Genetic Algorithm Fitting Procedure

The RMSE minimisation technique described above has one inadequacy which needs

to be addressed. The angular offset Δθ is obtained by finding the point of symmetry

in the data and then displacing that point so as to coincide with zero degrees. We

found no precise method for achieving this, other than finding the mid point between

corresponding features in the data which are subject to experimental error. Instead,

we developed an alternative data fitting algorithm that finds the value of Δθ as well

as α and L. This alternative data fitting procedure uses a genetic algorithm to breed

an optimal set of input parameters for a nonlinear least squares (NLS) fit. While this


is not the first time genetic algorithms have been applied to data fitting [116–118] the

approach is quite uncommon in literature despite its effectiveness.

The details of the algorithm are summarised below:

1. The algorithm begins by generating an initial population, subject to upper and

lower bounds, of potential fits in the form of a vector of the form:

Fn = [αn, Ln,Δθn] (8.10)

where Fn is the nth member of the population with guess values for the scale

factor αn, nonlinear thickness Ln and an additional parameter Δθn which removes

any angular misalignment from the measurement by shifting the data set about

until it is centred on 0◦ (the value of Δθ is typically less than about ±2◦). We

typically use a population of 500 members and the upper and lower bounds used

will depend on the sample under study. For example: The quartz reference we use

can have its thickness measured mechanically with a micrometer to an uncertainty

of ≈ ±2.5μm.

2. Next, the algorithm assesses the fitness of each member of the population by using

its parameters as the input for a NLS fit. The input for the fit requires upper U ,and lower bounds L, in which to search for a good fit and these are determined

from Equation 8.10 in the following way:

Un = [αn + δαn, Ln + δLn]

Ln = [αn − δαn, Ln − δLn]

where 0 < δ < 1, typically ≈ 10−5. We keep δ small to prevent the NLS from

wandering too far from the initial guess values. Note that the angular offset Δθ is

not an input into the NLS fit. This is because we add Δθ to the angular position

of the measurement before performing the NLS fit, hence simplifying the solution

space for the NLS fitting algorithm.

3. We compile the RMSE for each potential fit. This is used as the so called fitness

function that the GA requires to guide the next stages of the algorithm.

4. The next step in the algorithm is called crossover and is akin to sexual reproduction

in animals. This step is performed by pairing members of the initial population

and exchanging their parameters. For example: Member a and b are paired each

with parameters Fa = [αa, La,Δθa] and Fb = [αb, Lb,Δθb] which after crossover

Chapter 8 163

could look like:

Fab1 = [αa, Lb,Δθb]

Fab2 = [αb, La,Δθa] .

We have indicated the ‘children’ of Fa and Fb as Fab1 and Fab2. Members of the

population are paired preferentially based on fitness.

5. After crossover we also apply some mutation to the new ‘children’. This has the

effect of preventing the GA form converging onto local minimum by introducing

some freak members of the population that may (or may not) accidentally acquire

superior qualities. 20% of the population is subject to mutation. The mutation is

performed by randomly selecting members and adding a random number to one

or all of the parameters. This random number is subject to the upper and lower

bounds imposed on the population from the outset.

6. Once the new population has been produced we return to Step 2. This process

is repeated until we satisfy the halting criterion, which is reached if there is no

improvement in the fitness for 5 consecutive generations.

8.5 Results and Discussion

8.5.1 Quartz Reference Measurements

The chosen reference material was a sample of y-cut quartz, cut to 2 mm thickness

and optically polished. This material was chosen for a number of reasons: It possesses

a second order nonlinearity. Quartz is a very stable material. It is not hygroscopic

in contrast to some nonlinear materials. Quartz has a relatively high laser damage

threshold ensuring that the samples will not be damaged when exposed to the pulsed

laser source. Quartz possesses a relatively low nonlinear coefficient and thus will not

require excessive attenuation to avoid saturation in the detection system. Finally, it is a

well studied material with reliable refractive index and second order nonlinear coefficients

data available in the literature. For future reference, the optical parameters of quartz

that are used in this work are given in Table 8.1.

We measured the Maker fringes for the quartz reference sample with p-polarised laser

excitation and p-polarised detection. The SH power was recorded for incidence angles

between ±45◦ with an angular resolution of 0.2◦. A neutral density filter with ND = 2.0

was used to decrease the SH power to a level sufficient for the detection system to not

be saturated.


Parameter Value Units

n1064 1.53413 -n532 1.54702 -d11 0.49 pm.V−1

Table 8.1: Optical parameters for quartz reference sample. Refractive index valuestaken from [119]. Nonlinear coefficient taken from [114]

Figure 8.10 shows the recorded data (blue dots). The central region of the data contains

the interference fringes resulting from the interaction between the generated SH and the

SH reflected at the material/air interface. The Maker fringes model we are using does

not account for this interference. The data was first treated by removing the central

±10◦ to omit the SH interference, thereby reducing the fitting error. We then analysed

this data using the two methods outlined in Section 8.4. We summarise the results for

the two methods below:

Root Mean Square Minimisation

From the raw data an estimate of the angular offset Δθ was obtained by taking equivalent

points in the fringes and finding the difference in their angular position. By applying this

method to several points an estimate of Δθ ≈ −1.5◦ was obtained. We then computed

the RMSE for a range of fitting parameters 0.1 ≤ α ≤ 1.5 with increments of 0.0005 and

1.8 mm≤ L ≤ 2.2 mm with increments of 0.0005 × 10−3 mm. The parameters which

resulted in the lowest RMSE and therefore best fit are tabulated in Table 8.2.

Genetic Algorithm

The MF expression was also fitted to the data using the Genetic algorithm fitting pro-

cedure. The upper and lower bounds for the GA were:

0.5 � α � 2

1.99× 10−3 � L � 2.10× 10−3

and −2 � Δθ � 2.

The optimised fitting parameters are listed in Table 8.2. We note that the two methods

Method α L [mm] Δθ

RMSE Minimisation 1.113 2.035 -1.5Genetic Algorithm 1.116 2.036 -1.500

Table 8.2: Optimised fitting parameters for y-cut quartz Maker fringes as determinedby the RMSE minimisation and GA fitting algorithms.

provide values for the coefficients that are in good agreement, within 0.3% for α and

0.05% for L. Further, the GA has arrived at the same value for Δθ as did we, i.e. −1.5◦.

Chapter 8 165

−40 −30 −20 −10 0 10 20 30 400

0.5

1

1.5

2

2.5

3

Incidence Angle θi [°]

P 2ω [a

rb. u

nits

]

Figure 8.10: Optimised fit to y-cut quartz Maker fringes data. Blue dots: RecordedMaker fringes data. Red line: Best fit as determined by GA fitting procedure.

Using the fitting parameters from the GA method we plot the Maker fringes (red line

in Figure 8.10) fitted to the experimental data (blue dots in Figure 8.10). Note, that

in the central ±10◦ there is a vertical spread in the data about the fitted curve. This

is due to the interference between the generated SH and the SH that is reflected at the

material/air interface. The interference is only observed within the ±10◦ region due to

the finite width of the beam.

The thickness of the quartz sample was measured with a micrometer which yielded

2.039±0.0025 mm, in close agreement with the value determined from the Maker fringes

analysis. Thus validating the Maker fringes measurement.

8.5.2 Thermally Poled Infrasil

The Maker fringes of the thermally poled Infrasil were recorded using p-polarised input

light and p-polarised detection for incidence angles between ±80◦ and at a resolution of

0.5◦. A neutral density filter of OD = 0.6 was used to decrease the SH power to avoid

saturation in the detection system. The acquired data was analysed using the two data

fitting techniques as described below.

Root Mean Square Minimisation

We first established an estimate for the angular offset in the data of Δθ = 0.33 by

averaging the difference in the angular position of three pairs of corresponding points.

The algorithm then computed the RMSE for fits to the experimental data with input

parameters ranging over 0.1 ≤ α ≤ 1 with increments of 0.001 and 1.0 mm≤ L ≤ 20 μm


with increments of 0.001μm. The optimal fitting parameters obtained from this method

are tabulated in Table 8.3.

Genetic Algorithm

When applied to the data for thermally poled glass a problem arises. Despite the ability

of the GA to avoid getting stuck in a local minimum in the RMSE landscape, the

algorithm if run multiple times returns very different parameters for fits with a range

of RMSEs. A scheme was developed to overcome this difficulty, the details of which are

summarised below:

1. We choose an educated guess value for the nonlinear thickness, say 1μm then we

tighten the upper and lower bounds on the nonlinear length. We typically use

L± 0.5μm.

2. The algorithm is then run for this guess value for the nonlinear length.

3. We obtain the optimised fit parameters and the RMSE.

4. Next, we increment the guess value for the nonlinear thickness and re-run the

algorithm.

5. This process is repeated over a range of valued of L. We obtain a plot of RMSE

vs L and by using value of αr and Equation 8.8 a plot of RMSE vs d33 as shown

in Figure 8.11.

Figure 8.11: Convergence of Maker fringes fitting parameters for thermally poledInfrasil. Left: Thickness of the nonlinear region, L. Right: Nonlinear coefficient, d33.

Chapter 8 167

It is clear from Figure 8.11 that there is indeed an optimal set of parameters despite the

inability of the GA to find these without being made to scan the parameter space. The

optimised parameters are tabulated in Table 8.3.

Method α d33 [pm.V−1] L [μm] Δθ

RMSE Minimisation 0.196 0.035 11.70 0.33Genetic Algorithm 0.192 0.033 11.79 0.589

Table 8.3: Optimised fitting parameters for thermally poled Infrasil Maker fringes asdetermined by the RMSE minimisation and GA fitting algorithms.

Comparing the fitting results from the two methods (Table 8.3) we see that the agreement

is good. In particular the percentage differences are 2% for α, 5.7% for d33 and 0.8%

for the thickness of the nonlinear region L. The discrepancies can be attributed to the

difference in the values of Δθ used in each method. In our assessment, the value for

Δθ as determined by the GA technique is more accurate because this particular value

optimises the fit, whereas, the value use in the RMSE minimisation method was simply

an estimate based on a smaller set of experimental data points. As such, we conclude

that the GA data fitting algorithm has increased the accuracy of the measurement of

d33 by almost 5.7%. Although, it must be stated that one could conceive of a more

complicated scheme for obtaining Δθ from the experimental data and then feed this

into the RMSE minimisation method. In this case the expectation would be for the

parameters from each technique to converge. The GA method simply provides a single

technique for determining all of the fitting parameters.

Plotted in Figure 8.12 are the measured data (blue dots) and the fitted curve (red line)

using the optimised fitting parameters obtained from the GA method. In Section 8.6

we present independent measurements of the thickness of the nonlinear region for the

thermally poled Infrasil.

Given that we used a ND = 0.6 neutral density filter in the detection system and the

dynamic range of the DAQ is 16 bits, we estimate that the minimum detectable second

order nonlinear coefficient is in the order of 1× 10−4 pm.V−1.

8.5.3 Thermally Poled Tellurite

The angular dependence of the SH was recorded for the thermally poled TZN3 sample

(discussed in Chapter 7). The experimental conditions were identical to conditions used

to measure the the thermally poled infrasil (refer to Section 8.5.2). Figure 8.13 shows the

experimental data. There are several points to make regarding this data. Specifically,

P2ω does not go to zero at 0◦ as would be expected. Also, the fringes are not perfectly


−80 −60 −40 −20 0 20 40 60 800

0.5

1

1.5


P 2ω [a

rb. u

nits

]

Figure 8.12: Optimised fit to thermally poled Infrasil Maker fringes data. Blue dots:Recorded Maker fringes data. Red line: Best fit to data provided by GA fitting routine.

symmetric about 0◦. There are several possible causes for this. These include: The

creation of an inhomogeneous nonlinear region caused by imperfect contact between the

TZN3 sample and the borosilicate cover slip. Ablation of surface contaminants by the

laser. One potential source of surface contamination are oxides of sodium (or other

alkalis) that precipitated after the poling treatment.

−80 −60 −40 −20 0 20 40 60 800

0.1

0.2

0.3

0.4

0.5

0.6

0.7


P 2ω [a

rb. u

nits

]

Figure 8.13: Measured angular dependence of second harmonic power for thermallypoled (CI) TZN3 at 230◦C and 3 kV for 60 min.

Both of the afore mentioned fitting techniques were applied to the data for the TZN3

sample. Neither technique provided a fit with reliable parameters. In particular the

Chapter 8 169

RMSE minimisation technique predicts a value for d33 in excess of 100 pm.V−1. The

validity of this results is highly dubious, considering this is at least two orders of mag-

nitude higher than any previously reported second order nonlinear coefficient observed

for tellurite glass. As for the GA method, we find no converging solution. From this we

can only conclude that fitting a Maker fringes expression to this data is unjustified, due

to its poor quality. Accordingly, we have no estimate for the strength of the induced

nonlinearity for this sample.

8.6 Measurement Techniques for the Thickness of the Non-

linear Region

To verify the effectiveness of the Maker fringes fitting algorithms an independent

verification of the width of the nonlinear thickness, otherwise referred to as the de-

pletion region, is necessary. We employed two complimentary techniques for determining

the nonlinear thickness second harmonic microscopy (SHG microscopy) and differential

etching.

8.6.1 SHG Microscopy

SHG microscopy is becoming a common imaging technique in the physical and biological

sciences. The technique looks at a materials second order nonlinear response on the scale

of ≈ 500 nm and upward. This is therefore a useful technique for analysing thermally

poled glasses as the region of nonlinearity is typically very thin, in the order of several

microns.

A sample was prepared from the thermally poled Infrasil for SHG microscopy in the

following way2:

1. The thermally poled glass disc was cleaved in two along a diameter by scoring with

a diamond scribe and bending of the sample about this scribe mark.

2. One half of the disc was then sandwiched between two microscope slides and fixed

with glue.

3. A thin slice was cut from this assembly and this was fixed with glue to another

microscope slide.

2This sample preparation was performed by a technician at the University of Sydney’s ElectronMicroscopy Group


4. The exposed surface of the poled glass was polished to an optical finish for viewing

in the SHG microscope.

SHG microscopy was performed on an inverted Leica DMIRBE microscope equipped

with a Leica TCS2MP confocal system and coherent Verdi-Mira tunable pulsed titanium

sapphire laser3. This laser provided the fundamental excitation at 830 nm, with pulses

of approximately 150 fs in duration in addition to a continuous wave optical channel, at

543 nm, for sample viewing. The weak SH signal was separated from the optical channel

with a dichroic mirror and recorded by photomultipliers.

Figure 8.14 is composed of a schematic illustration of the sample configuration (Figure

8.14 (a)), an optical micrograph of the sample assembly (Figure 8.14 (b)) and an overlay

of the optical channel and the SHG channel from the SHG micrograph (Figure 8.14 (c)).

The glue that fixed it to the microscope slides is observed as a strip of dark markings on

the SHG micrograph. From the optical channel we were able to calibrate the position of

the SHG signal with respect to the edge of the glass (i.e. the edge of the glued region).

Using MATLAB we took a line scan of the SHG signal which was averaged over the entire

image. One can naively deduce that by taking the square root of the SHG intensity signal

a spatial profile for the second order nonlinear (SON) susceptibility can be determined.

This is because P2ω ∝ (d33)2EDC . Figure 8.15 shows the square root of the SHG

intensity as a function of scan position, where the anode side of the glass is to the right

of the SON profile plot.

The plot in Figure 8.15 displays the characteristic shape displayed by thermally poled

silica [86, 110]. There is a sharp increase in the SON profile near the anodic surface

of the glass which rises to a maximum a few micron into the glass. The signal then

decreases at a slower rate further into the glass.

It appears that the width of the SON profile is ≈ 16 μm (i.e. from a scan position of

93 μm to 109 μm), however, the actual spatial extent of the SON profile is most likely

shorter than this. The reason for this statement is as follows: As we have exposed a

part of the glass that contains excess charge, this charge produces fringing fields. Thus

we have disturbed the electric field that existed inside of the glass and consequently the

recorded SON distribution is not exactly representative of the distribution that exists

inside of the glass.

3SHG microscopy was kindly performed by Mr. Guy Cox at the University of Sydney’s ElectronMicroscopy Unit.

Chapter 8 171

Figure 8.14: Top left: A schematic representation of the sample assembly used forSHG microscopy. The poled Infrasil is sandwiched in between two microscope slidesand glued in place. Right middle. The sample is orientated with the anodic face ofthe poled Infrasil towards the bottom of the page: An optical micrograph of the regionof interest for the SHG microscopy. The highly polished Infrasil can been seen at thetop and the microscope slide at the bottom. In between the two glass layers there is alayer of glue ≈ 40 μm thick. Left bottom: An overlay of the optical (green) and SHG(false colour orange) channels taken from the SHG microscope. The darker region to

the bottom of the SHG is the glue layer.

Figure 8.15: Graph: Mean line scan of the SHG channel taken from an SHG micro-graph of thermally poled Infrasil with the anodic side of the glass to the right of thepeak. Inset: False colour image from the SHG channel. Note: the red dot to the rightof the inset figure is an SHG response from a contaminant and has been removed from

the line scan.


8.6.2 Differential Etching

It has been established that the depletion region formed in a thermally poled silica glass

displays a different etching rate in HF acid than the unpoled glass [104, 120]. It was

shown that the depletion of ionic species from a region in fused silica reduces the rate at

which HF acid etches that region by approximately 1/2. This effect has been exploited

in order to reveal the spatial extent of the depletion region by several authors [86, 101].

There are various experimental techniques that have been developed to glean information

from the HF etching of poled silica. In particular an interferometric technique was

developed by Margulis and Laurell [120] which simultaneously measures the amount of

material being removed and the SHG signal being generated from a pump laser. This

technique allows accurate measurement of the spatial profile of the nonlinear region

and represents the ultimate characterisation experiment for poled glasses. We, however,

have opted for a much simplified version of this technique. The poled glass was simply

etched and then the depletion region was imaged with an electron microscope so that

measurements of the width of the depletion region could be made.

As with the SHG sample we sandwiched the cleaved glass disc between two microscope

slides, fixed in place with a contact adhesive, and polished the assembly to provide a

flat surface, perpendicular to the poling direction. The microscope slides were removed

from the sample by immersion in dichloromethane for several hours. We then etched

the polished face of the sample in a 45 w.t.% solution of hydrofluoric acid for 60 s. The

sample was then mounted for viewing on an electron microscope. The etched surface

was imaged in the secondary electron emission configuration.


The SEM micrographs of the HF etched thermally poled Infrasil are shown in Figures

8.16 and 8.17. An etch rate of ≈ 1μm.min−1 for 45 w.t.% HF acid on fused silica is

reported in [121] and, as stated in [104], the etching rate of the ion depleted region

should be ≈ 1/2 the rate of the undepleted glass. Despite this we see clear evidence that

the etch rate of the anodic surface was indeed higher than this. With reference to Figure

8.17 we see that the anodic surface of the poled glass has developed large (≈ 2 μm) open

holes in a 2 μm thick layer below the anodic surface. The implication is that the etch

rate was closer to 2 μm.min−1 for the anodic layer. It is likely that this result stems

from the documented phenomenon of H+ injection that is associated with long poling

times [102]. Furthermore, it has been observed by Triques et al. that the initial ≈2 μm

of glass does indeed etch faster than the undepleted glass [99].

Chapter 8 173

The edges of the depletion region are indicated by the dashed lines in Figure 8.16. The

top line indicates the position of the glass surface prior to etching, the position of which

was calculated via the argument above. The lower dashed line coincides with a ridge

resulting from the different etch rates of the ion depleted region and the pristine glass.

We estimate the thickness of the depletion region to be approximately 12 μm (see Figure

8.16).

Figure 8.16: SEM of the etched depletion region of thermally poled Infrasil. Assumingan etch rate of ≈ 2 μm.min−1 we have indicated the approximate position of the glass

surface prior to etching.

Figure 8.17: SEM of the anodic face of thermally poled infrasil. A region of higheretch rate is clearly visible at the top of the image.

We have overlaid the trace obtained from the SHG microscopy with the SEM of the

depletion region as shown in Figure 8.18. There was some freedom with respect to

the precise positioning of the SHG profile so it was positioned by eye to provide best

overlap with the proposed thickness of the depletion region. When this is done we can


see that the peak of the SHG response is located in the region of maximal etching that

we hypothesise is rich in H+ due to charge injection during poling.

Figure 8.18: Overlay of SON profile with SEM of depletion region. SON profile (ingreen) is overlaid with the SEM of the depletion region. The thickness of 12 μm is

indicated to show the approximate position of the surface of the unetched glass.

It has previously been reported that there is indeed a peak in the SHG response within

the first couple of microns of a thermally poled Infrasil sample for long poling durations

[102]. Figure 8.19, which is reproduced from [102] shows (white circles) that for an

Infrasil sample that has been poled for 100 min at 250◦ and 4.0 kV there is an initial

peak in the value of the second order nonlinear susceptibility, χ(2). As the amount of

SHG is determined by χ(2) it is therefore clear that a peak in the SHG response should

also be observed.

Additionally, the SON profile in Figure 8.18 has reasonably distinct knees at either

side of the peak which closely coincide with the edges of the depletion region. It is

possible that the discontinuities in electric field at the edges of the charged depletion

are responsible for the knees in the SON profile. However, to verify this claim more

investigations are required.

Chapter 8 175

Figure 8.19: Second order nonlinear susceptibility as a function of depth under theanodic surface. White circles: This data shows that there is an initial peak in the SON

response in Infrasil in the long poling regime. Reproduced from [102]

8.7 Conclusion

AMaker fringes measurement experiment was constructed that was capable of deter-

mining the angular dependence of the second harmonic power generated in a poled

glass sample. The apparatus provided measurements of SH power with a maximum er-

ror of 1%. Based on a measurement of a prepared sample of thermally poled Infrasil,

the apparatus can measure second order nonlinear coefficients of at least 0.03 pm.V−1.

Further, we estimate that second order nonlinear coefficients as low as 1× 10−4 pm.V−1

could be measured with this system.

We developed two methods for fitting the Maker fringes expression to the measured

data for determining the strength of the induced nonlinearity and the spatial extent of

the thermally poled region. Both methods were in close agreement with one another

when the sample was very think as compared to the coherence length. For poled glass

the absence of fringe detail in the Maker fringes data made it difficult to obtain an

accurate estimate of the angular offset. The GA method showed superiority to the

RMSE minimisation method in that a more accurate measure of the angular offset was

obtained leading to more accurate values for the thickness of the nonlinear region and

the second order nonlinear coefficient. Measurement of the thermally poled tellurite

sample yielded data from which neither algorithm was able to yield valid results. This is

primarily due to the poor quality of the data that resulted from surface contamination

during the thermal poling procedure.



Independent measurements of the thickness of the nonlinear region of the thermally

poled Infrasil sample were made. Both the SHG microscopy and differential etching

results are in good agreement with the thickness determined via the data analysis.

Chapter 9

Fibre Preliminaries

9.1 Introduction

This Chapter comprises some preliminary work that was undertaken as a first step

towards fabricating optical fibre devices. This was conducted in parallel with

the production and characterisation of the tellurite glasses reported in the previous

Chapters. Several computational models were developed to give qualitative indications

of the performance of a range of potential optical fibre designs for electro-optic fibre

devices as well as rules of thumb for the design of fibres with internal electrodes. The

details and results from these computational models are found in Section 9.2.

In addition to modelling the properties of optical fibres with internal electrodes, some ex-

perimental work in establishing fibre processing capabilities, necessary for the fabrication

of optical fibres with internal electrodes, was performed. Techniques such as fabrication

of extruded optical fibre preforms with holes with which to accommodate electrodes.

As well as electrode insertion techniques were developed. The work on electrode in-

sertion was greatly facilitated by a collaboration with Walter Margulis at ACREO in

Stockhlom. During a two week visit by the Author to ACREO’s research facility, fibre

electrode insertion techniques were learnt and developed further. The techniques were

adapted so as to be more generally applicable to optical fibres with microstructuring.

The details of this work are discussed in Section 9.3.2.1.

Also discussed in this Chapter are the preliminary fibre fabrication trials dedicated

towards developing the capability to produce core/clad optical fibres made from tellurite

glass. In the future such core/clad fibres could be fabricated with internal electrodes,

which would be a significant milestone on the path to creating practical tellurite glass

based electro-optic fibre devices.

177

178 Fibre Preliminaries

9.2 Computational Modelling of Electro-optic Optical Fi-

bres

Electro-optic fibre devices require internal electrodes positioned close to the core

of the fibres in order to manipulate the light propagating through them. The

degree to which the refractive index is modified is related to the strength of the electric

field across the core, a relation that varies for the two specific cases of χ(3) and χ(2)

devices. The relationship that describes the change in index for a χ(3) device is given in

Equation 2.73. Where Eext is the strength of the applied electric field (and EDC = 0).

Typical values for χ(3) are in the order of 10−20 m2.V−2, thus Eext needs to be in the

order of 108 V.m−1 to obtain changes in the refractive index of around 1 part in 1000.

Note that the relationship is quadratic in the applied electric field. Typical electrode

separations would be in the order of 10 μm and thus voltages in the range of several kV

would be necessary.

For fibres that have been thermally poled a permanent DC electric field EDC , exists

across the core. The expression for the index change when an additional external field

Eext, is applied is given by the relationship given in Equation 2.73 (in this case EDC is

non zero). Accordingly, the change in refractive index is linear with respect to the applied

external electric field which, by virtue of the size of the frozen-in-field typically being in

the order of 108 V.m−1, can be as low as 106 V.m−1 to achieve similar refractive index

variations as in the case of χ(3) devices. [105]. For electrodes separated by ≈ 10 μm this

equates to tens of volts of potential. It is for this reason that thermally poled electro-

optic devices are desirable over χ(3) devices as the required strength of the applied field

is so much lower.

Much of this Chapter addresses the issue of providing optical fibres with internal elec-

trodes and the effects that electrodes would have on the optical properties of the fibre.

There are several methods for introducing the electrodes, each with its advantages and

disadvantages. Below, we have listed some of the more common techniques with discus-

sion regarding the advantages and disadvantages of each:

� Wire insertion: An optical fibre is fabricated with approximately 30 - 50 μm

diameter holes running along the length of the fibre parallel to the core as per

Figure (make the figure). Thin tungsten wire with a diameter as similar to the

holes in the fibre as piratical are then manually inserted into the fibre [122]. This

technique is limited as it can only produce optical fibres with internal electrodes

of up to approximately 10 cm and there is always an air gap between the electrode

and the surrounding glass.

Chapter 9 179

� Simultaneous fibre+wire drawing: In this process the internal electrodes are

introduced into the fibre during the drawing process. In the fibre drawing tower

the fibre preform has a spool of thin tungsten wire above it and as it is drawn

down into the fibre the wire is drawn with it [123]. Fibres with internal electrodes

in excess of 200 m have been produced in this manner and there is no gap between

the electrode and the glass. However, the draw back with this technique is that

stress in introduced into the fibre due to the difference in the thermal expansion

coefficients of the cooling glass/metal combination.

� Liquid metal injected electrodes: Electrodes are introduced by first producing

an optical fibre with 20-30 μm diameter holes running the length of the fibre

parallel to the core. Then one end of the fibre is sealed in a pressure vessel

immersed in a molten solution of metal and placed into a furnace. Typical alloys

used are BiSn and AuSn solders with melting temperatures of 170 ◦C and 280 ◦C

respectively. Under the application of high pressure (10-30 bar) the liquid metal

is pushed into the holes of the fibre [124, 125]. The fibre+metal combination is

allowed to cool slowly by gradually removing the fibre from the furnace from the

end furthest from the pressure vessel. In this way the liquid metal is allowed to

contract longitudinally and therefore a minimum of stress in introduced into the

fibre. Fibres with internal electrodes of ≈100 m have been produced in this way

and indeed this process could be scaled further. Additionally, this technique allows

multiple fibres to be filled simultaneously.

In the subsequent sections we analyse the properties of such a fibre. Specifically, the

DC electric field that can be produced between the electrodes and how the structure

of the fibre may effect the strength of the field across the core region. We have also

calculated the optical attenuation that inevitably results from having metal placed near

a propagating optical mode. This attenuation is then analysed for different optical fibre

types, i.e. core/clad and MOF as well as the influence of the distance from the optical

field and the electrodes.

9.2.1 Electric Fields Between Internal Electrodes

The strength of the electric field between the internal electrodes of the optical fibre is

an important factor for determining the performance of any device fabricated from such

a fibre. We have modelled the electric field that would exist in the core region of several

representative fibre types. The fibres we considered were a core/clad step index fibre

(SIF), a hexagonal three ring MOF (HexMOF) and a wagon wheel MOF (WWMOF).

In principle we can use the results for optimising of the positions of the electrodes for


electro-optic modulators and poling fibres and to better understand how poling might

take place in optical fibres with microstructured regions.

Using the generalised electromagnetic toolbox in COMSOL, a finite element software

package, we computed the electric field distributions over a range of electrode separa-

tions. The results for each fibre type are presented separately below:

� Step Index Fibre (SIF): The SIF we modelled is based closely on a particular

fibre reported by Myren et al [126]. This fibre represents the state of the art in

electro-optic fibres, thus providing an excellent point of comparison. Table 9.1

details the parameters used in the model.

Parameter Value/s

Fibre diameter 125 μmCore diameter 4.3 μm

Electrode diameter 29.5 μmAnode potential 4.0 kVCathode potential 0 V

Electrode separation 6.2 � de � 32.3 μm

Boundary conditions:Fibre surface Ground

Core ContinuityAnode Electric potential (4.0 kV)Cathode Ground

Table 9.1: Input parameters for SIF electric field model. Optical fibre parameterstaken from [126]

The most difficult aspect of setting up this model was that of boundary condition

selection. We chose, for the fibre surface, a grounded boundary condition. This

may seem like an odd condition to use for a non-conductive material, however, by

comparing modelled potential fields with imaged depletion regions for real poled

fibres [126] we see in Figure 9.1 that this boundary condition gives the best agree-

ment with experiment. Note in Figure 9.1, left; the depletion region has extended

towards the fibre surface from the top of the anode. It is only possible for this to

occur if there is a potential difference between the anode and the fibre surface. The

simulation of the electric filed in the left of Figure 9.1 where a grounded boundary

condition was used for the fibre surface displays, qualitatively, the same shape as

the depletion region.

Further to this, a reported experiment in which two anodes were used proved

conclusively that the surface of the fibre is indeed grounded [108]. In this work

it was established that there is a mechanism for charge neutralisation at the fibre

Chapter 9 181

Figure 9.1: Comparison between experiment and simulation for a poled SIF and themodelled electric field distribution. Left: The chemically etched depletion region of athermally poled fibre viewed with a phase contrast microscope [126]. Right: Simulatedelectric field distribution for a similar fibre using a grounded boundary condition at the

fibre surface.

surface. The neutralisation is most likely to be produced by ionised species from

the air being attracted to the surface and negating the surface charge.

Figure 9.2 shows the electric field distribution for one particular electrode separa-

tion. The blown up core region (Right of Figure 9.2) shows that the field is fairly

uniform across the core region of the fibre. The electric field in the centre of the

core is plotted as a function of electrode separation in Figure 9.5 (Blue line). The

electric field falls away with electrode separation slightly faster than a typical 1/r2

relation. This is because the grounded boundary condition on the fibre surface

serves to bend the field lines towards it and as the electrode separation increases

this effect becomes more pronounced.

� Hexagonal Array Microstructured Optical Fibre (HexMOF): A represen-

tative geometry was chosen for analysis of the electric field produced in the core

region of a microstructured optical fibre with a hexagonal array of holes (Hex-

MOF). We chose a design that is both possible to fabricate given our current

fabrication capabilities and, importantly, has close to the best confinement of the

optical mode. This confinement is determined by the ratio of the hole diameter

to their pitch, d/Λ = 0.5 for this fibre, as well as the number of rings of holes, in

this case 3. The need for high optical confinement will become apparent when we

analyse the optical attenuation of these fibres (see Section 9.2.2). The parameters

for the HexMOF model are listed in Table 9.2.


Figure 9.2: Modelled electric field distribution for a step index fibre with internalelectrodes. Left: The entire fibre cross section. Right: Magnified core region.

Parameter Value/s

Fibre diameter 125 μmPitch (Λ) 2.0 μm

Hole diameter (d) 1.0 μmd/Λ 0.5

Electrode diameter 29.5 μmAnode potential 4.0 kVCathode potential 0 V

Electrode separation 12 � de � 28 μm

Boundary conditions:Fibre surface GroundInternal holes Continuity

Anode Electric potential (4.0 kV)Cathode Ground

Table 9.2: Input parameters for HexMOF electric field model.

The boundary condition for the air hole/glass interfaces in the microstrucured re-

gion of the fibre was chosen to be continuity. It is possible that, like the fibre

surface, these boundaries will in fact be grounded, however, we have no evidence

that this is the case and therefore we chose the simplest possible boundary condi-

tion that makes the fewest assumptions. The spatial extent of the microstructured

region prohibits the electrodes from being positioned close to the core. This is why

we have considered a smaller range of electrode positions than for the SIF.

It can be seen in Figure 9.3 that the electric field in the air holes of the fibre is

≈ 3×108 V.m−1. This exceeded the break down field strength of air by two orders

Chapter 9 183

Figure 9.3: Modelled electric field distribution for a hexagonal three ring MOF withinternal electrodes. Left: The entire fibre cross section. Right: Magnified core region.

of magnitude1. The existence of such high electric fields in the air holes can be

understood in terms of the continuity condition for the tangential components of

the electric field at the interface can be written as

Et1 = Et2 (9.1)

where Et1 is the component of the electric field that lays tangential to the interface

in region 1 and Et2 is the tangential component of the electric field in region 2.

However, for the normal components the boundary condition is written as

ε1En1 = ε2En2 (9.2)

The change from one material to another at the interface implies that there will

be a change in the value of ε at the interface. Thus there is a discontinuity in the

normal component of the electric field En, across the boundary. The ratio of ε1/ε2

for the glass/air boundary is ≈ 2 which explains the observed difference between

the electric field in the glass and that seen in the air holes.

This result is concerning, as it would appear to limit the maximum possible field

strength to a value insufficient for thermal poling and Kerr modulation. However,

this result is predicated on the validity of the continuity boundary condition at the

air/glass interface of these holes, an assumption which may prove to be invalid. As

has been shown by Margulis et al, there is a mechanism for charge neutralisation

1Dielectric strength of air is approximately 3× 106 V.m−1 [127]


at the surface of the glass [108]. However, there is as yet no report of this occurring

within the microstructured region of and optical fibre.

Further to this, the question of how the depletion region would form in such a

fibre is an interesting one. For a first approximation, we would assume that during

poling the migrating species follow the field lines. The is no doubt that this would

be the initial situation. However, after the charges have migrated some distance

there would be a change to the net electric field, due to the non-equilibrium charge

distribution. To assess this more thoroughly a time dependent model would need

to be constructed. We leave this for future work.

This assumption is tested in Figure 9.1 and is shown to be approximately correct.

Thus, the depletion region which would form in this fibre would be very compli-

cated and it is difficult to predict how well it would overlap with the core. This

being so, there is at least one report of a fibre with a similarly complex holey

region being successfully thermally poled [128].

The dependence of the electric field in the centre of the core on the separation

of the electrodes is plotted in Figure 9.5 (red line). It is observed that the field

strength is slightly smaller than for the equivalent electrode separation in the

SIF. Coulomb’s law predicts an inverse square dependence of electric field on the

separation of the charges. However, this is only valid for charges in a medium of

constant permittivity. The differing permittivities of the air and glass produce the

observed difference between the SIF and HexMOF cases.

� Wagon Wheel Microstructured Optical Fibre (WWMOF): The wagon

wheel optical fibre is extreme in terms of the amount of air surrounding the core of

the fibre. As such it is an interesting fibre to analyse in this way. There are many

benefits to such a fibre including low confinement loss, high mode confinement and

thus large fibre nonlinearity as well as large NA. The fibre considered in the model

is a straight forward design for fabricate and can be applied to many materials.

As with the HexMOF, we employed the continuity boundary condition at the

air/glass boundary of the internal holes surrounding the core. Furthermore, due

to the spatial extent of the air holes we are limited in terms of the proximity of the

electrodes to the core region. For the purposes of this simulation we had to choose

an orientation of the structure within the fibre. It was determined that the most

logical orientation is with one of the three struts aligned along the imaginary line

joining the two electrodes. This is because the air holes serve to shield the core

from the electric field and if we want charge migration to occur in the core region

we need to minimise this shielding.

Chapter 9 185

Parameter Value/s

Fibre diameter 125 μmEffective core diameter 1.0 μmElectrode diameter 29.5 μmAnode potential 4.0 kVCathode potential 0 V

Electrode separation 13 � de � 37 μm

Boundary conditions:Fibre surface GroundInternal holes Continuity

Anode Electric potential (4.0 kV)Cathode Ground

Table 9.3: Input parameters for wagon wheel structured electric field model. Note,Effective core diameter is defined as the diameter of the largest circle that fits inside of

the triangular core region.

Figure 9.4: Modelled electric field distribution for a wagon wheel MOF with internalelectrodes. Left: The entire fibre cross section. Right: Magnified core region.

Again, as in the HexMOF case, the field in the air holes is prohibitively high with

respect the the dielectric break down of air. In terms of the possible evolution

of a depletion region the wagon wheel fibre looks promising. There exists a large

electric field in the core of the fibre and if we assume the ions will migrate along

the field lines then one would expect the depletion region to spread out to occupy

the entire core region (see Figure 9.4).

Figure 9.5 shows the electric field in the core for various electrode separations and

reveals that the wagon wheel provides the lowest field strength of the three fibres.

This is determined by the amount of air surrounding the core.


5 10 15 20 25 30 35 400

1

2

3

4

5

6

7 x 108

Electrode Separation [μm]

Elec

tric

File

d [V

.m−1

]Wagon wheelStep indexHexagonal

Figure 9.5: Core electric field strengths for three representative fibre types withinternal electrodes calculated over a range of electrode separations. Blue: SIF. Red:

Hexagonal three ring MOF. Green: Wagon wheel MOF.

9.2.2 Electrode Induced Optical Attenuation

The presence of internal metal electrodes in an optical fibre will result in attenuation of

the optical field. This additional loss, despite being unavoidable, should be minimised.

To gain insight into how this might be achieved we modelled the loss induced by the

electrodes over a range of electrode to core separations using the finite element method.

This is, to the best of our knowledge, the first time this attenuation has been analysed

in this manner. We note that Myr’en reports a computation of electrode induced atten-

uation in his Thesis [31]. Their method involved using commercial beam propagation

software (BeamProp) and specifying the absorption of the metal (in their case Bismuth)

with a complex refractive index. Our investigations with finite element methods showed

that this approach leads to non-physical outcomes, with electric filed lines not meet-

ing the conductive surfaces at 90◦. Instead, we specify, within the software, that the

electrodes are metallic with finite conductivity.

Figure 9.6 shows an optical fibre with internal electrodes in cross section. We have

highlighted the upper right plane of the diagram to indicate that we performed a quarter

plane analysis [129].

When using a quarter plane analysis, the boundary conditions for the edges along the

x and y axis need to be chosen correctly to produce the correct optical modes and

polarisations. For this analysis we have only considered the fundamental LP01 mode of

the fibre, furthermore, the internal electrodes produce birefringence and therefore there

Chapter 9 187

are two non-degenerate orthogonally polarised LP01-like modes. One has its electric

field Ex, aligned with the x axis of Figure 9.6, let it be denoted LP x01 . The other has

its electric field Ey, aligned with the y axis, denoted LP y01. To produce these two modes

we use the perfect electric conductor E0, and perfect magnetic conductor H0, boundary

conditions such that the LP x01 mode is obtained with the E0 condition on the x axis and

the H0 condition on the y axis. Conversely for the LP x01 mode is obtained with E0 on

the y axis and H0 on the x axis.

Figure 9.6: Optical fibre with internal electrodes used for modelling of electrodeinduced loss. Left: Optical fibre cross section with the electrode-core spacing indicatedd. The 1/4 plane used for the calculations is highlighted with the annulus of high meshdensity in the electrode shown. Centre: Regions of important mesh density have beenindicated. Right: The boundary conditions used to obtain the two non-degenerate

orthogonally polarised LP01 type modes.

Parameter Value/s

Fibre diameter 100 μmCladding index 1.438Core diameter 4.3 μmCore index 1.453

Electrode diameter 29.5 μmElectrode surface resistivity 0.1×10−6 Ω.m

Electrode conductivity 6.67×106 S.m−1

Core to electrode spacing 1 � d � 14 μm

Table 9.4: Input parameters for electrode induced loss model.

In the electrode region the optical field decays extremely rapidly. The depth over which

the current density decays to the 1/e value is the so called skin depth and can be


estimated via:

δ =1√πμ0

√ρ

μrν≈ 503

√ρ

μrν. (9.3)

Where ρ is the resistivity and μr is the relative permeability of the metal and ν is the

frequency of the electromagnetic wave. Taking the values for BiSn as ρ = 1.29 μΩ.m2

and μr ≈ 1 and considering an incident wave at 1550 nm we obtain a skin depth of

≈ 41 nm. To obtain accurate calculations the region of the electrode over which the

optical field decays requires mesh elements with a maximum size less than the skin depth.

We performed a convergence calculation whereby the imaginary part of the propagation

constant (converted into optical loss in dB.m−1) for the two polarisations of the LP01

mode at 1550 nm was determined over a range of decreasing mesh element size. The

results of these calculations are presented in Figure 9.7. It can been seen that the value

for the loss is converging for decreasing mesh size. Convergence to 5 significant figures

was obtained.

0.0 5.0x10-8 1.0x10-7 1.5x10-7 2.0x10-7

1.10

1.11

1.12

1.13

1.14

1.15

1.16

1.17

E x Los

s [dB

.m-1

]

Maximum Element Size [m]

10.9

11.0

11.1

11.2

11.3

11.4

11.5

11.6

Ey L

oss [

dB.m

-1]

Figure 9.7: Convergence of electrode induced loss as mesh element size is decreased.Blue: Loss of the LP x

01 mode. Red: Loss of the LP y01 mode.

We next computed the loss for the two polarisations of the LP01 mode at 1064 nm and

1550 nm over a range of electrode to core separations. The results of these calculations

are presented in Figure 9.8 where we have changed the horizontal axis such that the 0

point conincides with the position of the mode field radius. This better illustrates the

dependence of the loss on the distance from the optical field. We calculated the mode

field radius by applying the Gaussian approximation for the fundamental mode of a SIF

2We are assuming that the resistivity of BiSn is approximately the same as that of pure Bismuth

Chapter 9 189

with core radius a given by [130]

w0 ≈ a

(0.65 +

1.619

V 3/2+

2.87

V 6

). (9.4)

The induced loss is sensitive to the distance between core and electrode. The computed

loss ranges over 4 orders of magnitude for a change in the position of the electrode

of only several micron. For a practical device the losses should be as low as possible.

Acceptable losses for the entire device are around 3 dB. Allowing for losses as the light

enters and exits the device (i.e. Fresnel losses) ,which could be as high as 1 dB, the loss

due to the electrodes can be no higher than 2 dB.

It is noteworthy to mention that the loss experienced by the y polarised mode is roughly

10× that of the x polarised mode. This can be understood if we consider that the electric

field lines must meet the metal surface at 90◦ thus the y polarised mode is coupled into

the metal much more effectively that the x polarised mode.

0.0 2.5 5.0 7.5 10.0 12.5 15.0-8

-6

-4

-2

0

2

4

6

Log(

dB.m

-1)

Mode field radius - Electrode Separation [μm]

Ey 1064 nm

Ex 1064 nm

Ey 1550 nm

Ex 1550 nm

Figure 9.8: Base 10 log of the electrode induced loss against mode field radius toelectrode separation. Blue (�): LP y

01 mode at 1064 nm. Blue (�): LP x01 mode at

1064 nm. Red (�): LP y01 mode at 1550 nm. Red (�): LP x

01 mode at 1550 nm.

Attempts were made to calculate the electrode induced loss for a wagon wheel MOF and

a HexMOF. In the case of the wagon wheel quarter plane analysis is not possible because

the wagon wheel structure has three fold symmetry. Thus, we needed to construct a


model for the entire fibre cross section. Just as for the SIF case we first attempted to find

a converged solution. Figure 9.9 shows the computed loss value for decreasing electrode

mesh element size calculated for a wagon wheel fibre with the same parameters as in

Section 9.2.2 and at a wavelength of 1550 nm. For this convergence test the electrode

was positioned as close to the core as possible (≈ 6 μm) to provide the largest possible

loss value.

2.0x10-8 2.5x10-8 3.0x10-8 3.5x10-8 4.0x10-8 4.5x10-8 5.0x10-8 5.5x10-8

-5.00E-008

-4.00E-008

-3.00E-008

-2.00E-008

-1.00E-008

0.00E+000

1.00E-008

2.00E-008

3.00E-008

4.00E-008

Ex Ey

Los

s [dB

.m-1

]

Maximum Element Size [m]

Figure 9.9: Electrode induced loss for a wagon wheel MOF calculated for variousmesh element sizes. Blue: LP x

01 mode. Red: LP y01 mode.

As indicated in Figure 9.9 a converged solution for this model was not obtained. We

can however state that when the electrodes are positioned as close to the wagon wheel

structure as possible, that is where the loss should be maximum, the model was unable to

resolve their influence on the light. Therefore we assert that the attenuation produced by

the electrodes is approximately zero. This indicates that the optical mode is, effectively,

completely shielded from the electrode. For example an equivalent electrode to core

separation for the SIF example produces a loss of ≈ 17 dB.m−1. Such high optical

confinement is expected given the high refractive index contrast between the core and

the cladding (i.e. the surrounding air).

A convergent solution was obtained for the HexMOF model. At approximately 6 μm

from the core the loss is 112 dB.m−1. This value is > 10× the equivalent electrode to

core separation for the SIF, a result which is consistent with the lower confinement of

optical modes in such fibres. The loss in such a fibre can, in principle be reduced by

increasing the size of the air holds and/or increasing the number of rings of holes. In

each case the refractive index distribution is becoming more like that of the step index

Chapter 9 191

fibre. However, as previously stated, this fibre geometry represents the best case for

optical confinement achievable with current fabrication capabilities.

9.2.3 Discussion of Results

The computational models indicates that the DC electric field strength in the vicin-

ity of the core varies approximately as 1/r2 where r is the electrode to core distance.

Fields of sufficient strength to induce the necessary electro-optical effects are possible,

in particular in the case of a thermally poled fibre were the required fields are much

lower.

We have shown that the loss induced by the internal electrodes varies exponentially with

core to electrode separation. This effect can be mitigated by confining the light more

strongly, i.e. higher refractive index contrast. The wagon wheel MOF and HexMOF

represent two extreme cases for electrode induced loss. The wagon wheel MOF, with

its very good modal confinement, experiences virtually no loss at all. On the other

hand, the HexMOF design considered here, has relatively poor mode confinement and

therefore displays high electrode induced loss.

It is thus clear that in order to minimise the attenuation produced by the internal

electrodes, the optical mode should be well confined to the core. This can be achieved,

in the case of a SIF, by using high refractive index contrasts. For MOFs this requirement

is met by incorporating large proportions of air in between the electrodes and the core.

9.3 Insertion of Electrodes into Optical Fibres

We have determined the liquid metal injection method (Section9.2) to be the supe-

rior method for providing optical fibres with internal electrode. This assessment

is based on the following observations drawn from the available literature: The entire

cross section of the electrode hole is filled with metal, unlike wire insertion wherein there

will be an air gap between the electrode and the fibre. The air gap leads to non-uniform

electric fields along the fibre. Furthermore, as we are able keep the majority of the

thermal contraction longitudinal to the fibre by slowly drawing it from the furnace the

stresses can be minimised. This is not possible with the simultaneous fibre+wire draw-

ing technique. As such we designed and built an apparatus for filling optical fibres with

liquid metal3.

3This was greatly facilitated by the advice and guidance of Walter Margulis at ACREO, Stockholm,Sweden


The following sections describe the theory and design of the filling apparatus and the

subsequent testing and filling results.

9.3.1 The Physics of Capillary Filling

The holes in an optical fibre for the insertion of electrodes are essentially capillaries and

therefore, to understand how they will fill with a liquid metal, we need to refer to the

theory of capillary filling as described by the Hagen-Poiseuille equation as given by:

Φ =|ΔP |πr4c8ηLc

. (9.5)

Where Φ is the volumetric flow rate, rc is the radius of the capillary, η is the dynamic

viscosity of the liquid, Lc is the length of the capillary and ΔP is the pressure difference

between the ends of the capillary. We can calculate the time taken for a capillary of

length Lc to fill by dividing the cross sectional area of the capillary by Φ to obtain

t (Lc) =8ηL2

c

|ΔP |r2c(9.6)

Figure 9.10 illustrates the specific example of pressure assisted filling of a capillary.

Figure 9.10: Schematic representation of pressure assisted filling of capillaries forwetting and nonwetting liquids. Left: Pressure assisted filling a capillary with a wettingliquid. Capillary pressure Pc, is positive and thus acts in the same direction as theapplied pressure Papp. Right: Filling a capillary with a nonwetting liquid. In this case

Pc is negative and thus works against Papp.

Chapter 9 193

In this case we can write ΔP as

ΔP = Papp − Pext − Pc (9.7)

Where Papp is the pressure applied to the pressure vessel, Pext is the external atmo-

spheric pressure and Pc is the capillary pressure which can be calculated from

Pc =2γ cos θc

rc(9.8)

In Equation 9.8 γ is the surface tension of the liquid (Bismuth tin solder has a surface

tension of γ = 0.0319 N.m−1 ) and θc is the contact angle that the liquid makes with

the surface of the capillary.

The contact angle θc, for a liquid on a solid substrate (as illustrated in Figure 9.11) is

determined by the thermodynamic equilibrium which is established by the three phases.

The liquid phase of the droplet, the solid phase of the substrate and the gas phase

which is a mixture of the atmosphere and the equilibrium concentration of the droplets

vapour. This equilibrium is established by balancing the solid-vapour interfacial energy,

the solid-liquid interfacial energy and the liquid-vapour energy (i.e. surface tension).

Figure 9.11: Illustration of the contact angles between a liquid on a solid substrate.Left: Wetting implies that the contact angle is less than 90◦. Right: For contact angles

> 90◦ the liquid is Nonwetting.

Contact angles fall into one of two distinct groups: Contact angles measuring less than

90◦ indicate that the liquid is wetting (left of Figure 9.11) the surface of the substrate.

The capillary pressure in this instance will be greater than zero as cos θc > 0 for 0 �θc < 90. If the contact angle is greater than 90◦ then the liquid is non-wetting for that

particular substrate (right of Figure 9.11). For 90 < θc � 180 the sign of the capillary

pressure is negative which serves to expel the liquid from the capillary.

The effect of the applied pressure is to push the liquid into the capillary, against gravity

for a wetting liquid and against the negative capillary force for a non-wetting liquid.


9.3.1.1 Contact Angle Measurements

In order to be able to calculate approximate filling times and the required pressures we

measured the contact angle for the BiSn alloy on a number of glass substrates including

silica4, bismuth borate5 and tellurite6. This was achieved in the following way:

1. A polished, clean and flat substrate was placed onto a electric hot plate.

2. We placed a small sample of the BiSn onto the substrate.

3. The temperature of the hot plate was gradually increased until the BiSn was

completely melted and formed a into a bead.

4. We then cooled the substrate and BiSn to room temperature.

5. The bead of BiSn was removed from the substrate and glued onto a flat piece of

aluminium.

6. A saw was used to cut the BiSn+aluminium in half then the exposed edge was

polished smooth.

7. Under a microscope we imaged the region of the BiSn bead which had been in con-

tact with the glass substrate and from this image we used image analysis software

to determine the contact angle (Figure 9.12).

Images of the BiSn beads and the contact angle are shown in Figure 9.12 and the results

of these measurements are summarised in Table 9.5.

Substrate Contact Angle [◦]

Silica 153Bismuth 166Tellurite 176

Table 9.5: Measured contact angles for BiSn solder on silica, bismuth and telluriteglass.

It is observed that the contact angle is increasing for increasing heavy metal content i.e.

silica¡bismuth¡tellurite. This is consistent with the general observation that the surface

tension of a glass decreases with increasing heavy metal content [131].

We can now apply the contact angle information with some reasonable approximations

for capillary dimensions to design a fibre filling apparatus.

4Commercial fused silica.5Ahahi Glass Co. Japan.6Produced in house.

Chapter 9 195

Figure 9.12: Photographs of BiSn contacting silica, bismuth and tellurite substrates.Contact angle measurements performed with graphics editing software (GIMP).

Electrode containing capillaries are typically in the order of 10 − 30 μm in diameter.

Furthermore, all measured contact angles range between ≈ 150− 175◦ which, translates

into capillary pressures in the range −0.4→ −1.3 bar. Accordingly we require pressures

larger that this to fill the fibre. With reference to Equation 9.6 we can determine

the applied pressure required to provide reasonable filling times. If we consider a 1 m

length of fibre a reasonable filling time would be in the order of 10 minutes, under these

requirements we calculate a required applied pressure of ≈ 1bar.

9.3.2 Design and Operation of the Fibre Filling Apparatus

An apparatus for filling optical fibres was constructed, the components of which can

been seen in Figure 9.13. The apparatus consists of a brass high pressure cell with a

removable crucible for holding the molten BiSn (or any other electrode material). A

teflon gasket was fabricated to act as a high temperature seal between the pressure cell

and its lid and the fibre was sealed using a teflon plug (Figure 9.14).

In the following list we outline the procedure for loading the fibres into the filling appa-

ratus.

1. Approximately 10−15 lengths of fibres are cut at about 1 m length.


Figure 9.13: Photograph of fibre filling apparatus.

2. The lower 2 cm of the fibres had the acrylite coating stripped using a mechanical

stripping tool.

3. We then cleave the fibres leaving ≈ 3 cm of stripped fibre which was cleaned with

an organic solvent. This step is important to ensure that the end of the fibre is

free from dirt or glass to avoid obstructing the holes during the filling.

4. All of the fibres are brought together into a bundle which is then threaded through

the pressure cell lid the fibre seal and fibre seal clamp from the un-cleaved end

first so as to avoid contamination.

5. Next, we carefully tighten the fibre seal clamp until it is no longer possible to move

the fibres.

6. The lid+fibre assembly is fitted to the pressure cell which has been preheated such

that the metal for filling is molten. It is important to ensure that the fibre ends

penetrate the surface of the molten metal.

7. The entire apparatus is placed into an oven and connected to the high pressure

gas line.

Chapter 9 197

Figure 9.14: Schematic of filling apparatus showing fibre positioning and sealingtechnique. Red arrows indicate the direction of forces as the fibre seal clamp is screwed

down to deform the teflon to produce a seal.

8. After approximately 1 h the apparatus should be at the same temperature as the

oven and importantly the teflon seals and remaining acrylite will now have softened

slightly. We then tighten the pressure cell lid bolts as much as possible. A small

pressure is applied to the cell such that escaping air can be heard from the fibre

seal. The fibre seal clamp is then tightened until this noise can no longer be heard.

We repeat this step gradually increasing the applied pressure until we have reached

the predetermined filling pressure.

9. The oven is then closed for the required duration for filling to occur.

10. Once the fibres have been filled the entire apparatus is cooled inside of the oven

with the pressure still applied.

9.3.2.1 Selective Filling of Optical Fibres

If we consider the additional difficulty of filling holes for internal electrodes in a MOF

it becomes immediately obvious that filling of the microstructured holes which provide

the guidance must be avoided. We therefore require a selective hole filling technique.


At present we do not have microstructured optical fibres with the necessary holes for

internal electrodes. Accordingly, to test the selective filling techniques we instead used a

twin hole silica fibre7. We were able to develop a simple technique for selectively filling

electrode holes which should be easily applicable to a microstructured optical fibre with

internal electrodes. The following is a step by step outline of the procedure:

1. We begin by sealing the holes we wish to fill with metal. This counter intuitive step

is performed because the electrode holes are always towards the outside of the fibre

away from any microstructure. The fibre is viewed in a stereoscopic microscope.

The large working distance of these microscopes is ideal for manipulating fibres in

this way. A small amount of UV curable glue on the end of a sharp object (such as

a pin or syringe needle) is gently brought into contact with the desired hole. The

best results were achieved by gently dragging the glue down the edge of the fibre

and allowing the wetting of the glue and the capillary forces do most of the work.

Figure 9.15: Illustration of manual fibre hole blocking. Left: With the aid of amicroscope and a steadied hand we draw a glue tipped needle past the hole we wish toblock. Right: The wetting action of the glue and capillary forces server to block the

hole if performed correctly.

Capillary forces draw the glue a small distance into the hole or holes. The glue

is then cured with exposure to UV radiation. Figure 9.16 shows a twin hole fibre

that has had one hole capped in this way. The other hole is unblocked. We were

able to reliably perform this step by hand to an accuracy of ≈ ±5 μm.

2. We next connect the uncapped end into a negative pressure cell. This was con-

strued from a small glass beaker and a thick rubber membrane. A large gauge

syringe needle is pushed trough the rubber membrane then the fibre is fed through

7Provided by Walter Margulis at ACREO, Sweden

Chapter 9 199

Figure 9.16: Photograph of an optical fibre with a manually blocked hole.

the needle until it is inside of the pressure cell. The syringe needle is then removed

from the seal leaving the seal around the fibre. A second syringe needle connected

to a syringe is pushed through the seal to provide a means of reducing the pressure

in the cell.

Figure 9.17: Photograph of an optical fibre with pressure assisted filling of UV glue.

The capped end of the fibre is immersed in a small quantity of UV glue after which

we apply suction to the pressure cell. This causes UV glue to be drawn into the

holes of the fibre that we wish block so that they will not fill with metal during the

electrode insertion process. The configuration for this filling set up is illustrated

schematically in Figure 9.18.

It is important to fill this hole significantly further than the capped hole i.e. ≈50 mm. With the negative pressure still applied a UV lamp is used to cure the

glue. It is important to keep the negative pressure applied to avoid air bubbles

from forming in the capillary. The result of this step can be seen in Figure 9.17

where the image shows one hole that is filled only a short distance (This is the

capped hole from step 1) and the other is filled several times further.


Figure 9.18: Illustration of UV glue pressure filling set up.

3. The next step is to cleave the fibre at a point between the capped hole and the

pressure filled hole as illustrated in Figure 9.19.

Figure 9.19: Photograph of an optical fibre prepared for selective filling demonstratingthe ideal cleave position.

Figure 9.20 shows the fibre end after cleaving. The cleave is very bad due to the

presence of the glue in the electrode hole.

4. Now we are left with an open hole which we wish to fill with metal and a very well

blocked hole that we wish to keep free of metal. We filled the blocked twin hole

fibre with BiSn and Figure 9.21 shows the result after cleaving the glued end from

the fibre to leave only metal filled fibre.

Therefore, we can conclude that under the conditions of high temperature (≈180 ◦C) and high pressure (≈ 12 bar) the UV glue is sufficient to block the hole.

Chapter 9 201

Figure 9.20: Photograph of the cross section of an optical fibre with one hole blockedfor selective filling.

Figure 9.21: Photograph of an optical fibre with a selectively filled electrode hole.

9.4 Optical Fibre Preform Fabrication

Afirst step towards producing optical fibres with internal electrodes is to produce

the optical fibre preforms. The key requirements for this preform are a central

region to act as the waveguide. This can be either a high index region, such as would

be found in a step index fibre. Alternatively, the central region can be formed from

MOF type structures (see Figure 1.1). Critical to electro-optical devices is the presence

of internal electrodes, thus requiring large holes in the preform, for later introduction of

metal.

Some methods for producing preforms with internal features, such as the ones described,

are: Direct casting, wherein a mould with the necessary shape is fabricated and the glass

is poured directly into it [132]. Glass billets can be ultrasonically drilled to produce the

necessary holes [133]. We currently use the extrusion method for creating optical fibre

preforms. This involves heating a glass billet above its transition temperature (Tg) and


forcing it through a metal die [134], which imprints the desired structure, as shown in

Figure 9.22

Figure 9.22: Schematic of the optical fibre preform extrusion apparatus. This crosssection shows the essential elements of preform extrusion. A glass billet is held in abody, this is heated above Tg and pushed through a die (arrow indicating the directionof the force). The preform that exits the die has imprinted in it the desired structure.

Modified from [135]

The process for fabricating the fibre then involves inserting the core (high index rod

or MOF preform) into the jacket (Figure 9.23) and drawing into fibre the assembled

preform on a fibre drawing tower.

In the following Section 9.4.1 we describe experiments that were carried out to develop

the capabilities required to produce the optical fibre preforms for electro-optic fibres.

9.4.1 Fabrication of the Electrode Jacket

Our initial investigations focused on the fabrication of the electrode jacket alone, as this

is required regardless of fibre type. Our goal was to produce a preform with a small

central hole, Diameter≈ 1 mm, and two larger outer holes for > 2× the central hole (see

left of Figure 9.23).

The photographs in Figure 9.24 show an example of an electrode jacket die, both the die

insert, which produces the features in the preform and the die outer, which is responsible


Chapter 9 203

Figure 9.23: Illustration of the extruded jacket and core for creating the preform fora step index optical fibre with internal electrodes. The electrode jacket has three holesin order to accommodate the fibre core and the two internal electrodes. A core madefrom a higher index glass is extruded and caned on a fibre drawing tower so that it fitssnugly into the core hole of the electrode jacket. This entire assembly is then drawn

into a fibre.

for determining the exterior shape of the preform. The key features are the pins that

create the holes for the core and electrodes and the many feed holes that allow the glass

to pass from the extrusion body and through the die.

Figure 9.24: Die for electrode jacket preform. Left: The components of the electrodejacket die. The die insert produces the features internal to the preform and the dieouter produces the exterior shape. Right: Shown is the assembled die. The regionshown is where the extruded glass exits the die and the features are imprinted onto thepreform.The array of many small holes in the die insert allow glass to flow from theextrusion body and into the die (see Figure 9.22). Pins are used to create the circular

holes for the core and electrodes.

To begin with, we chose an non-optimised design for the electrode jacket preform. These

trials were performed with the express purpose of solving fabrication related problems


inherent in the extrusion of a low rotational symmetry preform such as the electrode

jacket. Accordingly, the die design has the essential elements of the electrode jacket

without including carefully optimised dimensions. Once the fabrication issues have been

solved the optimal preform can then, in principle, be fabricated.

We experimented with various die designs in an effort to produce an electrode jacket

free from distortions. Shown in Figure 9.25 is the evolution of jacket extrusions as

modifications were made to the feed holes and die pins.

Figure 9.25: Electrode jacket preform extrusion trials. Top row: Photographs of theextruded preforms for each trial. Second row: Feed hole configurations, where a blackcircle indicates a hole blocked by a pin and red circles are blocked holes to mediate the

flow rate. Third row: The pin dimensions and distances. All dimensions in mm.

The following list details the conditions for each extrusion trial as well as a discussion of

the results from each trial. All extrusion trials were performed using a commercial lead

silicate glass (F2, Schott Glass Co.) to minimise cost. Glass billets of 30 mm diameter

and 30 mm height were used. The extrusion temperature for F2 is approximately 580◦

(Tg = 436◦) and the extrusions were carried out with extrusion speeds of 0.2 mm.min−1.

� Trial 1

In trial 1 we used a uniform distribution of equal size feed holes, with the exception

Chapter 9 205

of the holes around the electrode pins. These had to be smaller to account for the

diameter of these pins.

The resulting preform, shown in Figure 9.25 under Trial 1, is very distorted. There

is swelling of the regions to the left and right of the central hole. Also, the central

hole is itself distorted into an elliptical shape.

Deviations from circularity of the central hole present a significant issue. It is

critical for the central hole to remain circular as it must accept the cane. On the

other hand, distortion of the electrode holes is less important. This is because the

electrodes are introduced into the fibre as a liquid which will conform to the shape

of the holes. Additionally, during the fibre draw it is likely that the surface tension

of the molten glass will cause these holes to become circular.

� Trial 2

To reduce the swelling of the left and right regions and distortion of the central

hole we decreased the number of feed holes in the left and right regions, thereby

reducing the amount of glass flowing into these regions. This is indicated by the

red holes in Figure 9.25 under Trial 2. In addition to reducing flow, we increased

the length of the central pin. We based this decision on the assumption that the

flow of the glass becomes predominantly longitudinal the further it is from the exit

of the die.

We can draw the following conclusions from preform resulting from Trial 2: The

swelling in the left and right portions of the preform appears to be unchanged by

the reduction in glass flow caused by the blocked holes. Further, the lengthened

central pin produced a circular feature.

� Trial 3

Trial 3 was designed to assess the effect of the distance between central and elec-

trode pins on the preform. The central pin was kept at the same length as the

electrode pins for direct comparison with Trial 1.

The preform produced in Trial 3 (shown under Trial 3 in Figure 9.25) shows that

the distance between the central and electrode pins has been reduced, however, the

preform also displays significant swelling of the left and right regions, a distorted

central hole and electrode holes that are much smaller than the pins from which

they were formed.

9.4.2 Conclusion

It can be seen from the results of our extrusion trials that more work is required in order

to produce an electrode jacket preform free from distortions. The distortions that were


observed are due to the two-fold symmetry of the jacket. As glass flows through the

die the flow nearest the walls of the die and the pins is slowest due to friction. Thus in

regions with the fewest obstructions the flow is maximal. This results in these regions

swelling and consequently distorting the holes in the jacket. If these distortions are

translated into the optical fibre, the performance of a device based on this fibre would

be compromised.

The problem of guaranteeing a circular central hole is overcome by increasing the length

of the central pin. We were unable to mitigate the swelling the the regions to the left and

right of the central hole (see Figure 9.25). These distortions may be an inevitable conse-

quence of the two fold symmetry possessed by the die. As such, alternative fabrication

techniques, such as preform drilling etc., may need to be applied to this problem.

9.5 Preliminary Investigations of Optical Fibre Fabrica-

tion

To assess any potential increase in electro-optic performance offered by tellurite glass

over silica a direct comparison should be made. We therefore elected to fabricate

a fibre from tellurite glass that is otherwise as similar as possible to the state-of-the-art

silica electro-optic fibres.

At present the most efficient electro-optic fibre has been reported by Margulis et al [108].

They claim an induced χ(2) = 0.25 pm.V−1 in a silica fibre, produced via the dual anode

technique. To make a direct comparison requires fabricating an identical fibre made

from a glass with superior nonlinear properties, such as the tellurite glasses under study

in this thesis. This in turn requires us to develop fabrication techniques necessary to

fabricate a step index fibre from tellurite glass, a capability which we did not possess.

Considering our current fabrication facilities and experience we determined that an

extrusion based rod in tube method would be a logical first step. One that would require

minimal development and/or modifications of our facilities. The extrusion based rod in

tube method involves the extrusion of a tube, that will comprise the fibre cladding.

Dimension for this tube will be in the range of ≈ 10 mm outer diameter and ≈ 1 mm

inner diameter.

Following this a rod of glass with higher refractive index is extruded. This rod is extruded

with an outer diameter of approximately 10 mm. We then reduce the diameter of this

rod such that it fits into the extruded tube. This is achieved using a fibre drawing

tower, using the so called caning procedure. The cane is inserted into the tube and the

assembly which is then drawn into fibre using the fibre drawing tower.

Chapter 9 207

In order to close the small gap in between the cane and tube to produce a good interface

a vacuum is applied to the preform during the fibre drawing process.

In the following Section 9.5.1 we describe initial experiments related to the fabrication

of a tellurite step index fibre.

9.5.1 Tellurite Step Index Fibre Fabrication Experiments

For these preliminary experiments no attempt was made to produce an optimal geometry,

as in core size etc. We were simply concerned with determining the effectiveness of an

extrusion based rod in tube fabrication method using tellurite glass. From the results on

crystallisation stability (Section 5.3.1), thermal expansion (Section 5.3.2) and refractive

indices (Section 6.4) the TZN glass series was determined to be the best candidate for

this work.

To obtain the desired difference in refractive indices between core and cladding Δn, we

refer to the refractive index data for the TZN glass series (Table 6.3). If we plot the

refractive index value as a function of Zn content and perform a linear fit we obtain

an interpolation expression that predicts the refractive index for molar concentrations

of zinc ions such that 5 � [Zn] � 20 mol%, assuming a linear dependence. The fit in

Figure 9.26 we can see that a linear approximation is valid, the R2 value for the fit is

0.997. Using the fitted linear function:

n = −0.0043[Zn] + 2.0474, 5 � [Zn] � 20. (9.9)

With reference to the crystallisation stability data in Section 5.3.1 where it was noted

that the most stable composition under study was the TZN3 composition. As such, we

choose for the core and cladding glass the following two compositions respectively:

Core: 10Na2O.12ZnO.77TeO2

Cladding: 10Na2O.15ZnO.75TeO2

Both of these glass compositions will have excellent crystallisation stability and therefore

make ideal choices for optical fibre materials. Furthermore, the coefficients of thermal

expansion of these glasses have been determined to be decreasing, very slightly, with

increasing Zinc content (see Section 5.3.2). As such the two glasses will have closely

matched coefficients of thermal expansion whit the core having a slightly higher coeffi-

cient than the cladding. This has been deemed to be preferable as it means the cladding

is under compression resulting in a more robust fibre [60].


Figure 9.26: Linear fit to TZN refractive index data.

It was our goal to fabricate a fibre with a core of approximately 10 μm diameter core

and a 160 μm diameter cladding. We can estimate the mechanical stress that would be

present in this fibre by applying Equation 5.13. We first note that for the TZN glass

series the transition temperature Tg varies by approximately 2◦C. Specifically, within the

compositional vicinity of [Zn]= 15± 2 mol.% there is essential no variation in Tg above

the uncertainty of the measurements (see Table 5.2). Thus Tg2−Tg1 ≈ 0. Accordingly,

the second term in Equation 5.13 can be neglected. The values of the parameters used in

the calculation are: Tg = 293◦C for the core glass, α1 = 19.3× 10−6 ◦C−1 (interpolated

from data in Table 5.3), α2 = 18.8 × 10−6 ◦C−1 (measured). We assumed values for

Young’s modulus to be equal to 54.5 GPa and Poisson’s ratio to be equal to 0.253 [60].

The calculated stress is σ = −38 kPa, which is well below the tensile fracture strength

of tellurite fibres which is reported to be approximately 119 MPa [60]. Furthermore, the

negative stress is indicitive of a cladding under compression, which is considered ideal

for mechanical stability [60]. This result indicates that a mechanically stable fibre can

be fabricated.

We first extruded a tube from the cladding glass with a 10 mm outer diameter and

1 mm inner diameter. The length of the tube was cut down to 180 mm. Next, a rod

of the cladding glass was extruded which measured 10 mm in diameter. Following this

the rod was reduced in diameter in the fibre drawing tower to have a diameter equal to

that if the tube inner diameter. This process is commonly refered to as ‘caning’. We

Chapter 9 209

obtained the correct size cane by periodically selecting section of the cane during the

caning process and checking the fit with the tube. Once an appropriately sized cane was

produced, we drew > 50 m of bare fibre with a diameter of 160 μm.

We measured the optical attenuation of the fibre with the cut back method. This

measurement was made such that the lower limit on the attenuation of the eventual step

index fibre could be established. Provided we make the assumption that any additional

attenuation observed in the step index fibre is as a result of the interface between the

core and the cladding .

The measurements were made with a diode laser operating at 1550 nm with an initial

fibre length of 3 m. Plotted in Figure 9.27 are the data for the measurement. The

attenuation of the bare fibre was measured as 2.8±0.09 dB.m−1 at 1550 nm.

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0

2

4

6

8 Data Linear fit

Atte

nuat

ion

[dB

]

Total Cutback Length [m]

Figure 9.27: Cut back measurement data showing optical attenuation of the coreglass bare fibre.

We next assembled the rod in tube preform, which was then placed into the fibre drawing

tower and drawn down to a diameter of 160 μm. Initially during the draw there was a

large gap between the core and cladding. We subsequently applied a vacuum to the tube

with the pressure difference between ambient and internal ranging between 0.1 mBar and

10 mBar. This had the desired effect of closing the interface gap. However, small holes

were observed at the interface the presence and size of these holes was independent on the

strength of the applied vacuum beyond the minimum. Figure 9.28 A (top illumination)

and B (bottom illumination) show optical microscope images of the fibre where the core

is clearly visible. The core of the fibre was measured to be ≈ 11 μm in diameter.


As can be seen in Figure 9.28 B the fibre is guiding the light from the microscope and

there is a dark ring around the core. Further investigations showed that this dark ring

results from microscopic holes at the interface, as seen in the electron microscope images

in Figure 9.28 C and D. These holes are present along the entire length of fibre and are

randomly distributed. It is unclear to us what the small structure observed within the

interface hole is (shown in Figure 9.28).

Figure 9.28: Microscopy images of tellurite step index fibre. A) Illumination fromabove showing fibre core as a dark circle. B) Illumination from beneath, core shown asbright circle. C) Electron microscope image of the fibre core showing interface holes.

D) Electron microscope image of interface hole.

0.0 0.1 0.2 0.3 0.4 0.5

0

1

2

3

4

5

6 Data Linear fit

Atte

nuat

ion

[dB

]

Total Cutback Length [m]

Figure 9.29: Cut back measurement data showing optical attenuation of the telluritestep index fibre

Chapter 9 211

Using the cutback method we measured the optical attenuation of the step index fibre,

see Figure 9.29. We determine the loss to be 11.3±2 dB.m−1 at 1550 nm.

Subtracting the loss of the core material alone we obtain 8.5 dB.m−1, which we attribute

to the interface imperfections. This compares unfavourably with other reports of core

clad fibres fabricated via extrusion based rod in tube methods. For example Lousteau

et al claim 6.8 dB.m−1 at 1550 nm [136]. However, the optical attenuation will depend

heavily on core size and refractive index contrast (i.e. mode confinement) and therefore

it is difficult to make direct comparisons. Future work will involve experiments designed

to minimise the interface imperfections and hence the loss.

9.6 Conclusion

The qualitative analysis provided by the computational models for electrode induced

loss and the DC electric field across the core show us that for a efficient device

we require a well confined optical mode, as far as possible from the electrode in order

to minimise the loss. The strength of the DC field reduces linearly with separation and

can therefore be maintained at a high value (i.e. 108 V.m−1) while minimising the loss

which decreases exponentially over the distance of the wavelength of the propagating

light.

We have made good progress towards the ability to fabricate optical fibres with internal

electrodes. The technical challenge of selectively filling the fibres with metal electrodes

has been overcome and much progress towards fabricating a suitable fibre preform has

been made.

Finally, based on the material characterisations made in the previous chapters, we have

identified a pair of tellurite glass compositions that can be combined to produce a pro-

totype fibre. Steps toward the fabrication of a step index fibre made from these glasses

have been made and the key issue of interface imperfections was identified.

Chapter 10

Concluding Remarks

10.1 Conclusion of Thesis Findings and Results

We conclude this thesis by addressing the research goals stated in Chapter 1. Future

research in this area will benefit from an analysis of the factors, if any, that

impeded progress and/or the realisation of the stated goals.

The overall goal for this work was the fabrication of a prototype electro-optical fibre

modulator. This goal was not achieved. The contributing factors that prevented the

realisation of this goal can be separated into two types of experimental difficulties:

those that were unavoidable and those resulting from flawed initial assumptions. The

first category includes things such as: unreliable supply of raw materials that slowed

progress in the glass fabrication and malfunctioning equipment.

The second category of experimental difficulties represent serious issues that will need to

be overcome if work in this area is to develop further. The most fundamental error that

was made was not recognising that certain glasses can not be thermally poled via the

charge migration method (see Section 7.2). Our initial assumption that a tellurite glass

containing sodium ions should be able to be thermally poled by the charge migration

method was based on the evidence from silica poling wherein the sodium enables the

creation of a permanent χ(2). It is now evident that the situation if more complicated

than this.

A further difficulty that eventuated due to an incorrect assumption was the inability to

extrude an optical fibre preform with the necessary features for the subsequent intro-

duction of electrodes into the fibre. We encountered large distortions in the obtained

preforms which appear to be endemic to the low rotational symmetry of the geometry.

Indeed, in a private communication with collaborator Prof. Darren Crowdy at Imperial

College London, mathematical models of the glass flow have indicated that this type of

213

214 Concluding Remarks

geometry may always suffer from these distortions [137]. Presently, more investigations

are being undertaken to better understand the process.

Despite not achieving the final goal set at the outset of this work much progress was

made toward this goal. In particular, the sub-goals outlined in Chapter 1 are reiterated

below with comments made as to the various achievements for each:

1. To develop a large range of tellurite glasses and characterise fully their properties

so that informed decisions can be made regarding the choice of glass. Adding to the

collective understanding of this glass system and the origin of its properties this

knowledge can be applied to the design of devices and new glasses.

We produced several families of tellurite glass within each compositional variations

were explored. Of the glass families that were studied (TMN, TZN and TBN)

the TZN glass family stands out as being the most suitable candidate for optical

fibre fabrication. Its high crystallisation stability makes it a suitable materiel for

the processing required for optical fibre fabrication. The small variation in its

coefficient of thermal expansion over the range of compositions makes it an ideal

candidate for core/clad optical fibres. Furthermore, the liner variation in refractive

index with composition enables a wide range of index contrasts. Significantly, for

electro-optical applications, the nonlinear refractive indices of these glasses are in

excess of > 20× that of silica, the current material of choice for electro-optical

fibre devices.

2. To identify suitable tellurite glasses for nonlinear optical fibre devices.

The suitability of the TZN glasses was established via the fabrication of prototyp-

ical optical fibres.

3. To generate permanent second order nonlinearities in some of these glasses via

thermal poling, thus making possible efficient electro-optical devices for controlling

the passage of light in optical systems.

Thermal poling experiments were conducted on selected compositions. The com-

plexity of the process was underestimated and progress was limited. However, fu-

ture investigations into this area will be benefited by the knowledge gained herein.

Significant progress was made in the area of characterisation of the second order

nonlinear properties of thermally poled glass. The Maker fringes experiment that

was constructed had very high sensitivity due, mainly, to the novel data acquisition

system developed. Furthermore, the analysis techniques for the experimental data

were analysed in detail and improvements were made. In particular in terms of

the application of genetic algorithms to finding optimal data fits and therefore

measured parameters.

Chapter 10 215

4. To design and fabricate prototype electro-optical devices from in house fabricated

optical fibres.

Progress was made towards the design and fabrication of electro-optical devices.

That being so, we have determined useful information regarding influence of fibre

structure on the electric fields produced between the internal electrodes. These

results will compliment future work wherein the thermal poling of microstructured

optical fibres is explored.

Additionally, the attenuation produced by internal electrodes was studied via com-

puter models. Results indicate the the confinement of the optical mode has a large

influence on the strength of the attenuation. Certain mircostructured fibres such

as the wagon when fibre offer extreme confinement and thus, potentially, very low

loss alternatives to current step index designs.

Fabrication techniques such as selective electrode insertion and electrode jacket

preform extrusion were also explored. A sound technique for selectively filling

electrode holes within a microstructured fibre was developed. Thereby providing

one of the key elements required for fabricating electro-optical fibre devices.

10.2 Future Work

Future work towards the fabrication of electro-optical fibre devices will focus on the

refining the processing of the TZN glasses that were identified as the most suitable

candidates for this work. In addition to this, It will be useful to explore tellurite glass

compositions that do not contain sodium as a constituent. Following from the results of

the thermal poling experiments, glasses that have only trace amounts of mobile species

may indeed be preferable for poling. In this way the glasses are expected to behave

somewhat more like silica during poling.

Our fabrication trials for the preform jacket all resulted in significant deviations from

the target preform shape. Further extrusion trials will be necessary to determine if this

can be overcome, or indeed, if an alternative preform fabrication method is required.

Finally, our preliminary step index tellurite fibre experiments, although successful in

creating a fibre that guides light, resulted imperfect interfaces which produced unaccept-

ably high optical losses. More work is required to refine this process and/or determine

whether or not the extruded rod in tube method has any merit.

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