Non-Symmetric

Microstructured Optical Fibres

Introduction

• Information Age – Computers, CD’s, Internet• Need a way to transmit data – Optic Fibres• Other uses – medicine, surveillance

The story so far…• Currently use conventional optic fibres• Began in the 60’s, first used in the 80’s• So far, so good• Moore’s Law + Economics = Need for better fibres

Problems…

• Losses – 0.18dB/km at best = lose 4% of power/km

• Restricted wavelength

• Dispersion

Microstructured Optical Fibres(MOFs)

• First thought of 10 years ago

• Fibre + air holes = MOF

• Lower losses

• Much greater versatility

Simple Concepts• Light is contained in the fibre by the holes• Light propagates along many modes• Intermodal Dispersion - coupling between modes• Only want single mode fibres (fundamental mode)

Polarisation Mode Dispersion

• Fundamental mode – two polarisations

• Coupling between different polarisations

• Theory – degenerate modes, no coupling

• Heat, stress, manufacture = imperfections

• Reality – non-degenerate modes, coupling

Solution?

• Create a non-symmetric fibre – birefringence

• Fundamental mode no longer degenerate

• Use only one polarisation – eliminate polarisation mode dispersion

My Experiment

• Investigate modes in non-symmetric MOFs

• Computer simulations, using programs written by Boris Kuhlmey

• Input parameters and structure

• Program gives information about modes

Basic parameters

• Used three rings of holes – six holes in the first ring, 12 in the second, 18 in the third

• Kept hole size constant at 1.30 m

• Kept wavelength constant at 1.55 m

• Kept fibre size and refractive indices constant

Ellipses

• Used Ellipses, varying eccentricity while keeping the semi-major axis constant (length a) Eccentricity = e = (1-b2/a2)0.5

• Put cylinders equally along the arc

Problems/Constraints

• No formula for arc length of an ellipse – numerical integration

• Can’t have eccentricity too close to 1 – cylinders overlap, results inaccurate

• Took 0 =< e < 0.77

Input Data

The Fibre

Output

Output (continued)• The program generates two modes:

Mode 1 Mode 2The field shown is the Poynting Vector in the z-direction

The difference?• The same two modes:

Mode 1 Mode 2

The field shown is the E field in the x-direction

Important Numbers

• Refractive Index = = r + ii

• Real Component – “Normal” refractive index e.g. Snell’s Law

• Imaginary Component – Loss of the fibre

• Degree of Birefringence – Bm = |r,x - r,y|

• Bm > 10-4 = good fibre

LossesLoss vs Eccentricity

0.00000E+00

5.00000E-14

1.00000E-13

1.50000E-13

2.00000E-13

2.50000E-13

3.00000E-13

3.50000E-13

4.00000E-13

4.50000E-13

5.00000E-13

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Eccentricity

Loss

x-polarised

y-polarised

ResultsRefractive Index vs Eccentricity

1.42

1.42

1.42

1.43

1.43

1.43

1.43

1.43

1.44

1.44

1.44

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Eccentricity

Refr

acti

ve I

nd

ex (

real)

x-polarised

y polarised

More ResultsBm vs Eccentricity

0.00000E+00

2.00000E-04

4.00000E-04

6.00000E-04

8.00000E-04

1.00000E-03

1.20000E-03

1.40000E-03

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Eccentricity

Bm

Trends?Bm

0.5 vs Eccentricity

y = 0.1648x4 - 0.1407x3 + 0.0519x2 + 0.015x + 8E-05

R2 = 0.9999

0.00000E+00

5.00000E-03

1.00000E-02

1.50000E-02

2.00000E-02

2.50000E-02

3.00000E-02

3.50000E-02

4.00000E-02

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Eccentricity

Bm

0.5

Summary

• Losses decrease with eccentricity, with i,x less than i,y - can create

• Real part of refractive index decreases with eccentricity, with r,y less than r,x

• Bm increases with eccentricity according to a power law

• Can create highly birefringent fibres using this method

References• Govind P. Agrawal, Fiber-Optic Communication Systems (Wiley and Sons, New York,

2002)• Thomas White, “Microstructured Optical Fibres – a Multipole Formulation”, University

of Sydney, October 2000• Boris T. Kuhlmey, “Theoretical and Numerical Investigation of the Physics of

Microstructured Optical Fibres”, University of Sydney, 2003• Boris T. Kuhlmey, Ross C. McPhedran, C. Martijn de Sterke, “Modal cutoff in

microstructured optical fibers”, 2002