On Fibre Tip Graphene-based Ultrathin Flat Lens Towards ...

On Fibre Tip Graphene-based Ultrathin

Flat Lens Towards High-Resolution

Endoscopes

A thesis submitted for the degree Doctor of Philosophy

by

Guiyuan Cao

Centre for Translational Atomaterials

Faculty of Science, Engineering and Technology

Swinburne University of Technology

Melbourne, Australia

2020

i

Declaration

I, Guiyuan Cao, declare that this thesis entitled:

“On Fibre Tip Graphene-based Ultrathin Flat Lens towards High-Resolution Endoscope”

is my own work and has not been submitted previously, in whole or in part, in

respect of any other academic award.

XGuiyuan Cao

Mr

Centre for Translational Atomaterials

Faculty of Science, Engineering and Technology

Swinburne University of Technology

Melbourne, Australia

October 2019

ii

Abstract

Optical lenses, one of the most important components for many areas of modern science and

technology, are facing a great challenge of miniaturization and integration. Conventional

optical lenses are bulky because of their working principle based on refraction, in which phase

modulation accumulates when the light wave propagates through the lens. The accumulated

phase modulation is decided by Δn×Δt×k, where Δn is the refractive index difference between

the lens and the surrounding medium (usually air), Δt is the thickness of the lens, and k=2π/λ is

the wavenumber, and λ is the light wavelength in vacuum. However, owing to the limited

refractive index of naturally available transparent dielectric materials, a beam should propagate

over an optical path that is much longer than the wavelength of light to realize the desired

wavefronts. Therefore, the conventional refractive lenses are fundamentally incapable to

achieve subwavelength thickness. In addition, the manufacturing process requires very high

accuracy to control the surface profile to achieve accurate phase modulation, otherwise,

aberrations may be introduced. Furthermore, it is extremely challenging to integrate phase

modulation function with conventional refractive lenses, such as the aberration compensation

and the generation of specialized intensity distribution, such as optical needle beams,

multifocal array, and phase vortices, which are necessary to achieve multifunctions

With the rapid development of nano-fabrication techniques and methods, miniaturization and

integration are desired for photonic devices. It becomes possible to fabricate ultrathin flat

lenses composed of nanostructures, such as plasmonic structures or metasurfaces. Ultrathin flat

lenses have the advantages of astigmatism and coma aberrations free, even when the numerical

aperture (NA) is very high. They act as one of the most important components for the nano-

photonics and integrated photonic systems, as well as electro-optical applications, such as solar

cells and fibre communication systems.

A variety of flat lenses have been proposed and fabricated, such as negative refraction lenses,

metasurface lenses, and graphene oxide (GO) lenses. The negative refraction lenses refract the

incident light to the same side of the surface normal. Therefore, the light from a point source

will be focused On the other hand of the flat negative refraction lens. In addition, the negative

refraction lens is able to break the diffraction limit of light focusing as it is able to amplify

evanescent waves, which is essential for maintaining high spatial frequency components.

However, the negative refraction lens can only work in the near field region, as the focused

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evanescent wave decays exponentially from the surface. Thus, it is impossible to construct a

lens based on negative refraction for far-field applications.

On the other hand, the Fresnel zone plate focuses light by diffraction from a binary mask that

modulates the amplitude of the incident radiation. Although the Fresnel Zone Plate achieves

focusing effect with deep subwavelength thickness, the diffractive efficiency is low due to the

block of light and the wavefront cannot be accurately controlled to achieve high focusing

performance. On the other hand, a more advanced solution is represented by the Fresnel lens,

which introduces a phase-only modulation varying along the radial direction to focus light more

efficiently, affording the minimized absorption losses, and well-controlled wavefront.

Furthermore, the aberration can be pre-compensated by carefully designing the phase

modulation structure, leading to the advantages of high NA and better focusing resolution for

optical systems. To guarantee a smooth spherical phase profile for efficient light focusing, the

Fresnel lens thickness has to be at least equal to the effective wavelength λeff = λ/n where n is

the refractive index of the medium. In addition, the thicknesses of the flat lenses need to be

continuously tapered, which inevitably adds burden on fabrication techniques. Therefore, it is

desired to achieve an ultrathin flat lens design which modulates the phase and amplitude of the

incident light simultaneously for high focusing performance with subwavelength thickness.

Alternatively, flat diffractive optical devices can be designed based on nanostructure

engineering, such as plasmonic nanostructures and metasurfaces. These are structural building

blocks engineered to have specific optical properties of resonance and scattering, thus

providing phase or amplitude modulations as a new type of optical materials. Recent

developments in multilayers cascaded optical elements and coalescing two types of meta-atoms

offer new opportunities to simultaneously modulate the phase and amplitude of the incident

light. However, plasmonic nanostructures and metasurfaces need to be fabricated either by e-

beam lithography (EBL) or focused ion beam (FIB), both are expensive and not scalable

processes that are not suitable for post-processing customization. In addition, the multilayer or

the coalesce structures either require prohibitive precise alignment between different layers or

suffer from low conversion efficiency due to the spatial multiplexing methods, which adds

extra complexity to the designs and the fabrication.

In contrast, taking advantages of the conversion of GO material to reduced graphene oxide

(rGO) under a laser reduction process, a graphene-like material, is possible to simultaneously

modulate phase and amplitude at a single position with an area that is only defined by laser

resolution. This allows simpler device design and fabrication and further miniaturization of

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ultrathin photonics devices. The graphene lenses have demonstrated attractive properties, such

as nanometre thickness, high focusing resolution and efficiency, high mechanical strength and

flexibility, and fast and low-cost fabrication process. In addition, the graphene ultrathin flat

lens can potentially be integrated into various optical components to change or optimize their

functionalities, such as conventional optical lenses, fibre tips, and on-chip optical systems.

To fully explore the great potential of graphene lenses, accurate design and performance

prediction of the graphene lenses should be developed. The current design method for graphene

lenses is based on the traditional Fresnel zone plate mechanism, which is only applicable for

lenses with a low numerical aperture (NA) satisfying the paraxial approximation. And the

performance prediction method is based on the Fresnel diffraction theory, which is not able to

accurately predict the focusing performance. The vigorous finite difference time domain

(FDTD) method is able to provide an accurate simulation of the focusing performance, but the

required computational time increases cubically with the simulated geometry size. A

simulation of a 10 µm3 geometrical model takes a few days. Therefore, to promote practical

GO lens applications, it is necessary to develop a theoretical modelling method that is able to

accurately design the GO lenses, and precisely calculate the focusing process of GO lenses

with arbitrary NA and focal lengths with high speed and efficiency and low computational cost.

Based on the Rayleigh-Sommerfeld (RS) diffraction theory, in this thesis, we have developed

an accurate method without the paraxial constrain to design GO lenses, and an accurate RS

model to predict the focusing performances of the GO lenses. The new design method gives

the ring radii of the desired GO lens directly from the RS diffraction theory without the

optimization process. Compared with the other design methods, such as iterative, local

optimization algorithm and global-search-optimization algorithm, the new design method

increases the design efficiency greatly. Our theoretical and experimental results have

demonstrated that the new design method is able to design GO lenses with arbitrary NA, size

and focal length. Most importantly, the demonstrated design method can be equally applicable

to other ultrathin flat lenses, including metasurface lenses and lenses made of other 2D

materials. On the other hand, the accuracy and efficiency of the RS model have been

demonstrated theoretically and experimentally. It increases our focusing prediction efficiency

significantly and maintains high accuracy compared with the FDTD method.

Due to the multifold advantages of graphene ultrathin lenses, they are expected to be used in

many applications, such as in aerospace to decrease cost incurred by weight; microfluidic

devices, where miniaturization holds the key; and biological devices, where high-resolution in-

v

situ observation is vital. However, in these applications, harsh and/or extreme environments

are included, such as extremely high/low temperatures, strong ultraviolet (UV) radiation,

atomic oxygen (AO), bio-chemicals, or corrosive chemical condition. Considering the active

chemical and physical property of GO, we have designed and fabricated ultrathin flat lenses

using pure reduced rGO(a material derived from GO, and with properties very close to

graphene). Based on the extraordinary stability of graphene, it is possible that the ultrathin flat

rGO lenses can maintain their structural integrity and preserve the outstanding performance

under those harsh conditions with low maintenance. We have experimentally simulated the

harsh environments in the lab according to the parameters in the applications, namely low Earth

orbit (LEO) environment, strong corrosive condition, and biochemical conditions. We have

compared both the surface morphologies (structural integrity) and the focusing performances

(focal intensity distributions) before and after each experiment. The results show that the rGO

lenses can maintain extraordinary focusing performance under almost all harsh environments

except the long-time exposure under AO radiation. Thus, we demonstrate a resilient ultrathin

flat lens that can be readily applied in multiple harsh environments for the first time. The

encouraging results suggest the rGO lenses are ultra-stable for a variety of practical

circumstances, in particular where harsh environments and low maintenance are required for

example strong corrosive chemical condition or biochemical condition without any protection.

Optical endoscopes play a pivotal role in medical imaging, early diagnosis and treatment of

conditions, and minimally invasive surgery. In particular, fibre-based endoscopes are widely

used in clinical diagnosis and treatment due to their highly integratable capability, small size,

high image quality, and low patient damage. The best existing fibre-optic endoscopes are based

on gradient index optical lenses to focus the transmitted light through the optical fibre to

achieve the goals of illumination and imaging of the lesion. However, due to the complex

process in controlling the gradient of the refractive index, it is technically difficult to achieve

miniaturized integration. Existing fibre optical endoscopes are between 5-10 mm in size.

Therefore, it is difficult to achieve minimally invasive or non-invasive surgery. On the other

hand, since the gradient index lens is theoretically unable to achieve a large NA, its imaging

resolution is low, typically around 10 microns. Such resolution can be used to image organisms

and cells, but it is not enough to clearly see the different parts of the cell to achieve early

screening of diseases. Therefore, there are varieties of methods that have been developed, for

example, the integration of metasurface lens on the fibre tip, besides the improvement of the

resolution of the endoscope, the method also increases the fabrication difficulty and the

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complexity of an endoscope. On the other hand, there is a possibility through the image

reconstruction method to realize miniaturized endoscope using a single multimode fibre with

limited spatial resolution. As a result, a new type of endoscope, which has high resolution,

miniaturization and can easily be fabricated, is desired to be designed and developed.

The developed graphene lenses have a minimum size of 5 to 10 microns, which is less than

one-tenth of the diameter of a human hair. On the other hand, graphene lenses based on precise

laser processing can achieve ultra-high resolution on the order of submicron. In addition, the

graphene-based ultrathin flat lens can be integrated into various optical components to change

or optimize their functionalities, such as conventional optical lenses, fibre tips, and on-chip

optical systems. The biological compatibility allows the graphene lenses to work in biological

environments, such as human tissue and blood vessels. Therefore, it is potentially feasible to

design and fabricate a new type of endoscope based on the graphene ultrathin flat lenses. We

have designed and fabricated on fibre tip GO lenses to demonstrate the possibility. And

subwavelength focal spots have been achieved theoretically and experimentally. The results

pave the way to achieve ultra-compact fibre optics endoscope devices.

The work in this thesis explores the graphene ultrathin lens from both theoretical and

experimental studies, based on which we further suggest the potential applications and studies

on the graphene ultrathin flat lens in the future.

vii

Acknowledge

On January 5th, 2016, I came to Australia for my Ph.D., and spend nearly four years at

Swinburne University of Technology. I am very happy that I am going to complete my Ph.D.

and move on now. Remembering my Ph.D. life, it is rich and colourful. Surely, I should give

my thanks to all of the following kind persons, without their help and participation, my Ph.D.

life would not be so wonderful.

First of all, I would like to give thanks to my supervisor Prof. Baohua Jia, I am very appreciative

that she gives me the opportunity to study under her supervision. During my Ph.D. study, Prof.

Jia has always been available. From the discussions of the experiment to the paper revisions,

her scientific view and rigorous scientific attitude have a far-reaching influence on me, both

my researches and daily life.

Secondly, I would like to give thanks to my supervisor Assoc. Prof. Xiaosong Gan. Prof. Gan

joined my supervisor team in the second year of my Ph.D. study, this has not decreased his

important role in my Ph.D. life.

Third, I would like to give my thanks to my supervisor Dr. Han Lin. Dr. Lin spends a large

amount of time on my Ph.D. study, from the experiments in the laboratory to paper writing for

publications. His guidance and help have great significance in my Ph.D. study.

I would like to give my thanks to my parents, their financial and spiritual support make my

Ph.D. life easier.

Finally, I would like to give my thanks to my classmates and colleagues. Many thanks to the

senior students, Dr. Shibiao Wei, Dr. Zhixing Gan, Mr. Scott Fraser, Dr. Shuo Li, Dr. Xiaorui

zheng, Dr. Yunyi Yang, Dr. Muhammad Khattab, Dr. Shuangyang Zou, Dr. Jun Ren, Dr.

Blanca Del Rosal Rabes. Many thanks to the Junior students, Mr. Yao Liang, Mrs. Xueyan Li,

Mr. Weichao Yan, Mrs. Chunhua Zhou. Many thanks to my colleagues, Mr. Dan Kapsaskis,

Dr. Tania Moein, Dr. Tomas Katkus. Many thanks to them, too many to name them all, they

made my Ph.D. life so wonderful.

Guiyuan Cao

Melbourne, Australia, 29th October 2019

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Contents Declaration .................................................................................................................................. i Abstract ...................................................................................................................................... ii

Acknowledge ........................................................................................................................... vii

List of Figures ........................................................................................................................... xi

List of Tables ....................................................................................................................... xviii Chapter 1 .................................................................................................................................... 1

Introduction ........................................................................................................................ 1

1.1 Introduction to ultrathin flat lenses ....................................................................... 1

1.2 Introduction to endoscopy .................................................................................... 6

1.3 The content of this thesis ...................................................................................... 7

Chapter 2 .................................................................................................................................. 10

Literature review .............................................................................................................. 10

2.1 Introduction ........................................................................................................ 10

2.2 Negative refraction lens ...................................................................................... 10

2.2.1 Left-handed material lens ........................................................................... 11

2.2.2 Negative refraction Photonic crystal lens ................................................... 14

2.2.3 Summary of the negative refraction lens .................................................... 19

2.3 Metasurface lens ................................................................................................. 19

2.3.1 Theoretical design ....................................................................................... 19

2.3.2 Fabrication and applications ....................................................................... 23

2.4 Graphene oxide ultrathin flat lens ...................................................................... 26

2.4.1 Graphene oxide and reduced graphene oxide ............................................. 26

2.4.2 Theoretical design of graphene oxide lens ................................................. 28

2.4.3 The fabrication of an ultrathin flat graphene oxide lens ............................. 30

2.5 Fresnel diffraction theory ................................................................................... 31

2.6 GO film fabrication ............................................................................................ 33

2.7 Direct laser writing technology .......................................................................... 36

2.8 State-of-the-arts of endoscope technologies ....................................................... 38

2.8.1 Direct lens fabrication on the fibre tip ........................................................ 40

2.8.2 Spatial light modulator ............................................................................... 42

2.9 Chapter summary ................................................................................................ 45

Chapter 3 .................................................................................................................................. 47

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Development of an accurate theoretical model for designing graphene-based ultrathin flat lens .............................................................................................................. 47

3.1 Introduction ........................................................................................................ 47

3.2 Rayleigh-Sommerfeld diffraction theory............................................................ 48

3.3 Accurate lens design based on Rayleigh-Sommerfeld theory ............................ 50

3.4 Designed result and comparisons ....................................................................... 53

3.5 Chapter summary ................................................................................................ 58

Chapter 4 .................................................................................................................................. 59

Fabrication and characterization of graphene-based ultrathin flat lens..................... 59

4.1 Introduction ........................................................................................................ 59

4.2 Fabrication of GO lens ....................................................................................... 60

4.2.1 GO film preparation .................................................................................... 60

4.2.2 Laser reduction of GO for lens fabrication ................................................. 61

4.2.3 Focusing characterization ........................................................................... 62

4.3 Fabrication of rGO lens ...................................................................................... 66

4.3.1 rGO film fabrication ................................................................................... 66

4.3.2 Ablating rGO film to fabricate a rGO lens ................................................. 67

4.3.3 Focusing characterization ........................................................................... 69

4.4 Chapter summary ................................................................................................ 70

Chapter 5 .................................................................................................................................. 72

Harsh environment tests of the rGO lens ....................................................................... 72

5.1 Introduction ........................................................................................................ 72

5.2 Low Earth orbit environment test ....................................................................... 73

5.2.1 Ultraviolet radiation .................................................................................... 74

5.2.2 Extreme heat and cold ................................................................................ 75

5.2.3 Ultra-high vacuum ...................................................................................... 77

5.2.4 Atomic oxygen radiation ............................................................................ 79

5.3 Strong corrosive environment ............................................................................ 83

5.3.1 Strong acid condition .................................................................................. 83

5.3.2 Strong alkaline condition ............................................................................ 85

5.4 Biochemical environment ................................................................................... 87

5.5 Chapter summary ................................................................................................ 89

Chapter 6 .................................................................................................................................. 90

Fibre endoscope with Graphene-based lens ................................................................... 90

6.1 Introduction ........................................................................................................ 90

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6.2 On fibre tip graphene lens design ....................................................................... 91

6.2.1 Fibre modes ................................................................................................ 91

6.2.2 Design of graphene oxide lens for the fundamental mode ......................... 96

6.2.3 Design results ............................................................................................. 97

6.3 Fabrication of the GO lens on the fibre tip ....................................................... 101

6.4 Focusing characterization ................................................................................. 104

6.5 Chapter summary .............................................................................................. 109

Chapter 7 ................................................................................................................................ 110

Conclusion and outlook .................................................................................................. 110

7.1 Conclusion of this thesis ................................................................................... 110

7.2 Outlook and future work................................................................................... 112

Reference ............................................................................................................................... 114

Publications of the author ...................................................................................................... 123

xi

List of Figures

Fig. 1- 1. Schematic of a Fresnel zone plate. .......................................................................................................... 2

Fig. 1- 2. (a) Four resonator element examples for metalens design [18-21]. (b) Gold robs array according to

phase modulation from 0 to 2π. (c) The phase modulation corresponding to the gold robs. (d) Phase modulation

of a metasurface lens along the radial direction. ..................................................................................................... 4

Fig. 1- 3. (a) A GO lens measured by AFM. (b) Schematic of the transmission and phase profile of a GO lens. . 5

Fig. 1- 4. Schematic of a prototype endoscope. ...................................................................................................... 6

Fig. 1- 5. A prototype schematic of the end detector of the optical fibre endoscopy. ............................................ 7

Fig. 2- 1. A negative refractive index lens. ........................................................................................................... 12

Fig. 2- 2. (a) The line unit cells with and without loads [38]. (b) The experimental setup to demonstrate the

focusing ability of the planar LHM lens. .............................................................................................................. 12

Fig. 2- 3. (a) The measured vertical electric field of the entire structure [38]. (b) The measured vertical electric

field along the white dashed line in (a). ................................................................................................................ 13

Fig. 2- 4. Schematic of optical superlens imaging [40]. (a) The imaging system of the superlens, object is

fabricated with chrome, the superlens is fabricated by silver. And PR represent negative photoresist to record the

image. (b) FIB image of the object. (c) AFM of the developed image on photoresist with a silver superlens. (d)

AFM of the developed image on photoresist when the 35-nm-thick silver superlens was replaced by PMMA

spacer. Scaler bar: 2 μm. ....................................................................................................................................... 14

Fig. 2- 5. The equifrequency surface schematics [41]. (a) The equifrequency surface for a beam incident from

air to a dielectric material. (b) The equifrequency surface for a diffraction grating. ............................................ 14

Fig. 2- 6. Effective index versus frequency [41]. (a) Effective index versus frequency of the TE modes in a 2D

GaAs pillar photonic crystal. (b) Effective index versus frequency of the TM modes in a 2D GaAs air-hole

photonic crystal..................................................................................................................................................... 16

Fig. 2- 7. The schematics of negative refraction in photonic crystal [42]. (a) Negatively refracted beams by a

photonic crystal. The thick arrows indicate group-velocity directions, the thin arrows indicate the phase-velocity

directions. (b) The refracted rays in a photonic crystal structure. (c) The all-angle negative refraction frequency

range highlighted by the red region. ..................................................................................................................... 16

xii

Fig. 2- 8. Point source imaging by a photonic crystal lens [42]. (a) The photonic crystal lens focuses the Hz field

of a point source. (b) The photonic crystal lens focuses the Ez field of a point source. Blue, white and red

corresponds to negative, zero and positive value. ................................................................................................. 17

Fig. 2- 9. Negative refraction observed in a photonic crystals [43]. (I) The three-dimensional photonic crystals

with a hexagon structure fabricated on a silicon substrate. (II) Negative refraction observed in the photonic

crystals. ................................................................................................................................................................. 18

Fig. 2- 10. Imaging by a negative refraction photonic crystal flat lens [44]. (a) Electric field on the cross-section

of the lens. (b) Electric field on the cross-section after the source was moved up by 4 cm. ................................. 18

Fig. 2- 11. Schematic of the abrupt phases change between two media [17]. ..................................................... 19

Fig. 2- 12. V-shaped antenna design and phase change [17]. (a) Symmetric and antisymmetric modes of the V-

shaped antennas. (b) An array of the V-shaped antennas and the corresponding phase changes. ........................ 21

Fig. 2- 13. Schematic of the flat lens design [21]. (a) The phase shift of the points on the flat lens. (b)

Hyperboloidal phase distribution. ......................................................................................................................... 21

Fig. 2- 14. Theoretical design of the aberration-free ultrathin flat lens [21]. (a) The phase shift and scattering

amplitude of the designed eight V-shape elements. (b) The focal spot intensity profile of the flat lens. ............. 22

Fig. 2- 15. Schematic of V-shaped antenna for creating an ultrathin flat lens [20]. (a) The geometrical structure

of the V-shaped antenna. (b) Theoretical phase shift and scattering amplitude of eight designed V-shaped

antenna. (c) Phase shift arrangement of the antenna to create the ultrathin flat lens. ........................................... 22

Fig. 2- 16. Theoretical results of the ultrathin lens [20]. (a) The intensity distribution of the focal spot in the

axial plane. (b)The intensity distribution along the white dasheded line in Fig. 2-16(a). ..................................... 23

Fig. 2- 17. SEM image of the fabricated metasurface ultrathin flat lens and the phase shift distribution [21]. .... 24

Fig. 2- 18. Theoretical calculations and experimental results of the intensity distribution in the focal region [21].

(a) The theoretical intensity distribution on the axial plane. (b) The experimental intensity distribution on the

axial plane. (c,d) the theoretical and experimental intensity distributions on the lateral planes alongthe white

dasheded lines in Figs. 2-18a and b. (e) The normalized intensity distribution along the colourful lines in Figs.

2-18c and d. .......................................................................................................................................................... 24

Fig. 2- 19. Different types of ultrathin metasurface flat lens [18-20, 49]. (a) The SEM image of the flat lens

fabricated with the V-shaped slit antenna. (b) Schematic of the TiO2 nanofins on SiO2 substrate. (c) SEM image

of the fabricated metalens with nanofins. (d) Schematic of the TiO2 nanopillar on SiO2 substrate. (e) SEM image

of the fabricated metalens with nanopillar. ........................................................................................................... 25

Fig. 2- 20. Schematic of the GO and rGO structure model [54, 55, 57]. (a) The chemical model of GO. (b) The

chemical model of rGO. ....................................................................................................................................... 26

Fig. 2- 21. UV-visible absorption spectroscopy of GO and rGO films [62]. Insets: GO and rGO films. ............. 27

Fig. 2- 22. The refractive index modulation of rGO with the femtosecond laser power [65]. .............................. 27

Fig. 2- 23. Design of the ultrathin flat GO lens. (a) The schematic of a laser fabricated GO lens. (b) Amplitude

and phase modulations induced by the reduction of GO. (c) Schematic of a uniform plane wave focused by the

GO lens [50]. ........................................................................................................................................................ 28

Fig. 2- 24. The theoretical model illustration of a GO lens. ................................................................................. 29

Fig. 2- 25. Thickness characterization of a high-quality GO film measured by a 3D optical profiler; the inset is

the image of the GO film on a substrate [50]........................................................................................................ 30

xiii

Fig. 2- 26. (a) Surface profile of the GO lens measured by a 3D optical profiler [50]. (b) Theoretical focal

intensity distributions in the lateral and axial plane. (c) Experimental focal intensity distributions in the lateral

and axial plane. ..................................................................................................................................................... 31

Fig. 2- 27. Schematic of point P surrounded by a closed surface S. ..................................................................... 31

Fig. 2- 28. Mirror symmetry points P and 𝑷 for a Green’s function. ................................................................... 32

Fig. 2- 29. Schematic of the optical wave diffracted in a cylindrical coordinate system. ..................................... 32

Fig. 2- 30. GO film fabrication by the vacuum filtration method. (a) Filtration assembly with GO solution. (b) A

GO film on a membrane. ...................................................................................................................................... 34

Fig. 2- 31. Schematic of a self-assembly GO film on the cover glass [79]. .......................................................... 35

Fig. 2- 32. Schematic of the layer-by-layer SA method to fabricate a GO-PDDA film on a cover glass [79]. .... 35

Fig. 2- 33. The GO-PDDA films fabricated by the SA method. ........................................................................... 36

Fig. 2- 34. Schematic of a direct laser writing system setup [90]. ........................................................................ 37

Fig. 2- 35. rGO fabrication by laser [64, 65]. (a) Optical image of the laser-irradiated rGO channel, the laser

reduction is based on the thermal mechanism. (b) The rGO thickness and linewidth with laser power, the laser

reduction is based on photochemical mechanisms. .............................................................................................. 37

Fig. 2- 36. A direct imaging endoscopy with fibre bundle and GRIN lenses [35]. (a) Fibre bundle connects to a

GRIN lens group. IL: image lens; OL objective lens. (b) Schematic of the experimental imaging system with a

fibre endoscope. .................................................................................................................................................... 39

Fig. 2- 37. Schematic of the needle tip of a single fibre endoscope. Inset: Image of the DCF with a GRIN lens.

DCF: double-clad fibre; NCF: no-core fibre; GRIN: graded index lens. [107]. ................................................... 39

Fig. 2- 38. Design and fabrication of a triplet lens system on the fibre tip using DLW [109]. (a) Ray-tracing

design of the triplet lens system in ZEMAX. (b) Simulated image of the triplet lenses. (c) SEM image of the

fabricated triplet lenses. (d) Experimental image of the fabricated triplet lenses. (e) SEM image of the whole on

fibre tip triplet lens system. .................................................................................................................................. 40

Fig. 2- 39. Metasurface endoscope design and fabrication [110]. (a) Schematic of the metasurface endoscope tip.

(b) Image of the end of the metasurface endoscope under a microscope. (c) Schematic of an individual a-Si

nanopillar on a glass substrate. (d) SEM image of a part of the fabricated metasurface lens. .............................. 42

Fig. 2- 40. A common endoscopic system with SLM, BS: beam splitter; PMT: photomultiplier tube. ............... 43

Fig. 2- 41. Schematic of the beam modulation by an SLM [111]. (a) The schematic of the output beam

controlling by an SLM. (b) The output beam spots obtained by an SLM............................................................. 43

Fig. 2- 42. A micro-lens on the fiber tip to improve resolution [113]. (a) The focusing schematic of the designed

micro-lens by a ray-tracing method. (b) SEM image of the micro-lens on the MMF core. (c) The experimental

setup of the focusing characterization of the on fibre tip micro-lens, L: lens, D: dichroic mirror. ....................... 45

Fig. 3- 1. The volume V with two closed surfaces Sr and S. ................................................................................. 48

Fig. 3- 2. The mirror symmetry points P and 𝑷 for a Green’s function. ............................................................... 49

Fig. 3- 3. Diffraction schematic of a GO ultrathin flat lens in cylindrical coordinate systems. ............................ 51

Fig. 3- 4. Differential coefficient 𝒅𝑰𝒅𝑹 versus R. ................................................................................................ 53

Fig. 3- 5. Comparison of ring radii versus ring number m based on the RS and Fresnel design model. .............. 54

xiv

Fig. 3- 6. The intensity distribution of the two designs simulated based on the RS diffraction theory. (a) Intensity

distributions in the lateral and axial planes. (b) Cross-sectional intensity distribution along the black dashed lines

in the axial planes. (c) Cross-sectional intensity distribution along the black dashed lines parallel to the x-axis in

the lateral planes. .................................................................................................................................................. 55

Fig. 3- 7. Intensity distributions of theoretical and experimental results of Lens1. (a) Intensity distributions in

the lateral and axial planes. (b) Intensity distribution along the black dashed lines in the axial planes. (c)

Intensity distribution along the black dashed lines parallel to the x-axis in the lateral planes. ............................. 56


the lateral and axial planes. (b) Intensity distributions along the black dashed lines in the axial planes. (c)

Intensity distributions along the black dashed lines in the lateral planes. ............................................................. 57

Fig. 4- 1. Different thickness GO film measured by AFM. (a) A GO film with ~250 nm thickness. (b) ~200 nm

thickness. (c) 100 nm thickness. (d) 50 nm thickness. .......................................................................................... 60

Fig. 4- 2. Experimental setup of the laser fabrication system. ES: electronic shutter; BES: beam expanding

system; BS1 and BS2: beam splitter; LED: light-emitting diode; Sample: GO film; OBJ: objective; CCD1 and

CCD2: charge-coupled device. ............................................................................................................................. 61

Fig. 4- 3. AFM images of the two designed GO lens. .......................................................................................... 62

Fig. 4- 4. Schematic of the GO lens characterization system. BES: beam expanding system; OBJ: objective. ... 63


the lateral and axial planes. (b) Intensity distribution along the black dashed lines in the axial planes. (c)

Intensity distribution along the black dashed lines parallel to the x-axis in the lateral planes. ............................. 64


the lateral and axial planes. (b) Intensity distributions along the black dashed lines in the axial planes. (c)


Fig. 4- 7. rGO film fabrication. (a) The UV light reduction setup for reducing GO to rGO. (b) The rGO film

sample. (c) The thickness measurement of the rGO film by AFM. ...................................................................... 67

Fig. 4- 8. Laser fabricated lines in rGO film. (a) Under microscopy. (b) AFM image of rGO lines fabricated with

a laser power of 30 μw. (c) AFM image of rGO lines fabricated with a laser power of 60 μw. ........................... 68

Fig. 4- 9. Relationship between linewidths and laser writing power. (a) For the rGO prepared base on a GO film

fabricated by the filtration method. (b) For the rGO prepared base on a GO film fabricated by the SA method. 69

Fig. 4- 10. rGO ultrathin flat lens. (a) Transmission optical microscopic image of an rGO lens. (b) Topographic

profile of the rGO ultrathin flat lens measured by an optical profiler and the cross-sectional profile marked by

the white dashed line in (b). .................................................................................................................................. 69

Fig. 4- 11. Intensity distributions in the focal area. (a) Intensity distribution in the y-z plane of the experimental

results. (b) Intensity distribution in the x-y plane of the experimental results. (c) Intensity distributions along the

black dashed lines in the axial planes. (c) Intensity distributions along the black dashed lines in the lateral

planes. ................................................................................................................................................................... 70

xv

Fig. 5- 1. Applications of rGO flat lenses in different environmental scenarios. (a) Imaging optical element for a

satellite in aerospace. (b) Observing strong acid/alkaline chemical reactions. (c) Biophotonic microfluidic

devices. ................................................................................................................................................................. 73

Fig. 5- 2. UV radiation test of rGO lenses. (a) rGO lenses under microscopy before and after 24 hours of UV

radiation. (b) Intensity distributions on the lateral plane of the focal spots. (c) Intensity distributions on the axial

plane of the focal spots. (d) Intensity distributions along the black dashed lines in the axial planes. (e) Intensity

distributions along the black dashed lines in the lateral planes. ........................................................................... 75

Fig. 5- 3. Extreme cold and heat experiments. (a) rGO lenses immersed in liquid nitrogen. (b) The vacuum oven

for extreme heat experiment. ................................................................................................................................ 76

Fig. 5- 4. The Extreme cold and heat tests of rGO lenses. (a) rGO lenses under microscopy before and after

experiments. (b) Intensity distributions on the lateral plane of the focal spots. (c) Intensity distributions on the

axial plane of the focal spots. (d) Intensity distributions along the black dashed lines in the axial planes. (e)


Fig. 5- 5. The digital vacuum drying oven in the experiment. .............................................................................. 78

Fig. 5- 6. The ultra-high vacuum tests of rGO lenses. (a) rGO lenses under microscopy before and after




Fig. 5- 7. rGO lens treated by AO radiation. (a) The reactive ion etching equipment (b) Scheme of AO radiation.

(c) Thickness changes with the increase of AO radiation time. ............................................................................ 80

Fig. 5- 8. The AO radiation experiment of rGO lenses. (a) rGO lenses under microscopy before and after




Fig. 5- 9. Scheme of strong acid/alkaline tolerance tests. ..................................................................................... 83

Fig. 5- 10. rGO lenses in acid solution (PH=0). ................................................................................................... 84

Fig. 5- 11. The strong acid tolerance test of rGO lenses. (a) rGO lenses under a microscope. (b) Intensity

distributions on the lateral plane of the focal spots. (c) Intensity distributions on the axial plane of the focal

spots. (d) Intensity distributions along the black dashed lines in the axial planes. (e) Intensity distributions along

the black dashed lines in the lateral planes. .......................................................................................................... 85

Fig. 5- 12. rGO lenses in acid solution (PH=0). ................................................................................................... 85

Fig. 5- 13. The strong alkaline tolerance test of rGO lenses. (a) rGO lenses under a microscope. (b) Intensity

distributions on the lateral plane of the focal spots. (c) Intensity distributions on the axial plane of the focal

spots. (d) Intensity distributions along the black dashed lines in the axial planes. (e) Intensity distributions along

the black dashed lines in the lateral planes. .......................................................................................................... 86

Fig. 5- 14. rGO lens in PBS solution. ................................................................................................................... 87

Fig. 5- 15. The biological workable test of rGO lenses. (a) rGO lens under a microscope. (b) rGO lens measured

by the 3D optical profiler. (c) Intensity distributions on the lateral plane of the focal spots. (d) Intensity

distributions on the axial plane of the focal spots. (e) Intensity distributions along the black dashed lines in the

axial planes. (f) Intensity distributions along the black dashed lines in the lateral planes. ................................... 88

xvi

Fig. 6- 1. The schematic of a standard step-indexed optical fibre. ....................................................................... 91

Fig. 6- 2. The LP01 and LP02 modes in the standard step-indexed fibre. (a) β/k0 versus V. (b) The corresponding

electric field modes. .............................................................................................................................................. 94

Fig. 6- 3. The LP11 and LP21 modes in the standard step-indexed fibre. (a) β/k0 versus V. (b) The corresponding

electric field modes. .............................................................................................................................................. 95

Fig. 6- 4. The schematic of a GO lens on a step-indexed fibre. ............................................................................ 96

Fig. 6- 5. Theoretical design results of the first on fibre tip GO lens. (a) Intensity distributions in the axial plane.

(b) Intensity distributions in the lateral plane. (c) Intensity distributions along the black dashed lines in the axial

planes. (d) Intensity distributions along the black dashed lines parallel to the x-axis in the lateral planes. ......... 98

Fig. 6- 6. Theoretical design results for the correctional on fibre tip GO lens. (a) Intensity distributions in the

axial plane. (b) Intensity distributions in the lateral plane. (c) Intensity distributions along the black dashed lines

in the axial planes. (d) Intensity distributions along the black dashed lines parallel to the x-axis in the lateral

planes. ................................................................................................................................................................... 99

Fig. 6- 7. Theoretical design results for the on fibre tip GO lenses with longer focal lengths (50 μm and 100 μm).

(a) Intensity distributions in the axial plane for the GO lens with a 50 μm focal length. (b) Intensity distributions

in the lateral plane for the GO lens with a 50 μm focal length. (c) Intensity distributions along the black dashed

lines in the axial planes. (d) Intensity distributions along the black dashed lines parallel to the x-axis in the

lateral planes. (e) Intensity distributions along the black dashed lines in the axial planes for the GO lens with a

100 μm focal length. (f) Intensity distributions along the black dashed lines parallel to the x-axis in the lateral

planes for the GO lens with a 100 μm focal length. ........................................................................................... 100

Fig. 6- 8. Cut fibre tip under a microscope. (a) Side profile of a cut fibre. (b) The surface of the cut fibre. ...... 101

Fig. 6- 9. GO film transfer on naked fibre tips. (a) Holes mode for naked fibre. (b) GO film transferred on the

surface of the hole measured by a microscope. (c) Microscope image of the holes after the GO film was

transferred onto the fibre tip. (d) The surface of the cut fibre with GO film. ..................................................... 101

Fig. 6- 10. GO film preparation on a fibre tip with FC/PC connector. (a) A fibre with an FC/PC connector. (b)

The surface of the fibre tip. (c) The surface of the fibre tip with a GO film. ...................................................... 102

Fig. 6- 11. Locating of the fibre core. (a) Homemade fibre holder for the DLW system. (b) The fundamental

mode and the circle mark. ................................................................................................................................... 103

Fig. 6- 12. GO lens fabrication on a fibre tip. (a) On fibre tip GO lens without the coupling beam. (b) On fibre

tip GO lens with the coupling beam. .................................................................................................................. 104

Fig. 6- 13. Large GO lens on a fibre with a 100 μm core diameter. ................................................................... 104

Fig. 6- 14. Schematic of the on fibre tip GO lens characterization system. 3D: three dimensional. PC: personal

computer. ............................................................................................................................................................ 105

Fig. 6- 15. Comparison of theoretical and experimental results for the first on fibre tip GO lens. (a) Intensity

distributions in the axial plane. (b) Intensity distributions in the lateral plane. (c) Intensity distributions along the

black dashed lines in the axial planes. (d) Intensity distributions along the black dashed lines parallel to the x-

axis in the lateral planes. ..................................................................................................................................... 106

Fig. 6- 16. The diffraction distributions on the z-axis of the first four fibre modes. ........................................... 107

xvii

Fig. 6- 17. Theoretical and experimental results comparison for the correctional on fibre tip GO lens. (a)

Intensity distributions in the axial plane. (b) Intensity distributions in the lateral plane. (c) Intensity distributions

along the black dashed lines in the axial planes. (d) Intensity distributions along the black dashed lines parallel

to the x-axis in the lateral planes. ........................................................................................................................ 108

xviii

List of Tables Tab. 3- 1. Radii of Lens1 and Lens2..................................................................................................................... 55

Tab. 3- 2. Focal lengths f and FWHMs of the theoretical and experimental results of Lens1 and Lens2 ............ 56

Tab. 4- 1. Radii of the rGO lens rings designed with 30-μm-focal length, unit: μm. ........................................... 67

Tab. 6- 1. Radii of the rings for the GO lens. ....................................................................................................... 97

Tab. 6- 2. Radii of the rings for the GO lens. ....................................................................................................... 99

1

Chapter 1

Introduction

1.1 Introduction to ultrathin flat lenses

Lenses are one of the most important optical elements that have been widely used in human

life to scientific researches, such as eyeglasses, camera lenses, microscope, telescope, laser,

satellite and so on. The earliest lenses on record are around 2770 years ago [1], it is made from

polished crystal. As time goes on, both the types and technological levels of lenses have been

developed boomingly. However, the imaging mechanism of lenses has not changed, only the

materials of lenses have been changed, from crystal to glasses, transparent plastics and resins,

and so on. The imaging mechanism of the conventional lenses is relied on a gradual phase

accumulating along the optical path as shown in Fig. 1-1(a), the phase modulation is decided

by Δn×Δt×k, where Δn is the refractive index difference between the lens and the surrounding

medium (usually it is air), Δt is the thickness of the lens, k=2π/λ. Given the fact that naturally

available materials have limited refractive index, the wavefront modulation of conventional

lenses mostly relies on the thickness. The thickness of the conventional geometrical lenses is

fundamentally large than the wavelength of light (λ). With the development of nanofabrication

technology, devices have been miniaturized, the bulky volume of the conventional lenses has

become the bottleneck to adapt to the nano-optics and photonic systems.

To overcome the thickness dilemma of lenses, scientists turn their eyes on the Fresnel zone

plate, which has been proposed by Augustin Fresnel a hundred years ago [2, 3]. The concept

of the Fresnel zone plate is to block out the light from alternate half-periods, as shown in Fig.

1-1(b). The dark zones are blocked, while the grey zones are transparent. Take the optical path

of a plane wave propagates to the focal position F along the axis as a reference. The phase

change Δφ increases 2π after each zone group, namely at the mth zone group, the phase change

Δφ =2mπ. In 1985, Wiltse [4] described the Fresnel zone plate as a planar lens. According to

Chapter 1

2

the different wavefront modulation objectives, there are two types of the Fresnel lenses, one is

based on the amplitude modulation, the other is based on the phase modulation. In theory, the

thickness of the former one can be unlimited thin as long as a complete blockage of light can

be obtained. However, as it focuses light by using a binary mask to modulate the amplitude of

the incident beam [5], half of the light and information are blocked, the diffraction efficiency

is low, and the wavefront cannot be accurately controlled to achieve high focusing performance.

Then, phase modulations have been introduced into the Fresnel lenses, with the proper phase

modulations along the radial direction, the focusing efficiency of the Fresnel lenses increases

greatly (100% is possible in theory), and the wavefront is accurately controllable [6].

Furthermore, carefully designing the structure can compensate aberration, which leads to high

NA and resolution for optical systems. However, to guarantee a smooth spherical phase profile

for efficient light focusing, thicknesses of the Fresnel lenses have to be at least equal to the

effective wavelength λeff = λ/n, where n is the refractive index of the medium. And the precise

phase modulation requires nanofabrication technology, which dramatically increases the

fabrication difficulty and cost.

Fig. 1- 1. Schematic of a Fresnel zone plate.

A negative refraction lens is another member of the ultrathin flat lenses. In 1968, Veselago [7]

hypothesized a peculiar material with both negative dielectric permittivity and magnetic

permeability and analysed their characteristics, such as negative refraction index. The peculiar

materials are known as left-handed materials (LHM) now. Based on the LHM or negative

refractive index materials, Pendry et al. have proposed a concept of ‘perfect lens’ [8], The

‘perfect lens’ or negative refraction lens is a flat slab, it can refocus a light source to the other

Chapter 1

3

side of the lens. Benefit from the propagation or amplification of the evanescent waves, the

negative refraction lenses are possible to break the diffraction limit and offer a high resolution.

However, the design of a negative refraction index lens is extremely complicated, and the

bandwidth is very narrow, a tiny change of the incident beam wavelength will lead to the

imaging ability degradation dramatically. On the other hand, the fabrication of a negative

refraction index lens requires extremely high precision, which limits the demonstrated negative

refraction index lens only operating in the microwave region. And the amplified evanescent

waves damping exponentially which limits the focal length of the negative refraction index

lens within half a wavelength. Therefore, it is still challenging to realize the practical

application of the negative refraction index lens.

Metasufaces [9-14] or plasmonic [15, 16] lenses are another types of ultrathin flat lenses. The

concept was first proposed and demonstrated by Yu et al. [17] in 2011. By nanostructure

engineering a new type of optical material has been designed and fabricated. This new type of

optical material offers specific optical properties of resonance and scattering, namely optical

phase discontinuities. A variety of nanostructure elements with different materials or structures

have been designed and fabricated, as shown in Fig. 1-2a [18-21]. By modulating the

geometrical structures of the resonator elements, phase modulations from 0 to 2π can be

obtained, as shown in Fig. 1-2b and c. Then by arraying the elements according to the phase

distribution of a Fresnel lens (Fig. 1-2d), a metasurface lens can be achieved.

The nanometre thick metasurfaces are also potentially used as optical components such as

polarizers, vortex plates, anti-reflection coatings, filters and so on. These optical components

play very important roles in the fields of integrated optics, holograms, flat displays, energy

harvesting. Furthermore, the recent developments in multilayers cascaded optical elements [12,

22] and coalescing two types of meta-atoms [9, 10] offer new opportunities to simultaneously

modulate the phase and amplitude of the incident light.

However, the metasurface lenses are naturally suffered from the narrowband and low focusing

efficiency. In addition, the fabrication process of metasurface lenses is complex, expensive and

inefficient. The complex composite structures of metasurface lenses require high precision in

the fabrication process, by using either e-beam lithography (EBL) or focused ion beam (FIB).

The fabrication is costly and unable to be scale, also it is not suitable for post-processing

customization. In a word, although a substantial amount of effort has been devoted to the

Chapter 1

4

metasurface and plasmonic nanostructure lenses, it remains a great challenge for the practical

applications of these lenses to be explored.

Fig. 1- 2. (a) Four resonator element examples for metalens design [18-21]. (b) Gold robs

array according to phase modulation from 0 to 2π. (c) The phase modulation corresponding to the gold robs. (d) Phase modulation of a metasurface lens along the radial direction.

Graphene oxide (GO) ultrathin flat lens [11, 14, 15], which have been proposed and fabricated

recently is a new conceptual design of diffractive lenses. Taking advantage of the conversion

of GO material to rGO(a graphene-like material) under the laser reduction process, both phase

and amplitude can be modulated simultaneously. Based on our quantitative phase-amplitude

dependency analysis, the positions of the concentric rings and the corresponding reduction

extent of GO are precisely designed. Thus, the amplitude and phase modulations can be

Chapter 1

5

accurately controlled, and more elaborately focused optical fields could be achieved in the case

of GO lenses. Fig. 1-3a [23] is the atomic force microscopy (AFM) image of a GO lens, the

thickness and refractive index differences between the GO and rGO contribute to the phase

modulation, the transmission difference contributes to the amplitude modulation (Fig. 1-3b).

The GO ultrathin flat lenses have demonstrated attractive properties, such as nanometre

thickness, high focusing resolution and efficiency, and high mechanical strength and flexibility.

In addition, the GO ultrathin flat lenses can potentially be integrated into various optical

components to change or optimize their functionalities, such as conventional optical lenses,

fibre tips, and on-chip optical systems. Furthermore, due to the maskless, one-step direct laser

writing (DLW) fabrication, the GO lenses can be fabricated in a large scale with high efficiency.

Furthermore, the simple design and fabrication are able to further miniaturize the ultrathin

photonic devices, which are stable in aerospace, chemical, and biological harsh environments

[24]. All these properties provide the GO ultrathin flat lens with a broad application prospect.

Fig. 1- 3. (a) A GO lens measured by AFM. (b) Schematic of the transmission and phase

profile of a GO lens.

The focusing and imaging ability of the above-mentioned lenses is based on the diffraction and

interference of incident beam rather than refraction. Therefore, they offer advantages of flat

construction, ultra-thin, ultra-lightweight compared with the conventional lens. As

miniaturization and integration are the trends of instrumentation and optical devices, the flat

lenses with subwavelength thicknesses have an enormous potential to become alternatives to

conventional lenses. The ultrathin flat lenses offer new opportunities for myriads of

miniaturization and integrational applications, such as visual reality/augmented reality helmet-

Chapter 1

6

mounted display systems, miniaturized cameras [14, 25], and other functional devices [13, 15,

16, 26-31].

1.2 Introduction to endoscopy

Endoscope is one of the most important tools to study the human body and detect areas that are

hard to reach. With the development of optical fibre, optical fibre endoscopy has been

developed for several decades [32, 33]. The schematic of the first prototype endoscope is

shown in Fig. 1-4, the collected images from the distal lens is guided by a flexible tube to a

computer, the controller is used to modulate the imaging areas. Due to virtue of optical fibres,

the key features of an optical fibre endoscope are its mechanical flexibility and compact size.

Therefore, optical fibre endoscopy is unique to in-situ image with minimal invasion, which is

hard to accomplish using a conventional optical microscope. Endoscopy has been a widely

used tool in the industrial, military, especially the medical field.

Fig. 1- 4. Schematic of a prototype endoscope.

However, low resolution is still a limitation of the endoscopes, and the size of the endoscopic

fibre is still large, which is at a centimetre scale. The most important part of an endoscope is

the detection end. As shown in Fig. 1-5, a fibre is protected by a fibre housing, a gradient index

(GRIN) lens is added to increase the resolution and increase the signal collection of the

endoscopy. According to the scanning method, there are two types of endoscopes. One is using

Chapter 1

7

a fibre bundle [34, 35], the other one is using a single fibre with a lens on the fibre tip. Each of

them has advantages and disadvantages. For example, the fibre bundle endoscope is able to

directly acquire images without scanning, but it has low spatial resolution and a small number

of pixels. The spatial resolution is limited by the size of a single fibre in the bundle and the

number of pixels depends on the total number of fibres. In comparison, the single fibre

endoscope is able to increase the resolution by using a high NA focusing lens. However, it

needs a scanning mechanism, which leads to the bulk design of the fibre endoscope. Therefore,

it is a stringent requirement to develop an endoscope with both high resolution and

miniaturization characteristics.

Fig. 1- 5. A prototype schematic of the end detector of the optical fibre endoscopy.

Due to the integrability, and the virtues of nanometre thickness and high focusing resolution,

GO lens can be potentially integrated with a fibre to work as an endoscope. In this thesis, the

GO lens is directly fabricated on top of an optical fibre to form a new generation of the

endoscope with high spatial resolution and ultrahigh compactness.

1.3 The content of this thesis

The objective of this thesis is to design the ultrathin flat graphene-based lenses and explore its

applications in fibre optics endoscopy. To design the graphene-based lenses accurately, we use

the more rigid Rayleigh-Sommerfeld (RS) diffraction theory instead of the Fresnel diffraction

theory, which is only applicable under the paraxial approximation condition. The new design

method is also used for fibre tip ultrathin flat graphene-based lens design. Furthermore, to study

the complex and harsh environments that the graphene-based lenses are potentially

experiencing, for example, the biological condition that the graphene-based lens acts as an

endoscopy, we tested the graphene-based lens in different harsh environments. Based on the

objective, this thesis is outlined as follows:

Chapter 1

8

In chapter 2, flat lenses with different mechanisms have been reviewed. First, negative

refraction lenses have been discussed. The different principles of two types of negative

refraction lenses, and also the state of the art experimental demonstration of both types of

negative refraction lenses are reviewed. Second, metasurface lenses are discussed. The review

provides the theoretical design and experimental fabrication of metasurface lenses. Then, the

following section starts with the introduction of the component materials of the GO lenses, then

both theoretical design mechanism and experimental fabrication are reviewed. Fourth, the

Fresnel diffraction theory is reviewed as the most commonly used design method for ultrathin

flat lenses. In the process of the derivation of the Fresnel diffraction theory, the paraxial

approximation is analysed, which limits the application range of the Fresnel diffraction theory.

Fifth, the GO film fabrication methods are introduced, the details of the two methods: the

vacuum filtration and self-assembly method are reviewed. Sixth, as the fabrication technique

for graphene-based lenses, the fabrication mechanism and system of the state-of-the-art DLW

technique are reviewed. Finally, two different types of endoscopes are reviewed, one is using

a fibre bundle to obtain the images directly, and the other one is using a single fibre with a

high-resolution lens integrated onto its tip.

In chapter 3, the ultrathin flat lens design method based on the RS diffraction theory is

demonstrated. First, the detailed derivation processes of the RS diffraction theory are given.

Second, combined with the extremum principle, the lens design method based on the RS

diffraction theory has been derived. Finally, the comparisons of the design results between the

new design method and the Fresnel design method are discussed. Based on the GO lens model,

the theoretical results from finite-difference time-domain (FDTD) have been demonstrated to

compare and show the accuracy and the efficiency of the new design method based on the RS

diffraction theory.

In chapter 4, the fabrication and characterization of graphene-based lenses have been discussed.

The GO lens fabrication by using the DLW method is demonstrated. Then, the focusing

characterization of the GO lens is discussed, the experimental results match well with the

theoretical results, it demonstrates the accuracy of our new design method experimentally. In

a similar way the fabrication and characterization of the rGO lens, which is able to withstand

harsh environments, is demonstrated.

In chapter 5, the performance stability of the rGO lens in harsh environments is introduced.

First, the low earth orbit (LEO) environment is considered, four most important characteristics

of the LEO environment have been simulated, namely, the ultraviolet (UV) radiation, the

Chapter 1

9

extreme temperature condition, the ultra-high vacuum, and the atomic oxygen radiation. The

experimental results have demonstrated that the rGO lenses are able to maintain their focal

qualities except for the atomic oxygen (AO) radiation. Second, the strong corrosive

environment, including the strong acid and alkaline conditions, are used to test rGO lenses.

The 7 days treatments in each condition demonstrate the resilience of the rGO lenses. Finally,

the biochemical environment is simulated. The rGO lenses were immersed in a phosphate-

buffered saline solution for 24 hours, and the experimental results demonstrated the resistance

of the rGO lenses in the biochemical environment.

In chapter 6, the fabrication and characterization of the on fibre tip GO lenses are introduced.

First, based on the fibre modes theory, the design method for the on fibre tip graphene-based

lens is derived. Second, on fibre tip GO lens fabrications by the DLW method is demonstrated

experimentally. Finally, the characterization of these on fibre tip GO lenses is performed. The

on fibre tip GO lenses shows good focusing ability, and the experimental and theoretical results

match well.

In chapter 7. A summary of this thesis is given, the conclusion and the outlook of the future

work are discussed.

10

Chapter 2

Literature review

2.1 Introduction

With the rapid development of nano-optics, ultrathin flat lenses have been a hot topic. Ultrathin

flat lenses have the advantages of astigmatism and coma aberrations free, which are otherwise

common problems for conventional bulky and curved surface lenses, especially when the NA

is high [36]. In addition, flat lenses offer a compact design for a myriad of the rapid

development of nanophotonics and integrated photonic systems, as well as electro-optical

applications, such as solar cells and fibre communication systems. Therefore, the research on

the ultrathin flat lens is an important topic.

In this chapter, the flat lenses based negative refraction are reviewed. There are two types of

negative refraction lens, one is based on negative refraction materials, and the other one is

based on photonic crystal. Furthermore, metasurface lenses are reviewed. Following that, the

GO lenses are reviewed, including the details about the material, the focusing mechanism, the

fabrication method, as well as the performance prediction theory. As one practical application

of GO lens demonstrated in this thesis, the structure, mechanism and performance of fibre-

optics endoscope are reviewed. Finally, a summary is given to state the advantages,

disadvantages and challenges of the reviewed flat lenses and current state-of-the-art fibre optic

endoscopes.

2.2 Negative refraction lens

Because of the abnormal refraction mechanism, a flat negative refraction lens can focus a light

beam to the other side of the lens directly. Compared with the conventional geometrical lens,

the curved shape is not essential for the negative refraction lens. Therefore, the negative lens

Chapter 2

11

is one of the hot topics of the ultrathin flat lens family. On the other hand, benefiting from the

propagation or amplification of the evanescent waves, the negative refraction lenses are

possible to break the diffraction limit [37]. There are two ways to obtain a negative refraction

lens, one is to fabricate a lens with left-handed material (LHM), and the other one is to construct

a lens with photonic crystal structures. Both methods have been demonstrated experimentally

to break the diffraction limit.

2.2.1 Left-handed material lens

In 1968, Veselago [7] analysed a kind of interesting substances, which are known as the LHM

now. By assuming that these substances are with both negative dielectric permittivity and

magnetic permeability, Veselago had proved the negative refractive index of these substances

theoretically. On the other hand, Veselago also proved that these substances are perfect matches

to vacuum space and there is no reflection on the interfaces. Veselago had introduced a

parameter p to rewrite the Snell’s law. The new formula of the relative refractive index n is

𝑛 = 𝑝√𝜀1𝜇1

𝜀2𝜇2 (2-1)

where ε1 is the dielectric permittivity, μ1 is the magnetic permeability of the main medium, ε2

and μ2 is the dielectric permittivity and magnetic permeability of the referenced medium,

separately. p equals to 1 when both chirality of the two mediums are the same, and it equals to

-1 when the chirality is different.

In 2000, Pendry et al. proposed a concept of ‘perfect lens’ [8], which is fabricated with these

left-handed or negative refraction index material. The lens is in the form of a parallel-sided

slab, as shown in Fig. 2.1. Assuming that the refractive index

𝑛 = −1. (2-2)

According to Snell’s laws, light is bent to a negative angle with the surface normal as it

transmits inside the slab. Light is focused inside the slab at B1 and focused again On the other

hand of the slab at B2. The second focus locates at

𝑙2 = 𝑑 − 𝑙1. (2-3)

Where d is the thickness of the slab, l1 is the distance between the light source A and the first

facet (close to the light source) of the slab. l2 is the distance between the second facet of the

slab and the second focus B2.

Chapter 2

12

Fig. 2- 1. A negative refractive index lens.

The negative refractive index provides a path to ‘a perfect lens’. As we all know the limited

resolution of a common lens is due to the exponential decay of the evanescent waves. Pendry

has demonstrated theoretically that the negative refractive index lens can amplify evanescent

waves, therefore, both propagating and evanescent waves participate in the rebuild of the image,

the resolution limit can be broken.

In 2004, Anthony and George [38] demonstrated the diffraction limit broken ability of a planar

LHM lens or superlens. The sample of the LHM lens is shown in Fig. 2-2b. It is a square array

of copper strips printed on a microwave substrate. The substrate is grounded, its thickness is

1.52 mm; its dielectric permittivity is 3. The copper strips loaded with chip capacitors and shunt

chip inductors are shown in Fig. 2-2a, its thickness is 17 μm; its width is 750 μm. The period

of the square array is 8.4 mm. Two same square copper strip arrays without capacitor and

inductors (as shown in Fig. 2-2a) are used as positive refraction index media. The sandwich

structure of the loaded and unloaded copper strips corresponding to a two-dimensional LHM

lens in positive refraction index media. A short vertical probe is used to detect the electric field

distribution, as shown in Fig. 2-2b.

Fig. 2- 2. (a) The line unit cells with and without loads [38]. (b) The experimental setup to

demonstrate the focusing ability of the planar LHM lens.

Chapter 2

13

The best experimental result was at 1.057 GHz. Fig. 2-3a is the vertical electric field

distribution detected by the probe 0.8 mm above the surface of the LHM lens. A focusing spot

is clearly seen On the other hand of the LHM lens. The measured half-power beamwidth is

0.21λ, which proves the break of the diffraction limit. More detail is shown in Fig. 2-3b, the

electric field alongthe white dashed line in Fig. 2-3a clearly indicates the growth of the

evanescent waves. The experimental results have demonstrated the theoretical predictions.

Fig. 2- 3. (a) The measured vertical electric field of the entire structure [38]. (b) The

measured vertical electric field along the white dashed line in (a).

More work has been done in the LHM lens field. In 2013, Xu et al. [39] fabricated a three-

dimensional superlens with the transmission-line approach. The experimental results match

well with the theoretical predictions.

The LHMs mentioned before were all artificially designed and structured, because of the

diminishing magnetic susceptibility, the working range of these lenses was limited to

microwave or terahertz regimes. In 2005, Nicholas et al. [40] proposed and fabricated a silver

superlens, which works at the optical frequencies. The mechanism of this superlens was only

based on negative permittivity. Fig. 2-4a is the experimental schematic, The illuminating

source was a 365 nm-wavelength beam, the object was fabricated by FIB on a chrome screen,

and a 40-nm-thick layer of polymethylmethacrylate (PMMA) was used to planarize the

objective. A 35-nm-thick silver film was the superlens, a 120-nm-thick negative photoresist

was used to record the near-field image. Fig. 2-4b is the FIB image of the object, the linewidth

is ~40 nm. Fig. 2-4c is the recorded image by the negative photoresist measured by AFM, the

linewidth is ~89 nm. Fig. 2-4d is the recorded image without the silver superlens, the linewidth

is ~321 nm. Therefore, a sub-diffraction-limited optical superlens has been achieved. However,

the super-resolution was only achievable in the near field, which was caused by the exponential

damping of the evanescent waves. Therefore, the focal length of the superlens is limited to a

Chapter 2

14

few wavelengths. On the other hand, the fabrication technology is complex and costly. All

these impede the practical application of the LHM lens.

Fig. 2- 4. Schematic of optical superlens imaging [40]. (a) The imaging system of the

superlens, object is fabricated with chrome, the superlens is fabricated by silver. And PR represent negative photoresist to record the image. (b) FIB image of the object. (c) AFM of

the developed image on photoresist with a silver superlens. (d) AFM of the developed image on photoresist when the 35-nm-thick silver superlens was replaced by PMMA spacer. Scaler

bar: 2 μm.

2.2.2 Negative refraction Photonic crystal lens

Fig. 2- 5. The equifrequency surface schematics [41]. (a) The equifrequency surface for a

beam incident from air to a dielectric material. (b) The equifrequency surface for a diffraction grating.

Scientists have found peculiar phenomena that with artful design the photonic crystals exhibit

negative refraction ability for a specific waveband. This provides a new way to design a

negative lens, which is able to break the diffraction limit and realize super-resolution with a

completely flat design. In 2000, Notomi [41] investigated the abnormal refractive phenomena

of photonic crystals when the Bloch photon is in the vicinity of the photonic bandgap.

Chapter 2

15

Notomi summarized light propagation in dielectric materials and diffraction gratings by

equifrequency surface (EFS) method. The theoretical schematic is shown in Fig. 2-5. In Fig.

2-5a, the simple light propagation from air to a dielectric material was described. The photonic

band EFS of the dielectric medium is a circle, and light always propagates parallel to the wave

vector k. Therefore, the Snell’s law for this case in the k space is:

𝑛1𝑠𝑖𝑛𝜃1 = 𝑛2𝑠𝑖𝑛𝜃2. (2-4)

When light propagates through a diffraction grating, the EFS circles are repeated along the

periodic axis. There are two excited waves in the grating, as shown in Fig. 2-5b. Wave A is the

transmitted wave, Wave B is the diffracted wave. Although wave B is not parallel to the k

vector, it is normal to the diffracted wave circle. The formula to express the refraction is:

𝑚𝜆 = 𝑑(𝑠𝑖𝑛𝜃1 + 𝑠𝑖𝑛𝜃2), (2-5)

where d is the period of the diffraction grating. Other than this, Notomi pointed out two special

points. For point C, due to the propagation direction is not parallel to the k vector, the phase

index here cannot be used to indicate the light direction. For point D, which is in the cross point

of the two circles, the light propagation direction changes rapidly when the wavelength is in

the special vicinity or the incident angle changes.

Further, Notomi investigated the large periodic modulation in photonic crystal. Bloch modes

can be expressed as the sum of plane wave and diffracted wave:

𝜓𝑘 = ∑ 𝑐𝐺exp[𝑖(𝑘 + 𝐺)𝑟]𝐺 , (2-6)

where k is the wave vector, G is a reciprocal vector. However, in the large periodic modulation

case, the mixing among different G components becomes more and more non-negligible near

the bandgap. Eq. 2-5 cannot predict the light propagation angle accurately. Based on the EFS

method, one sample for TE mode was numerically simulated in a two-dimensional (2D)

hexagonal GaAs pillar photonic crystal. The diameter of the pillar is 0.7a, a is the lattice

constant; the refractive index of GaAs is 3.6; the circumstance is air. Fig. 2-6a shows the

simulation results. Effective negative refractive indexes were found out in the range

0.575<ω<0.635. The other sample for TM mode was simulated in a 2D hexagonal GaAs air-

hole photonic crystal. The diameter of the air hole is 0.8a. As shown in Fig. 2-6b, the effective

refractive index is negative in the range of 0.24<ω<0.35.

Chapter 2

16

Fig. 2- 6. Effective index versus frequency [41]. (a) Effective index versus frequency of the TE modes in a 2D GaAs pillar photonic crystal. (b) Effective index versus frequency of the

TM modes in a 2D GaAs air-hole photonic crystal.

Fig. 2- 7. The schematics of negative refraction in photonic crystal [42]. (a) Negatively

refracted beams by a photonic crystal. The thick arrows indicate group-velocity directions, the

thin arrows indicate the phase-velocity directions. (b) The refracted rays in a photonic crystal

structure. (c) The all-angle negative refraction frequency range highlighted by the red region.

On the other hand, Luo et al. [42] found that negative refraction can exist in the photonic crystal

without negative effective index. The analysis was studied in a 2D photonic crystal, which has

a square Si air-hole structure. The hole diameter is 0.7a. The authors pointed out that if the

photonic crystal surface is along a k space vector, of which the contour is all convex, the

incident plane wave from air will propagate in the negative side in this crystal. As shown in

Fig. 2-7a, if the crystal surface is parallel to the Г-Μ direction, and the photonic crystal contours

are larger than the constant-frequency contours of air, the corresponding frequency will show

negative refraction at any incident angle. The frequency is limited:

ω ≤ 0.5 × 2πc/𝑎𝑠, (2-7)

where as is the surface-parallel period, c is the speed of light in vacuum. Fig. 2-7b indicates the

Chapter 2

17

transmission path of the incident plane wave from air. Fig. 2-7c shows the photonic band that

satisfies the all-angle negative refraction, this band has a positive group velocity and positive

refractive index, but a negative photonic ‘effective mass’.

The authors also simulated the superlens ability of the photonic crystal, the FDTD simulation

results are shown in Fig. 2-8. A point source is at 0.35a away from the surface of the photonic

crystal slab (the same square Si air-hole crystal). The surface of the slab is parallel to the Г-Μ

direction. The studied frequency is 0.195×2πc/a, which is in the lowest all-angle negative

refraction frequency range. A snapshot of the Hz field is shown in Fig. 2-8a, the image point is

at 0.38a. FDTD simulations of a dielectric pillar in air structure also have been performed.

The permittivity of the dielectric is 14; the diameter of the dielectric pillar is 0.6a. A snapshot

of the Ez field demonstrated the superlens phenomenon clearly again as shown in Fig. 2-8b.

Fig. 2- 8. Point source imaging by a photonic crystal lens [42]. (a) The photonic crystal lens focuses the Hz field of a point source. (b) The photonic crystal lens focuses the Ez field of a

point source. Blue, white and red corresponds to negative, zero and positive value.

In 1998, Hideo et al. [43] observed an exotic light propagation behaviour in a photonic crystal,

they called ‘super prism phenomenon’. The photonic crystal structure is shown in Fig. 2-9(I).

The substrate is patterned Si, Amorphous Si and SiO2 with the hexagonal structures alternately

stacked on the Si substrate. As shown in Fig. 2-9(I), the incident light wavelength is 0.956 μm.

The authors fabricated two photonic crystals with different lattice constants a=0.4 and 0.33 μm.

Fig. 2-9(II) shows the light propagation in the photonic crystal with the lattice constant a equals

to 0.33 μm. The incident light swings from +7˚ to -7˚, but the light in the crystal swings from

+70˚ to -70˚ in a negative path, which implies a negative refractive index of the photonic crystal.

Chapter 2

18

Fig. 2- 9. Negative refraction observed in a photonic crystals [43]. (I) The three-dimensional

photonic crystals with a hexagon structure fabricated on a silicon substrate. (II) Negative refraction observed in the photonic crystals.

The imaging ability of the negative refraction photonic crystal flat lens has been demonstrated

experimentally by Patanjali et al. [44]. Based on two key points: all-angle negative refraction

and low absorption, the designed photonic crystal lens can focus a point source On the other

hand as imaging. The photonic crystal consists of alumina rods in a square lattice. The diameter

of the rods is 0.63 cm, height is 1.25 cm, and permittivity is 9.2. The lattice constant is 1.8 cm.

With this design, a 17.5 cm thickness photonic crystal flat lens was fabricated. The best

focusing result is at 9.3 GHz. As shown in Fig. 2-10a, a point source that is 2.25 cm from the

flat lens is focused On the other hand of the lens at 2.75 cm. the photonic crystal lens On the

other hand. Further, in Fig. 2-10b, the point source is moved up by 4 cm, the corresponding

image moves up with the same distance. This proves the imaging ability of the negative

refraction photonic crystal flat lens again.

Fig. 2- 10. Imaging by a negative refraction photonic crystal flat lens [44]. (a) Electric field on the cross-section of the lens. (b) Electric field on the cross-section after the source was

moved up by 4 cm.

Chapter 2

19

2.2.3 Summary of the negative refraction lens

The negative refraction lens provides a way to break the diffraction limit and realize the super-

resolution lens. However, the intrinsic property of the evanescent waves limited the negative

refraction lens to near-field microscopic field, no matter fabricated by LHM, metal or photonic

crystal. On the other hand, the fabrication of these lenses is through multiple processes, which

are complex and costly. These obstacles should be resolved for the promotion and the practical

applications of the negative refraction lens. Therefore, even with the attractive super-resolution

property, the negative refraction lens was not selected in the project.

2.3 Metasurface lens

Metasurface materials consist of periodical subwavelength artificial metal or dielectric

structures, which are the outcome of the development of fabrication precision and method. The

thickness of this material is in the subwavelength scale. Therefore, new properties between

materials and electromagnetic waves have been proposed and demonstrated. The metasurface

lens uses a new mechanism to modulate the wavefront of an incident beam, which is totally

different from the phase accumulation method of the conventional lens.

2.3.1 Theoretical design

Fig. 2- 11. Schematic of the abrupt phases change between two media [17].

Chapter 2

20

In 2011, Yu et al. [17] proposed and demonstrated a novel concept that is optical phase

discontinuity, which occurs at the interface between two media. They have investigated the

generalized laws of reflection and refraction based on Fermat’s principle.

In Fig. 2-11 [45], the black solid line indicates the incident ray, the red lines represent the

reflected and refracted beams. According to Fermat’s principle and phase stationary principle,

the three-dimensional generalized Snell’s laws have been derived and rewritten by Francesco

et al. [46]. The generalized law of refraction is:

{𝑛𝑡 sin(𝜃𝑡) − 𝑛𝑖 sin(𝜃𝑖) =

𝑑𝛷

𝑘0𝑑𝑥

cos(𝜃𝑡) sin(𝜑𝑡) =𝑑𝛷

𝑛𝑡𝑘0𝑑𝑦

. (2-8)

The generalized law of reflection is:

{sin(𝜃𝑟) − sin(𝜃𝑖) =

𝑑𝛷

𝑛𝑖𝑘0𝑑𝑥

cos(𝜃𝑟) sin(𝜑𝑟) =𝑑𝛷

𝑛𝑖𝑘0𝑑𝑦

. (2-9)

Where ni and nt are the refractive indexes of the two media; θi, θt and θr are the incident and

refractive angles; k0 is the wavenumber of wavelength λ0 in vacuum. dΦ is the phase change.

Eq. 2-18 to 2-19 imply that if dΦ/dx does not equal to 0, the relationship between θi and θt(θr)

will be arbitrary, which means the incident light will refract and reflect in an arbitrary direction.

Therefore, the authors designed optically thin resonators with subwavelength separation to

achieve special phase change alongthe interface. The element unit of the resonators is a V-

shaped gold plasmonic antenna (Fig. 2-12a). By tailoring the angle Δ and length h of the

antenna, 0 to 2π range phase shifts could be designed for the wavelength λ0 equals to 8 μm (Fig.

2-12b). The authors have defined two unit vectors â and ŝ to describe the orientation of the V-

shaped antennas. Therefore, according to the excited modes by the electric field components

parallel to â or ŝ, there are symmetric and antisymmetric types of the V-shaped antennas, as

shown in Fig. 2-12a. Fig. 2-12b shows the theoretical results simulated in FDTD. In the

simulation, a normal incident y-polarized plane wave propagates from the silicon substrate of

each individual V-shaped antenna. Г is the unit cell length, equals to 11 μm. The simulated

scattered electric fields are under the V-shaped antennas, the phase difference between each

antenna is constant at π/4. Therefore, the 0 to 2π phase shifts can be covered, which means the

potential to fully control the wavefront has been realized.

Chapter 2

21

Fig. 2- 12. V-shaped antenna design and phase change [17]. (a) Symmetric and antisymmetric modes of the V-shaped antennas. (b) An array of the V-shaped antennas and the

corresponding phase changes.

Based on the generalized Snell’s laws and the optical phase discontinuities concept, Francesco

et al. [21] have proposed and fabricated an aberration-free ultrathin flat lens. To realize

aberration-free focusing, the wavefront after the flat lens should be in the hyperboloidal profile.

As shown in Fig. 2-13a, a point PL on the flat lens, the responding projection point SL is on the

surface of a sphere with a radius equal to f, which is the designed focal length. The phase shift

at PL is proportional to the distance PLSL. Fig. 2-13b shows the hyperboloidal phase distribution

corresponding to the flat lens in polar coordinates. The phase profile φL(x,y) satisfies

𝜑𝐿(𝑟) =2𝜋

𝜆(√𝑟2 + 𝑓2 − 𝑓). (2-10)

Fig. 2- 13. Schematic of the flat lens design [21]. (a) The phase shift of the points on the flat lens. (b) Hyperboloidal phase distribution.

To satisfy the hyperboloidal phase profile, two key points should be considered: phase shifts

cover 0 to 2π; the scattering amplitude differences of each element are ignorable, as the lines

shown in Fig. 2-14a. By adjusting the arm length d, angle θ and arm width w (Fig. 2-14a), the

authors have designed eight V-shaped elements (Fig. 2-14a), from 1 to 4, d=180, 140, 130 and

85 nm, θ=79, 68,104 and 175˚, w=50 nm; elements 5 to 8 are 90˚ counter-clockwise rotating

of elements 1 to 4. By arranging the elements following the hyperboloidal phase profile, the

authors have designed a flat lens with a 6 μm focal length for λ=1.55 μm. The FDTD simulation

result is shown in Fig. 2-14b, the achieved NA was 0.075.

Chapter 2

22

Fig. 2- 14. Theoretical design of the aberration-free ultrathin flat lens [21]. (a) The phase shift and scattering amplitude of the designed eight V-shape elements. (b) The focal spot intensity

profile of the flat lens.

Another design [20] of the metasurface flat lens is based on the equal optical path principle[47]

or the Fresnel diffraction theory [48]:

𝜑(𝑟) = 2𝑛𝜋 +2𝜋

𝜆(𝑓 − √𝑓2 + 𝑟2), (2-11)

where f is the designed focal length, n is an arbitrary integer. As shown in Fig. 2-15a, the

antenna element is a V-shaped slit in a 100 nm gold film, the substrate is silicon. By adjusting

the arm length, width, and angle, eight elements covering 0 to 2π and with nearly equal

scattering amplitudes have been designed, as shown in Fig. 2-15b. The authors arranged the

antennas according to the equal optical path principle, as shown in Fig. 2-15c.

Fig. 2- 15. Schematic of V-shaped antenna for creating an ultrathin flat lens [20]. (a) The geometrical structure of the V-shaped antenna. (b) Theoretical phase shift and scattering

amplitude of eight designed V-shaped antenna. (c) Phase shift arrangement of the antenna to create the ultrathin flat lens.

By using the FDTD method, the authors simulated the intensity distribution of the focal spot

of the designed planar cylindrical lens. The simulation results are shown in Fig. 2-16. The

incident light wavelength was 4 μm, the designed focal length was 4 mm. Fig. 2-16a is the

intensity distribution in the axial plane of the focal spot; Fig. 2-16b shows the intensity

Chapter 2

23

distribution along the white dashed line in Fig. 2-16a. The full width at half maximum (FWHM)

is 270 μm.

Fig. 2- 16. Theoretical results of the ultrathin lens [20]. (a) The intensity distribution of the focal spot in the axial plane. (b)The intensity distribution along the white dasheded line in

Fig. 2-16(a).

2.3.2 Fabrication and applications

In 2013, based on the metasurface theory, Francesco et al. [21] designed and fabricated an

aberration-free ultrathin flat lens. Eight gold V-shaped antenna elements were first designed to

cover the phase shift from 0 to 2π for 1.55 μm telecom wavelength, then the elements were

arranged following the hyperboloidal phase profile pattern to create an aberration-free flat lens.

The authors used the EBL method to fabricate the V-shaped antenna element pattern on a 60

nm thick gold film (50 nm gold, 10 nm titanium as the adhesion layer). The whole metasurface

was on a 280 μm thick silicon wafer substrate, which was evaporated with a 240 nm anti-

reflective coating film of SiO on the backside. Fig. 2-17 is the SEM image of the flat lens, the

radius of the flat lens is 0.45 mm, and the designed focal length is 3 cm. The V-shaped antennas

were arranged to satisfy the designed focal length and the hyperboloidal phase shift as shown

on the right side of Fig. 2-17, the separation distance of the elements is 750 nm. There was a

15 nm titanium and 200 nm silver film surrounding the antenna elements to reflect the

unwanted incident beam that is not refracted by the arrays.

Chapter 2

24

Fig. 2- 17. SEM image of the fabricated metasurface ultrathin flat lens and the phase shift

distribution [21].

Fig. 2- 18. Theoretical calculations and experimental results of the intensity distribution in the focal region [21]. (a) The theoretical intensity distribution on the axial plane. (b) The

experimental intensity distribution on the axial plane. (c,d) the theoretical and experimental intensity distributions on the lateral planes alongthe white dasheded lines in Figs. 2-18a and

b. (e) The normalized intensity distribution along the colourful lines in Figs. 2-18c and d.

The theoretical and experimental results are shown in Fig. 2-18. Figs. 2-18a and b are the

intensity distributions in the axial planes of the focal spot, the experimental result matches well

with the theoretical result. Figs. 2-18c and d are the intensity distributions in the lateral planes

along the white dasheded line in Figs. 2-18a and b. The normalized intensity distribution in Fig.

2-18e corresponds to the colourful lines in Figs. 2-18c and d. The results indicate that the

experimental results match quite well with the theoretical predications.

As the concept of metasurface was proposed, a number of different types of ultrathin flat lenses

with different types of resonant elements have been proposed and fabricated. In 2013, Dan et

al. [20] proposed and fabricated an ultrathin terahertz planar lens. The base elements are V-

Chapter 2

25

shaped slit antennas in a gold film, the phase shift profile was designed according to Fresnel

diffraction theory. By using the same V-shaped slit antennas in a gold film, Ni et al. [49]

proposed and fabricated a flat lens working at the visible light range. The SEM image of the

lens is shown in Fig. 2-19a. The experimental results demonstrated that this lens has the ability

to focus wavelength from 766 to 476 nm, and the focal length can be tuned from 7 to 10 μm.

In 2016, Mohammadreza et al. [19] proposed and fabricated a metalens with the subwavelength

resolution at visible wavelength. The base elements are TiO2 nanofins on SiO2 substrate, as

shown in Fig. 2-19b. Fig. 2-19c is the SEM image of part of the metalens. The NA of this lens

is 0.8, and the focusing efficiency is around 75%. In the same year, another ultrathin flat lens

[18] with TiO2 nanopillars on a glass substrate as the base elements was also proposed and

fabricated, as shown in Figs. 2-19d and e.

Fig. 2- 19. Different types of ultrathin metasurface flat lens [18-20, 49]. (a) The SEM image of the flat lens fabricated with the V-shaped slit antenna. (b) Schematic of the TiO2 nanofins on SiO2 substrate. (c) SEM image of the fabricated metalens with nanofins. (d) Schematic of

the TiO2 nanopillar on SiO2 substrate. (e) SEM image of the fabricated metalens with nanopillar.

The metasurface lens enables a new way to design the ultrathin flat lenses. However, the

complex design, ineffective and multi-step fabrication steps and narrow bandwidth greatly

limit its practical applications. On the other hand, the resolution of the metasurface lens is still

comparable to the conventional lenses, therefore, new materials and methods need to be

developed to design ultrathin flat lenses to serve practical applications.

Chapter 2

26

2.4 Graphene oxide ultrathin flat lens

GO ultrathin flat lens is a new concept of flat lens design based on the material GO. As one of

the most important derivation material of graphene, GO has attracted a great attention. GO can

be converted to rGO, during the processing, the optical properties, such as the transmission and

refractive index of GO change. GO ultrathin flat lens makes full use of the changes of optical

properties to modulate the wavefront of the incident beam, which makes the GO lens different

from other ultrathin flat lenses concepts. A number of attractive properties of the GO ultrathin

flat lenses [50-52] have been demonstrated, such as nanometre thickness (200 nm or smaller),

high focusing resolution (three dimensional (3D) resolution is λ3/5), high efficiency (~32%),

and fabricated by a fast and low-cost method, which make it extremely competitive in the

practical applications of integrated photonic devices.

2.4.1 Graphene oxide and reduced graphene oxide

GO is a layered material consisting of hydrophilic oxygenated graphene sheets decorated with

oxygen functional groups including hydroxyl, epoxy, and carboxylic acid groups located on

their basal planes and the sheet edges. Due to the complexity of GO material (variability from

sample to sample), there are still debates about the precise chemical structure even it has been

synthesized 150 years ago by Benjamin Brody [53]. Fig. 2-20a shows one of the chemical

structures of GO [54, 55]. As a precursor of graphene [56] and graphene-based materials, the

most attractive character of GO is that it can be produced inexpensively and efficiently in a

large scale by wet chemical method. rGO is considered as a chemical derivative of graphene,

it can be prepared by removing the oxygen functional groups of GO. Fig. 2-20b [57] indicates

the remaining chemical structure of the rGO, the oxygen functional groups indicate the

incomplete reduction of GO.

Fig. 2- 20. Schematic of the GO and rGO structure model [54, 55, 57]. (a) The chemical

model of GO. (b) The chemical model of rGO.

Chapter 2

27

Scientists have developed a few methods to reduce GO to rGO, such as thermal exfoliation [58,

59], chemical reduction [60-62], microwave reduction [63], laser beam reduction [64, 65] and

so on [66-69]. The optical characteristics, such as absorption and the refractive index of GO

change when it is reduced to rGO. Fig. 2-21 [62] indicates the UV-visible absorption spectra

of GO (line a) and rGO (line b), which are prepared by hydrothermal treatment at 180 ℃ for 6

hours. There is a redshift of the absorption peak, and the absorption at visible region increases

when a GO is converted to rGO. The insert are the GO and rGO films, an obvious colour

difference can be observed [70].

Fig. 2- 21. UV-visible absorption spectroscopy of GO and rGO films [62]. Insets: GO and

rGO films.

Fig. 2-22 [65, 71] reveals the refractive index changes of GO to rGO. The reduction of GO is

processing based on the two-photon mechanism by a femtosecond laser. An order of 10-2 to 10-

1 refractive index modulation (Δn ~0.8) has been observed by controlling the femtosecond laser

power [65]. The inset in Fig. 2-22 is the schematic illustration of the film thickness and

refractive index changes induced by the femtosecond laser.

Fig. 2- 22. The refractive index modulation of rGO with the femtosecond laser power [65].

The novel optical characteristics induced by the conversion of GO into rGO provide a new way

to design optical components, such as the ultrathin flat lens.

Chapter 2

28

2.4.2 Theoretical design of graphene oxide lens

As we mentioned in the last section, there are three physical property variations during the

conversion process of GO to rGO: film thickness decrease, refractive index increase and

absorption increase in the visible region [72]. These three tunable properties provide the

flexibility in designing an ultrathin flat lens. In 2015, Zheng et al. [50] proposed and fabricated

an ultrathin flat GO lens with three-dimensional subwavelength focusing capability. Fig. 2-23a

is the schematic of the ultrathin flat GO lens. By using a femtosecond laser, part of the GO film

is reduced to rGO and form an array of concentric rings. The transmission and phase

modulations are shown in Fig. 2-23b, which make the GO lens fundamentally different from

the conventional Fresnel lenses. Fig. 2-23c shows the wavefront of a uniform plane wave is

manipulated by the GO lens into a spherical wavefront, the zoom in figure is the sketch of the

3D focal spot predicted by the theoretical model.

Fig. 2- 23. Design of the ultrathin flat GO lens. (a) The schematic of a laser fabricated GO

lens. (b) Amplitude and phase modulations induced by the reduction of GO. (c) Schematic of a uniform plane wave focused by the GO lens [50].

Chapter 2

29

Fig. 2- 24. The theoretical model illustration of a GO lens.

Fig. 2-24 is the theoretical model of the ultrathin flat GO lens. A uniform plane wave impinges

a GO lens, both the amplitude and phase of it are modulated by the GO lens. Owing to the

interference of the outgoing beam from the GO and rGO zones, the GO lens can focus a beam.

The phase difference between the adjacent GO (zone 1) and rGO (zone 2) zones is:

Δ𝜙 =2𝜋

𝜆(𝑅2 − 𝑅1) + Δ𝜑, (2-12)

where Rm is the distance between the point on the zone edges to the focal spot, m is the ordinal

number of the zones, λ is the wavelength of the incident wave, Δφ is the phase modulation

between the GO and rGO zones. To guarantee a constructive interference, the whole phase

difference between all the adjacent GO and rGO zones should be fixed at 2π, namely ΔΦ=2π.

As a result, there is a relationship:

𝑅𝑚 − 𝑓 = 𝑚𝜆 − 𝜆Δ𝜑

2𝜋, (2-13)

where f is the focal length of the GO lens. Substituting the relationship of 𝑅𝑚2 = 𝑎𝑚2 + 𝑓2 into

Eq. 2-13, we can obtain:

𝑎𝑚 = √𝜆𝑓(2𝑚 − 𝛥𝜑/𝜋), (2-14)

Chapter 2

30

am is the radius of the rings. Therefore, we can design the GO with the expected focal length

easily.

2.4.3 The fabrication of an ultrathin flat graphene oxide lens

Ultrathin flat GO lenses have been fabricated and characterized by Zheng et al. [50]. The GO

lens consists of concentric rGO rings that are fabricated by reducing the GO film. Therefore, a

high-quality GO film should be prepared as the first step. Fig. 2-25 shows the surface profile

of a high-quality GO film fabricated by the filtration method, it was characterized by using a

Bruker ContourGT InMotion 3D optical profiler. Considering the transmission, thickness and

refractive index variations, the thickness of the GO film was controlled at ~200 nm to achieve

the optimum focusing efficiency. The roughness is less than 50 nm as shown in the surface

profile line in Fig. 2-25.

Fig. 2- 25. Thickness characterization of a high-quality GO film measured by a 3D optical

profiler; the inset is the image of the GO film on a substrate [50].

By using the high-resolution DLW method, a GO lens consisting of three-ring has been

fabricated on the 200 nm GO film. The 3D optical profiler image of the GO lens is shown in

Fig. 2-26a, the radius of the first ring a1=1.8 μm, the linewidth of the rGO ring is ~600 nm.

The surface profile along the white dasheded line shows a Gaussian approximation of the

reduced part, this is due to the fabrication laser focal spot is in a Gaussian shape after been

focused with an objective. Figs. 2-26b and c are the theoretical and experimental results. In the

experiments, far-field 3D subwavelength focusing resolution (λ3/5) has been achieved for a

broad wavelength range from 400 to 1500 nm, which matches well with the theoretical results.

Chapter 2

31

Fig. 2- 26. (a) Surface profile of the GO lens measured by a 3D optical profiler [50]. (b)

Theoretical focal intensity distributions in the lateral and axial plane. (c) Experimental focal intensity distributions in the lateral and axial plane.

2.5 Fresnel diffraction theory

To predict the performance of an optical lens or an imaging system, it is necessary to investigate

the natural property of light: diffraction. Fresnel diffraction theory is a convenient and widely

used approximation theory to describe a light wave propagates close to the optical axis of the

system. Considering a beam at point P, there is a rigorous equation to describe the beam field,

namely the Helmholtz equation:

(∇2 + 𝑘2)𝑈(𝑃) = 0, (2-15)

where U(P) is the spatial variation of light.

According to the Green’s theorem, the rigorous solution of Eq. 2-15 is:

𝑈(𝑃) =1

4𝜋∬ [𝑈

𝜕𝑈′

𝜕𝒏− 𝑈′

𝜕𝑈

𝜕𝒏] 𝑑𝑆

𝑠, (2-16)

where S is an enclosed surface, n represents the unit vector normally incident the surface S. r

represents the distance between P and an arbitrary point. As shown in Fig. 2-27.

Fig. 2- 27. Schematic of point P surrounded by a closed surface S.

Chapter 2

32

To solve Eq. 2-16, a Green’s function was assumed:

𝑈′ =exp(−𝑖𝑘𝑟)

𝑟−exp(−𝑖𝑘�̃�)

�̃�, (2-17)

where r is the distance from point P to point P1 on the surface S, and �̃� is the distance from the

point �̃� to point P1 on the surface S, r=�̃�. As shown in Fig. 2-28.

Fig. 2- 28. Mirror symmetry points P and �̃� for a Green’s function.

Fig. 2- 29. Schematic of the optical wave diffracted in a cylindrical coordinate system.

Substituting Eq. 2-17 into Eq. 2-16, we can obtain the solution, which is called the RS

diffraction theory:

𝑈(𝑃) =1

2𝜋∬ 𝑈(𝑃1)𝑆

(−𝑖𝑘 −1

𝑟)exp(−𝑖𝑘𝑟)

𝑟cos(𝒏, 𝑟)𝑑𝑆. (2-18)

When r>>λ, and considering the cylindrical coordinate system, as shown in Fig. 2-33, the RS

diffraction expression can be written as:

𝑈2(𝑟2, 𝜃2) =𝑖

𝜆∫ ∫ 𝑈1(𝑟1, 𝜃1)

∞

0

2𝜋

0

exp(−𝑖𝑘√𝑧2+𝑟12+𝑟2

2−2𝑟1𝑟2cos(𝜃1−𝜃2))

𝑧2+𝑟12+𝑟2

2−2𝑟1𝑟2cos(𝜃1−𝜃2)z𝑟1𝑑𝑟1𝑑𝜃1, (2-19)

where (r1,θ1) is the diffraction plane, (r2,θ2) is the observation plane. r is the distance between

two points on the diffraction and observation planes, respectively. And

Chapter 2

33

𝑟 = √𝑧2 + 𝑟12 + 𝑟2

2 − 2𝑟1𝑟2cos(𝜃1 − 𝜃2), cos(𝒏, 𝑟) =𝑧

√𝑧2+𝑟12+𝑟2

2−2𝑟1𝑟2cos(𝜃1−𝜃2)

. (2-20)

We use θ to represent θ1-θ2, and rewrite Eq. 2-19:

𝑈2(𝑟2, 𝜃2) =𝑖

𝜆∫ ∫ 𝑈1(𝑟1, 𝜃1)

∞

0

2𝜋

0

exp(−𝑖𝑘𝑧√1+𝑟12+𝑟2

2−2𝑟1𝑟2cos𝜃

𝑧2)

z+𝑟12+𝑟2


𝑧

𝑟1𝑑𝑟1𝑑𝜃1, (2-21)

When the observation point is not far away from the optical axis, namely the paraxial

approximation, also called the Fresnel approximation, we can assume:

𝑟12 + 𝑟2

2 − 2𝑟1𝑟2cos𝜃 ≪ 𝑧 (2-22)

On the other hand, by using the first-order Taylor approximation, we can assume:

√1 +𝑟12+𝑟2


𝑧2= 1 +

𝑟12+𝑟2


2𝑧2 (2-23)

Therefore, Eq. 2-21 can be simplified to:

𝑈2(𝑟2, 𝜃2) =𝑖

𝜆∫ ∫ 𝑈1(𝑟1, 𝜃1)

∞

0

2𝜋

0

exp(−𝑖𝑘(𝑧+𝑟12+𝑟2


2𝑧))

z𝑟1𝑑𝑟1𝑑𝜃1, (2-24)

Combining with the first-order Bessel function

𝐽0(𝑥) =1

2𝜋∫ exp(−𝑖𝑥cos𝑡)2𝜋

0𝑑𝑡, (2-25)

We can obtain a simplified expression to predicate the diffraction beam field, which is also

called Fresnel diffraction theory:

𝑈2(𝑟2) =𝑖2𝜋

𝜆𝑧exp(−𝑖𝑘𝑧)exp(−

𝑖𝑘𝑟22

2𝑧) ∫ 𝑈1(𝑟1)exp(−

𝑖𝑘𝑟12

2𝑧)

∞

0𝐽0(

𝑘𝑟1𝑟2

𝑧)𝑟1𝑑𝑟1 (2-26)

Compared with Eq. 2-19, the Fresnel diffraction greatly simplifies the expression of a

diffraction beam field. Therefore, the Fresnel diffraction has become a widely used theory to

simulate the diffraction field of a lens or optical system.

2.6 GO film fabrication

A number of methods have been developed to fabricate a GO film, such as drop cast [73],

vacuum filtration [74-76], spray coating [77, 78] and self-assembly (SA) method [79, 80]. We

used the vacuum filtration and the SA methods to fabricate a high quality GO film. The vacuum

Chapter 2

34

filtration method is simple and of high-efficiency, which reduces the overall experimental

difficulty and increases the experimental efficiency. The SA method offers a smooth and

ultrathin film, which is essential for extremely accurate experiments. We choose the

appropriate method based on the experiment precision requirement.

Fig. 2- 30. GO film fabrication by the vacuum filtration method. (a) Filtration assembly with

GO solution. (b) A GO film on a membrane.

The vacuum filtration is a method for separating particles and fluid in a suspension by adding

a filter through which only the fluid can pass. The filtration assembly is shown in Fig. 2-30a, a

GO suspension should be sonicated before poured into the filtration assembly. The size of the

microspores on the filter is nanoscale, which ensure that only water can pass through the filter.

And the size of the filter is centimetre-scale. By controlling the GO mass in the suspension,

GO films with different thicknesses can be prepared efficiently. Fig. 2-30b shows a 200 nm

GO film on the polyethersulfone membrane. By using water or ethanol, the GO films can be

easily peeled off from the membranes and transferred onto various substrates, the common one

of which is cover glass.

However, the vacuum filtration method has the drawback that the roughness of the fabricated

GO film is unwarrantable, the roughness average is around 10 to 50 nm. The constantly

drawing liquid through the film during the fabrication process can result in many cracks and

defects in the films. The transfer process also introduces extra roughness into the films.

Therefore, for some more precise experiments, we have to give up the quick and simple vacuum

filtration method and use the SA method to conquest the rough surface of a GO film.

Chapter 2

35

Fig. 2- 31. Schematic of a self-assembly GO film on the cover glass [79].

The SA method is a process that disordered components form an organized structure or pattern

by the local interactions among the components themselves without external direction. The GO

self-assembly is a layer-by-layer method [81, 82] based on the electrostatic force. Due to the

oxygen-containing groups in GO, the GO flakes are negatively charged. On the other hand,

poly (diallyl dimethylammonium chloride) (PDDA) is a material that is positively charged.

Therefore, the electrostatic force between the GO and PDDA can be used to fabricated a GO-

PDDA film in a layer-by-layer manner based on the self-assembly method. The schematic of a

GO-PDDA film is shown in Fig. 2-31 [79]. A sonicated GO solution and PDDA solution is

prepared first, the concentration of the GO solution is 3 mg/ml, the volume ration of the PDDA

solution is 2%. As the surface of the cover glass is negatively charged, the cover glass is

immersed in the PDDA solution first, followed by the GO solution, the immersed time is 30 s.

between each immersion process, the cover glass will be washed by distilled water and dried

by N2. The schematic of the process is shown in Fig. 2-32 [79].

Fig. 2- 32. Schematic of the layer-by-layer SA method to fabricate a GO-PDDA film on a

cover glass [79].

The thickness of one GO-PDDA layer is 2 nm. Therefore, by counting the number of layers,

one can easily control the film thickness with an extreme precision. Fig. 2-33 shows the GO-

PDDA films with different layers. As the layer number increases, the GO-PDDA film becomes

more opaque.

Chapter 2

36

Fig. 2- 33. The GO-PDDA films fabricated by the SA method.

2.7 Direct laser writing technology

GO reduction is a way to remove oxygen functional groups including hydroxyl, epoxy, and

carboxylic acid groups located on their basal planes and the sheet edges of the GO. There are

a number of methods developed to reduce GO, such as thermal annealing [58, 59, 74], chemical

reduction [62, 83-85], microwave reduction [63, 86], and DLW [64, 65, 71, 87]. Considering

the high efficiency and one-step fabrication capability of the DLW method, we use the DLW

to reduce GO and at the same time, pattern the GO lenses.

DLW is an efficient and convenient method to process two and three dimensional (3D) patterns

or structures [88, 89]. A schematic of the DLW system [90] illustration is shown in Fig. 2-34.

An expanded laser beam is reflected by a dichroic mirror, then being focused by an objective,

the objective can be changed to different NA according to the experimental requirements. A

sample is mounted onto a scanning stage, the surface of the sample is near the focal plane of

the objective. The reflected light from the sample is focused by a lens onto a charge-coupled

device (CCD) camera, which provides an in-situ monitoring of the fabrication process.

Chapter 2

37

Fig. 2- 34. Schematic of a direct laser writing system setup [90].

There are two mechanisms of laser writing reduction, one is based on the thermal reduction

which can only achieve minimum feature size >1 μm [64, 91], as shown in Fig. 2-35a. The

other one is based on the photochemical reduction mechanism [65, 71, 87]. The DLW reduction

method based on photochemical mechanism can achieve a higher fabrication resolution. As the

threshold photon energy of GO for photochemical reduction is 3.2 eV (λ=390 nm) [71], a

higher fabrication resolution [50, 65, 87] (~300 nm, Fig. 2-35b) have been achieved by using

a high peak power femtosecond laser, of which the operating wavelength is 800 nm. To

minimize the thermal effect, a low repetition rate, femtosecond pulsed laser beam (100 fs, 10

kHz, 800 nm) was applied [65]. The laser was focused by a high NA (0.8) objective, a record

small rGO line width of ~300 nm (0.38 λ) was achieved, Fig. 2-35b shows the thickness and

linewidth change versus the laser power.

Fig. 2- 35. rGO fabrication by laser [64, 65]. (a) Optical image of the laser-irradiated rGO channel, the laser reduction is based on the thermal mechanism. (b) The rGO thickness and

linewidth with laser power, the laser reduction is based on photochemical mechanisms.

Chapter 2

38

The DLW method is widely used in various research fields, and adjustments have been

introduced to improve the resolution of the DLW method, such as using an oil-immersed

objective, phase modulating of the incident beam by SLM [92, 93]. For our experiments, the

DLW is an efficient, 3D, high precision, environmentally friendly and easy to operate method.

We use the DLW method based on the photochemical reduction mechanism to fabricate high

resolution GO-based lenses and optical elements.

2.8 State-of-the-arts of endoscope technologies

Endoscope is one of the most important tools to study areas that hard to reach, such as the

inside of the human body. The earliest endoscope in record is around 2400 years ago [94]. But

the first endoscope with a light guiding system was invented 200 hundred years ago by Bozzini

[95]. In 1954, glass rods were used as the light guide system by Hopkins [96]. Then, as the

optical fibre fabrication technology became mature, the prototype optical fibre endoscopies

have been developed in several decades [32, 33]. Due to the mechanical flexibility and compact

size of optical fibre, endoscopes are able to in-situ image areas, which are hard to reach for a

conventional optical microscope with minimal invasion. Therefore, endoscope has been a

widely used tool in the industrial, military, and the medical field. Various applications based

on endoscopy have been developed, such as optical coherence tomography [97], fluorescence

lifetime imaging [98], second harmonic generation [99, 100] and third harmonic generation

imaging [101] and so on [102-104]. However, low resolution is still a limitation of endoscopes.

The resolution is still on the level of a-few-wavelength. On the other hand, miniaturization is

another challenge of the current endoscopes.

Based on the imaging methods, there are two types of endoscopies. One is to image the target

object directly, this typical representative is an endoscope with a fibre bundle [34, 35]. As

shown in Fig. 2-36a, a fibre bundle is connected to a GRIN lens system, which collimates and

refocuses the divergent beams emerging from each fibre core. Fig. 2-36b is the imaging setup

scheme, a scanning unit is used to choose the coupling fibre of the incident beam. The scanning

unit is far away from the target sample, which helps to miniaturize the endoscopy, but the fibre

bundle endoscope is inherently resolution limited by the intervals between the fibre cores.

Chapter 2

39

Fig. 2- 36. A direct imaging endoscopy with fibre bundle and GRIN lenses [35]. (a) Fibre

bundle connects to a GRIN lens group. IL: image lens; OL objective lens. (b) Schematic of the experimental imaging system with a fibre endoscope.

The other one is using a single fibre. Numerous of works have been conducted in this type of

endoscope to increase the resolution [105-110]. The common method is to add a high NA lens

on the fibre tip as shown in Fig. 2-37. A double-clad fibre (DCF) with a short section of no-

core fibre (NCF) was used to transmit signals [107]. The combination of the GRIN lens and

mirror helps to rotate scanning of the sample. There are two branches of this type endoscope,

one is to fabricate lenses onto the fibre tips directly, and the other one is to use an SLM to

achieve a focal spot. The single-fibre endoscope has the potential to increase the resolution and

miniaturize the system, more reviews will be introduced in the following sections.

Fig. 2- 37. Schematic of the needle tip of a single fibre endoscope. Inset: Image of the DCF with a GRIN lens. DCF: double-clad fibre; NCF: no-core fibre; GRIN: graded index lens.

[107].

Chapter 2

40

2.8.1 Direct lens fabrication on the fibre tip

Fig. 2- 38. Design and fabrication of a triplet lens system on the fibre tip using DLW [109].

(a) Ray-tracing design of the triplet lens system in ZEMAX. (b) Simulated image of the triplet lenses. (c) SEM image of the fabricated triplet lenses. (d) Experimental image of the

fabricated triplet lenses. (e) SEM image of the whole on fibre tip triplet lens system.

Fabricating a high NA lens onto the fibre tip is the most direct way to increase the resolution

of the endoscope. Gissible et al. [109] designed and fabricated multi-lenses on the fibre tip by

femtosecond two-photon DLW method. The lenses show high performances with resolution

Chapter 2

41

up to 1 μm. The authors used the software ZEMAX to design and optimize submicrometric

lenses. Fig. 2-38a is the ray-tracing design of a triplet lens system. Fig. 2-38b is the simulated

image of the designed triplet lens system, a clear and high-quality image can be obtained. Fig.

2-38c is the SEM image of the triplet lenses, the lenses have been cut out a 90˚ piece to allow

the observation of the inside of the lenses. Fig. 2-38d shows the experimental results by

imaging the USAF 1951 resolution test chart with the designed triplet lenses. Fig. 2-38e is the

whole coloured SEM image of the triplet lens attached to an optical fibre.

Metasurface lenses also provide potential solution for new endoscope design. Pahlevaninezhad

et al. [110] designed a metasurface lens considering the trade-off between transverse resolution

and depth of focusing. The metasurface lens is composed of arrays of amorphous silicon (a-Si)

nanopillars on a glass substrate, as shown in Fig. 2-39c. The height of the a-Si nanopillar is 750

nm, the square lattice is 400 nm. By changing the diameters of the a-Si nanopillars, a 0 to 2π

range of phase change can be achieved. Then, the authors arranged the a-Si nanopillars based

on the ray-tracing method to obtain a diffraction-limited spot. Fig. 2-39a is the schematic of

the metasurface endoscopy, the prism is used to change the direction of the signal beam. Fig.

2-40b is the image of the tip of the endoscopy. Fig. 2-39d is the SEM image of the fabricated

metasurface lens. The experimental results proved that this metasurface lens had three times

focal depth compared with an achromatic lens with the same NA.

Direct lens fabrication on fibre tip provides a way to achieve high-resolution endoscopy.

However, the unavoidable scanning part prevents the miniaturization of endoscopy. Combing

a single fibre and the far-end scanning method, one can keep both the high resolution and

miniaturization benefits of an endoscopy.

Chapter 2

42

Fig. 2- 39. Metasurface endoscope design and fabrication [110]. (a) Schematic of the

metasurface endoscope tip. (b) Image of the end of the metasurface endoscope under a microscope. (c) Schematic of an individual a-Si nanopillar on a glass substrate. (d) SEM

image of a part of the fabricated metasurface lens.

2.8.2 Spatial light modulator

To combine the far-end scanning method with a single fibre, a spatial light modulator (SLM)

has been used to replace the conventional scanning unit based on location moving. SLM is an

optical component that can modulate the phase and intensity of an incident beam. Therefore,

by modulating the intensity and phase distribution of an incident beam, the scanning ability of

SLM can be achieved. Researchers have done a number of works on this topic [111-117]. The

most common endoscopic system with SLM is shown in Fig. 2-40. The expanded incident

beam is reflected by an SLM, the phase and intensity of the beam are modulated by the small

units in the SLM. Then the modulated beam is coupled into a multimode fibre (MMF). On the

other distal end of the MMF, researchers can achieve a scanning focal spot. The spot is reflected

Chapter 2

43

by the sample, and collected by the same MMF. Then a photomultiplier tube (PMT) was used

to measure the collected beam. Therefore, the image of the sample can be obtained.

Fig. 2- 40. A common endoscopic system with SLM, BS: beam splitter; PMT:

photomultiplier tube.

Fig. 2- 41. Schematic of the beam modulation by an SLM [111]. (a) The schematic of the

output beam controlling by an SLM. (b) The output beam spots obtained by an SLM.

Fig. 2-41a is the detailed mechanism of an SLM based on the weighted Gerchberg-Saxton

algorithm [111]. There are two steps to study the beam propagation from SLM to the fibre tip.

The first step is to measure the fibre propagator. Usually, a discrete set of plane waves is chosen

Chapter 2

44

as the input beam. Therefore, according to the recorded amplitude distribution of the output

beam, the propagation matrix of the fibre can be addressed. The relationship between the input

and output complex amplitudes un, vm is:

𝑣𝑚 = ∑ 𝐺𝑚𝑛𝑢𝑛𝑛 , (2-27)

where Gmn is the propagation matrix of the fibre. The second step is to describe the relationship

between the SLM and the input facet complex amplitudes. As shown in Fig. 2-41a, the SLM

surface is on the Fourier plane of the input facet of the fibre, therefore, a Fourier transform can

describe the complex amplitudes relationship between the jth SLM pixel and the nth input point:

𝑢𝑛 = ∑ 𝐹𝑛𝑗𝑠𝑗𝑗 , 𝐹𝑛𝑗 =1

𝐽𝑒𝑥𝑝 [−𝑖

2𝜋

𝜆𝑓(𝑥𝑗𝑥𝑛 + 𝑦𝑗𝑦𝑚)], (2-28)

where J is the number of the SLM pixels, f is the effective focal length. Therefore, if we set

𝑠𝑗 = 𝐹𝑛𝑗∗ . (2-29)

The corresponding output beam intensity is

|𝑣𝑚|2 = |𝐺𝑚𝑛|

2. (2-30)

Thus, the output beam can be controlled by the SLM. Fig. 2-41b and c is the simulation results

that by controlling the SLM, a single spot and an array of spots can be realized on the output

facet of an MMF. The theoretical resolution of an MMF with an SLM is around 3λ. Therefore,

this endoscopic system still suffers from low resolution.

Further studies demonstrate that by adding a high NA lens [113], or even only a highly

scattering media [117] on the output facet of the MMF, the resolution of the endoscopy can be

increased to a subwavelength scale. Fig. 2-42a is the schematic of the micro-lens described by

ray-tracing. Fig. 2-42b is the SEM image of the micro-lens on an MMF. Fig. 2-42c is the

experimental setup schematic. With the micro-lens, the system shows an up to 0.93 NA

resolution, even the MMF is only 0.22 NA. These results provides interesting potentials to

achieve on fibere tip endoscope. Combing with the GO lens, a new way to design fibre

endoscope with both high resolution and miniaturization might be developed.

Chapter 2

45

Fig. 2- 42. A micro-lens on the fiber tip to improve resolution [113]. (a) The focusing

schematic of the designed micro-lens by a ray-tracing method. (b) SEM image of the micro-lens on the MMF core. (c) The experimental setup of the focusing characterization of the on

fibre tip micro-lens, L: lens, D: dichroic mirror.

2.9 Chapter summary

In this chapter, different ultrathin flat lenses have been reviewed. Particular details about the

ultrathin flat GO lens have been provided. Finally, as one of the practical applications,

endoscopes have been reviewed.

As a powerful candidate to break the diffraction limit, the negative refraction lenses have

attracted a great attention. Researches have demonstrated the breaking of the diffraction limit

with the negative refraction lens. However, this ability is limited in the near field, which greatly

hinders the practical application range of the negative refraction lens.

Based on the abrupted phase modulation mechanism, the metasurface lens has become a hot

topic from the moment it has been proposed. However, the complex multiple-step fabrication

makes it an expensive component for the optical system. In addition, the narrow bandwidth of

the metasurface lens limits it to specific wavelength ranges for imaging.

On the contrary, ultrathin flat GO lens achieves a 3D subwavelength resolution without the

near field limitation. The one-step DLW fabrication method offers the GO lens low cost as a

common optical component. In addition, GO ultrathin flat lens can potentially be integrated

into various optical components to change or optimize their functionalities, such as

conventional optical lenses, fibre tips, on-chip optical systems.

Chapter 2

46

The potential that integrating the GO lens onto a fibre tip provides a practical application

avenue for GO lens for endoscope. Therefore, we reviewed the recent advance of endoscopies.

We compared the different types of endoscopes, to obtain a high resolution, and miniaturization

endoscopy. By controlling the SLM, a high-resolution spot is potentially obtained.

47

Chapter 3

Development of an accurate theoretical model for designing graphene-based ultrathin flat lens

3.1 Introduction

As reviewed in Chapter 2, GO ultrathin flat lens has attracted much attention due to the

demonstrated attractive properties. Therefore, designing a GO lens with special parameters has

become a hot topic. The current GO lens design method is based on the Fresnel diffraction

theory, which was derived based on the paraxial approximation situation. This limits the current

design method only applicable to low NA lenses. To exploit the high NA lens design and

predict the lens performance, the vigorous FDTD method is a commonly used method.

However, it requires large amounts of computational resources, even for a GO lens with 10 μm

focal length, the FDTD method takes a few days to obtain accurate results.

Therefore, to develop a design method for an ultrathin flat lens with high or arbitrary NA, we

developed a method based on the Rayleigh-Sommerfeld (RS) diffraction theory, which is not

limited by the paraxial approximation. The values of the ring radii of the desired GO lens are

directly derived from the RS diffraction theory without the optimization process, which makes

this method of high efficiency and low computational cost. Based on the two design methods,

two GO lenses have been modelling. Compared with the FDTD simulation results, the RS

model has been theoretically demonstrated to be more accurate than the Fresnel model.

In this chapter, first, the RS diffraction theory is reviewed, the diffraction intensity distribution

formula is given. Then, the accurate lens design method based on the RS diffraction theory is

derived, the formula and method to design the GO lens are listed. Finally, the accuracy of the

new RS model and the comparisons with the Fresnel model have been theoretically

demonstrated by the FDTD methods.

Chapter 3

48

3.2 Rayleigh-Sommerfeld diffraction theory

RS diffraction theory is a time-independent theory to predict the scalar field of a

monochromatic wave at an arbitrary source-free point. The derivation of it can be started from

the Helmholtz equation. Considering a beam in a linear, isotropic and homogeneous medium.

U(P) represents the spatial variation of light at point P, it satisfies the time-independent and

rigorous Helmholtz equation [118], therefore, we have:

(∇2 + 𝑘2)𝑈 = 0, (3-1)

where k=2π/λ. At the same time, we assume a Green’s function 𝐺(𝑃1) =exp(𝑖𝑘𝑟0)

𝑟0 represents a

spherical wave expanding from point P, r0 is the distance from P to P1, as shown in Fig. 3-1.

Therefore, we have:

(∇2 + 𝑘2)𝐺 = 0, (3-2)

except for point P. Applying U×( Eq. 3-2)-G×(Eq. 3-1), we obtain:

𝑈∇2𝐺 − 𝐺∇2𝑈 = 0. (3-3)

Fig. 3- 1. The volume V with two closed surfaces Sr and S.

To apply Eq. 3-3 into the Green’s theorem, the functions G and P should be continuous within

the integral space. Therefore, we use a small spherical surface Sr with a radius r to exclude the

point P, as shown in Fig. 3-1. Volume V is the space surrounded by surfaces S and Sr. S is the

outside closed surface. n is the unit vector normal towards surfaces S and Sr. Therefore, we

obtain the relationship between functions G and U based on the Green’s theory [37]:

∭ 𝑈∇2𝐺 − 𝐺∇2𝑈𝑑𝑉 = ∬ (𝑈𝜕𝐺

𝜕𝒏− 𝐺

𝜕𝑈

𝜕𝒏)

𝑆′𝑑𝑆′ = 0

𝑉, (3-4)

where 𝑆′ = 𝑆 + 𝑆𝑟. Eq. 3-4 can be rewritten as:

Chapter 3

49

∬ (𝑈𝜕𝐺

𝜕𝒏− 𝐺

𝜕𝑈

𝜕𝒏)

𝑆𝑑𝑆 = −∬ (𝑈

𝜕𝐺

𝜕𝒏− 𝐺

𝜕𝑈

𝜕𝒏)

𝑆𝑟𝑑𝑆𝑟. (3-5)

When the point P1 is on the surface Sr, the vector r0 is opposite to n, and the scalar r0=r.

Therefore:

𝜕𝐺(𝑃1)

𝜕𝒏= cos(𝒏, 𝒓0) (𝑖𝑘 −

1

𝑟0)exp(𝑖𝑘𝑟0)

𝑟0= (

1

𝑟0− 𝑖𝑘)

exp(𝑖𝑘𝑟0)

𝑟0. (3-6)

Taking the limit that that 𝑟 → 0, namely𝑟0 → 0. The right side of Eq. 3-5 is

lim𝑟→0

∬ (𝑈𝜕𝐺

𝜕𝒏− 𝐺

𝜕𝑈

𝜕𝒏)

𝑆𝑟𝑑𝑆𝑟 = lim

𝑟0→04𝜋𝑟0

2 [𝑈 (1

𝑟0− 𝑖𝑘)

exp(𝑖𝑘𝑟0)

𝑟0−𝜕𝑈

𝜕𝑛

exp(𝑖𝑘𝑟0)

𝑟0] = 4𝜋𝑈(𝑃).(3-7)

Therefore, substrate Eq. 3-7 into the right side of Eq. 3-5, we obtain:

𝑈(𝑃) =1

4𝜋∬ (

exp(𝑖𝑘𝑟0)

𝑟0

𝜕𝑈

𝜕𝒏− 𝑈

𝜕

𝜕𝒏[exp(𝑖𝑘𝑟0)

𝑟0])

𝑆𝑑𝑆, (3-8)

which is known as the Kirchhoff diffraction integral. The derivation of Eq. 3-8 is the method

to develop the scalar theory of diffraction. Based on the choice of ‘boundary conditions’,

namely the choice of the Green’s function G, different diffraction theories had been derivated,

such as the RS diffraction theory.

Considering a planar opaque screen, as shown in Fig. 3-2, a closed surface surrounding point

P has three parts: the aperture surface Σ, the plane surface S1 behind the screen, the spherical

surface S2. Rayleigh and Sommerfeld choose a Green’s function that

𝐺 =exp(−𝑖𝑘𝑟)

𝑟−exp(−𝑖𝑘�̃�)

�̃�= 0, (3-9)

where r is the distance from point P to point P1 on the surface Σ, and �̃� is the distance from the

point �̃� to point P1 on the surface S, r=�̃�. The point �̃� is the mirror image of point P, as shown

in Fig. 3-2.

Fig. 3- 2. The mirror symmetry points P and �̃� for a Green’s function.

Chapter 3

50

The integral across the entire surface is:

𝑈(𝑃) =1

4𝜋∬ (𝐺

𝜕𝑈

𝜕𝒏− 𝑈

𝜕𝐺

𝜕𝒏)

𝑆1+𝑆2+Σ𝑑𝑆. (3-10)

When S2 tends to infinity, both U and G tend to zero, the integral on surface S2 contributes zero

to the whole integral. On the other hand, the screen is opaque, the integral on surface S1 should

be zero. Therefore, the simplified expression of Eq. 3-10 is:

𝑈(𝑃) =1

4𝜋∬ (𝐺

𝜕𝑈

𝜕𝒏−𝑈

𝜕𝐺

𝜕𝒏)

Σ𝑑𝑆. (3-11)

Substitute Eq. 3-9 into Eq. 3-11, we obtain:

𝑈(𝑃) =1

2𝜋∬ 𝑈(𝑃1)(−𝑖𝑘 −

1

𝑟)exp(−𝑖𝑘𝑟)

𝑟cos(𝒏, 𝒓))

Σ𝑑𝑆, (3-12)

which is called the RS diffraction formula. Our accurate lens design model is based on the RS

diffraction theory.

3.3 Accurate lens design based on Rayleigh-Sommerfeld theory

Zheng et al. [50] used the Fresnel diffraction model [119-121] to design the GO lens, however,

the Fresnel diffraction theory is based on the paraxial approximation, which limits the design

of the GO lens in the low NA range. For a high NA lens, the Fresnel diffraction theory-based

design model is not able to accurately predict the focusing performance. Therefore, we

developed a new design model based on the RS diffraction theory, which is able to accurately

predict the focusing process of an arbitrary NA and focal length GO lens. The new model will

promote the practical applications of the GO lens with a high efficiency and low computational

cost.

The schematic of a GO lens under the cylindrical coordinate system is shown in Fig. 3-3. A

plane beam (𝑈1(𝑟1, 𝜃1) = 1) propagates through the GO lens along the positive Z direction, the

GO lens is on the diffraction plane (r1,θ1). The beam field distribution immediately behind the

GO lens is 𝑈′1(𝑟1, 𝜃1)). (r2,θ2) is the observation plane, which is usually the focal plane. r is

the distance between the two points on the diffraction and observation planes, respectively. z

is the distance between the diffraction and the observation planes. We have:

𝑟 = √𝑧2 + 𝑟12 + 𝑟2

2 − 2𝑟1𝑟2cos(𝜃1 − 𝜃2), cos(𝒏, 𝒓) =𝑧

√𝑧2+𝑟12+𝑟2


. (3-13)

Chapter 3

51

The RS diffraction expression can be written as:

𝑈2(𝑟2, 𝜃2, 𝑧) =1

2𝜋∫ ∫ 𝑈′1(𝑟1, 𝜃1)(−𝑖𝑘 −

∞

0

2𝜋

0

1

√𝑧2+𝑟12+𝑟2


)exp(−𝑖𝑘√𝑧2+𝑟1

2+𝑟22−2𝑟1𝑟2cos(𝜃1−𝜃2))

𝑧2+𝑟12+𝑟2

2−2𝑟1𝑟2cos(𝜃1−𝜃2)z𝑟1𝑑𝑟1𝑑𝜃1, (3-14)

When field distribution of the beam 𝑈′1(𝑟1, 𝜃1)) is known, we can use Eq. 3-14 to calculate the

intensity distribution of the beam on the observation plane. Designing a GO lens is a process

that the intensity distribution on the observation plane is known. We find out a proper beam

distribution 𝑈′1(𝑟1, 𝜃1)), which satisfies the beam intensity distribution on the observation

plane.

Fig. 3- 3. Diffraction schematic of a GO ultrathin flat lens in cylindrical coordinate systems.

Focal length f and diameter D are the most important parameters of a GO lens, our design

method assumes that the two parameters are the known targets. As the GO lens is axially

symmetric, we only consider the intensity distribution on the z-axis, namely r2=0. Therefore,

the field distribution along the z-axis is:

𝑈2(𝑧) =1

2𝜋∫ ∫ 𝑈1′(𝑟1, 𝜃1)

∞

0

2𝜋

0

(−𝑖𝑘 −1

√𝑧2 + 𝑟12)exp (−𝑖𝑘√𝑧2 + 𝑟1

2))

𝑧2 + 𝑟12 𝑧𝑟1𝑑𝑟1𝑑𝜃1

= ∫ 𝑈1′(𝑟1)∞

0(−𝑖𝑘 −

1

√𝑧2+𝑟12)exp(−𝑖𝑘√𝑧2+𝑟1

2))

𝑧2+𝑟12 𝑓𝑟1𝑑𝑟1. (3-15)

For the GO lens, given the fact that the amplitude modulation contributes much more than the

phase modulation, we only consider the amplitude modulation. First, we consider the situation

without the GO lens, namely, 𝑈1′(𝑟1, 𝜃1) = 𝑈1(𝑟1, 𝜃1) = 1. In this situation, for a point F on

the Z-axis, the distance between it and the diffraction plane is f. The field distribution at point

F is:

Chapter 3

52

𝑈2(𝑓) = ∫ (−𝑖𝑘 −1

√𝑓2+𝑟12)exp(−𝑖𝑘√𝑓2+𝑟1

2))

𝑓2+𝑟12

∞

0𝑓𝑟1𝑑𝑟1 (3-16)

Eq. 3-16 indicates that with the known f, 𝑈2(𝑓) is decided by r1 only, which means the integral

range of r1 decides the field value at point F. Therefore, at a given condition √𝑓2 + 𝑟12>>λ, Eq.

3-16 can be simplified and written as a function of r1:

𝑈2(𝑟1) = −𝑖𝑘𝑓 ∫exp(−𝑖𝑘√𝑓2+𝑟1

2))

𝑓2+𝑟12

𝑟′

0𝑟1𝑑𝑟1, (3-17)

where 𝑟′ is the upper limit of the integral. Substrate 𝑅 = √𝑓2 + 𝑟12 into Eq. 3-17, we get:

𝑈2(𝑅) = −𝑖𝑘𝑓 ∫exp(−𝑖𝑘𝑅)

𝑅

√𝑓2+𝑟′2

𝑓𝑑𝑅. (3-18)

Based on the Euler’s equation, Eq. 3-18 can be rewritten as:

𝑈2(𝑅) = −𝑘𝑓(𝑖 ∫cos(𝑘𝑅)

𝑅

√𝑓2+𝑟′2

𝑓𝑑𝑅 + ∫

𝑠𝑖𝑛(𝑘𝑅)

𝑅

√𝑓2+𝑟′2

𝑓𝑑𝑅) (3-19)

Therefore, the intensity distribution at point F is:

𝐼(𝑅) = [|𝑈2(𝑅)|]2 = (𝑘𝑓)2 [(∫

cos(𝑘𝑅)

𝑅

√𝑓2+𝑟′2

𝑓𝑑𝑅)

2

+ (∫𝑠𝑖𝑛(𝑘𝑅)

𝑅

√𝑓2+𝑟′2

𝑓𝑑𝑅)

2

] (3-20)

The periodic-like change of the intensity I(R) predicts the ring radii of the GO lens with the

known focal length f. To find out the positions that contribute to the destructive interferences

of the intensity I(R), taking the derivative of Eq. 3-20, we can obtain the contribution of I(R) at

point F:

𝑑𝐼

𝑑𝑅= 2(𝑘𝑓)2 [(

cos(𝑘𝑅)

𝑅∫

cos(𝑘𝑅)

𝑅

√𝑓2+𝑟′

2

𝑓𝑑𝑅) + (


𝑅∫


𝑅

√𝑓2+𝑟′

2

𝑓𝑑𝑅)]. (3-21)

Even considering the dirichlet integral [122]:

∫ 𝑠𝑖𝑛(𝑅)

𝑅

∞

0𝑑𝑅 =

𝜋

2, (3-22)

there is no analytical expression of Eq. 3-21 with the upper limit being not infinite. Another

way is to use the Taylor expansion:

cos𝑅 = 1 −𝑅2

2!+⋯(−1)𝑛

𝑅2𝑛

(2𝑛)!, sin𝑅 = 𝑅 − 𝑅3

3!+⋯(−1)𝑛

𝑅2𝑛+1

(2𝑛+1)!, (3-24)

where n is an integer tending to infinity. Furthermore, when n → ∞,

Chapter 3

53

(−1)𝑛𝑅2𝑛

(2𝑛)!→ 0; (−1)𝑛 𝑅2𝑛+1

(2𝑛+1)!→ 0. (3-25)

We can decrease the calculation range according to the required accuracy and the computable

ability. The ring positions located in the regions between points that satisfy 𝑑𝐼𝑑𝑅= 0. The new

design model avoids the paraxial approximation, the high accuracy and efficiency to design an

ultrathin GO lens with an arbitrary NA will be demonstrated in the next section.

3.4 Designed result and comparisons

To demonstrate the accuracy and the efficiency of the new GO lens design model, we have

designed two GO lenses with the targeted focal length and simulated and compared their

focusing performance by the FDTD method [21, 123-125], Fresnel diffraction and RS

diffraction theory, respectively.

With a given diameter D and focal length f, according to Eq 3-21, the relationship between the 𝑑𝐼

𝑑𝑅 and R can be simulated. For a given f=3.1 μm and D= 20 μm (Lens1), at a wavelength of

0.633 μm, the 𝑑𝐼𝑑𝑅

versus R dependence is shown in Fig. 3-4.

Fig. 3- 4. Differential coefficient 𝒅𝑰

𝒅𝑹 versus R.

As mentioned in the last section, we choose the ring positions in the middle of each two

adjacent points that satisfy 𝑑𝐼𝑑𝑅= 0. On the other hand, the Fresnel design model [4] is:

𝑟𝑚 = √𝑚𝜆𝑓 + (𝑚𝜆/2)2 (3-26)

where f is the focal length, rm is the outer radius of the mth zone. In comparison, under the same

situation, we have calculated the radii based on the Fresnel model with the same targeted

Chapter 3

54

diameter D and focal length f. The first three radii comparison is shown in Fig. 3-5. There is a

significant difference of 13.9% for the first radii of the two models, the differences decrease as

the radii increase, 6.6% for the second ring, and 4.4% for the third ring.

Fig. 3- 5. Comparison of ring radii versus ring number m based on the RS and Fresnel design

model.

Based on the two designs, two GO lens models with a thickness of 200 nm, a ring width of 0.6

μm (the rGO zones) have been constructed. The focusing performances of both GO lenses have

been numerically simulated based on the RS diffraction theory. The results are shown in Fig.

3-6. Both designs provide a good focal spot (Fig. 3-6a), and the transverse FWHMs of the focal

spots are similar (1.0% difference) as shown in Fig. 3-6c. However, there is a non-negligible

difference between the focal lengths, the calculated focal length based on the RS model design

is 3.11 μm which satisfied the design target, whereas the calculated focal length based on the

Fresnel model design is 3.40 μm, which has a 9.3% deviation to the design target, as shown in

Fig. 3-6b. Considering the effective NA of both GO lenses is around 0.82, which was calculated

as NA = 0.61𝜆

FWHM. We have a conclusion that for high NA GO lenses, the Fresnel design model

is unable to design lenses according to the requirements with high accuracy.

Chapter 3

55

Fig. 3- 6. The intensity distribution of the two designs simulated based on the RS diffraction theory. (a) Intensity distributions in the lateral and axial planes. (b) Cross-sectional intensity

distribution along the black dashed lines in the axial planes. (c) Cross-sectional intensity distribution along the black dashed lines parallel to the x-axis in the lateral planes.

Furthermore, to demonstrate the accuracy and flexibility of the RS model, we designed another

lens (Lens2) with a 9.1 µm focal length. Together with Lens 1, the performance of both lens

was analyzed using the RS and Fresnel diffraction theories and compared with the FDTD

simulation results. The radii of the two lenses designed based on the RS model are listed in

Tab. 3-1.

Tab. 3- 1. Radii of Lens1 and Lens2 Lens1 (μm) Lens2 (μm)

a1 1.543 3.135 a2 2.665 4.670 a3 3.559 5.903

The theoretical results in Fig. 3-7a are the focal intensity distributions of Lens1 in the X-Y and

X-Z planes simulated by the three simulation methods. The polarization effect also has been

considered, the incident light polarization was parallel to the x-direction in the FDTD

simulation. The FWHM results are shown in Fig. 3-7c, for the FDTD results The FWHMs of

the focal spot along the x and y directions is ~0.50 μm (0.79 λ) and ~0.46 μm (0.73 λ),

Chapter 3

56

respectively (Tab. 3-2), which means the polarization effect is negligible; for the RS diffraction

theory; the FWHM of the focal spot is ~0.47 μm (0.74 λ) (Table 2), there is no remarkable

difference (< 6% in the x-direction and 2.1% in the y-direction) between the FDTD and RS

theoretical results. On the other hand, the calculated focal lengths (Fig. 3-7b) based on the

FDTD simulation and the RS theory match well, which are 3.07 μm and 3.11 μm (Tab. 3-2),

respectively. Considering the high effective NA of Lens1 (~0.82) and the good match results,

the scalar RS diffraction theory is able to accurately predict the focusing performance of the

GO lenses.

Fig. 3- 7. Intensity distributions of theoretical and experimental results of Lens1. (a) Intensity distributions in the lateral and axial planes. (b) Intensity distribution along the black dashed lines in the axial planes. (c) Intensity distribution along the black dashed lines parallel to the

x-axis in the lateral planes. Tab. 3- 2. Focal lengths f and FWHMs of the theoretical and experimental results of Lens1

and Lens2 Lens1 Lens2 f (μm) FWHM (μm) f (μm) FWHM (μm)

RS theory 3.11 0.47 9.14 0.54 FDTD (x-direction) 3.07 0.50 - - FDTD (y-direction) 3.07 0.46 - -

Fresnel theory 3.48 0.24 10.28 0.50

Chapter 3

57

However, a significant difference can be identified in the Fresnel theoretical results. First, the

focal spots are much smaller in both the x-y and x-z planes (Fig. 3-7a). Second, the focal length

(Fig. 3-7b) is 3.48 μm (Tab. 3-2), which is significantly different from the target focal length

(3.1 μm). Third, the FWHM (Fig. 3-7c) is only 0.24 μm (0.38 λ) (Tab. 3-2), which shows a

52.1% difference compared with the FDTD simulation result. Therefore, the Fresnel diffraction

theory failed to accurately predict the focusing performance of the GO lenses, which is as

expected.

Fig. 3- 8. Intensity distributions of theoretical and experimental results of Lens2. (a) Intensity distributions in the lateral and axial planes. (b) Intensity distributions along the black dashed lines in the axial planes. (c) Intensity distributions along the black dashed lines in the lateral

planes. For the Lens2 case, as both the focal length and diameter increase, the FDTD requires nearly

20 times of simulation resources and time for the Lens1 simulation. Therefore, only the RS and

Fresnel theoretical simulation have been processed, as shown in Fig. 3-8. It is noticed that

compared with Lens1, the differences of the focal spots in the x-y and x-z planes (Fig. 3-8a)

decrease. The FWHMs (Fig. 3-8c) and focal lengths are listed in Table 2. The FWHMs of the

Chapter 3

58

RS and the Fresnel theoretical calculations are 0.54 μm (0.86λ) and 0.50 µm (0.79λ),

respectively. The difference between the RS theoretical calculation and the Fresnel theoretical

result is 8%, although the difference is still larger, it is much smaller compared with the

previous case. The reason for this is that the effective NA (0.71) of Lens2 is smaller. On the

other hand, the focal length calculated by the Fresnel theory (10.28 µm) is 12.5% different

from the RS theory (9.15 µm). In addition, there is a false focal spot at around 5 μm in the

Fresnel diffraction model. Therefore, under such a circumstance, the Fresnel diffraction theory

still fails to give an accurate description of the performance of the GO lens.

3.5 Chapter summary

In conclusion, we have developed a design method based on the RS diffraction theory. The

new design model is able to design GO lenses with arbitrary focal length, arbitrary NA, and

diameter, in contrast to the Fresnel model, which is limited to low NA lens design. On the other

hand, the new design model is able to unambiguously predict the radii of each ring efficiently

without the optimization process. To prove the accuracy of the newly designed model, the GO

lens with the target focal length has been designed by both methods. The differences in the ring

positions are up to 13.9%. Furthermore, based on the two design data, the focusing

performances have been simulated by the RS diffraction theory. Compared with the desired

focal length, the RS design model shows the ignorable difference, whereas the Fresnel design

model provides a 9.3% difference. In addition, to prove the accuracy of the RS diffraction

theory, the GO lens designed by the new model has been simulated by the FDTD, RS, and

Fresnel diffraction theory. By using the FDTD results as the benchmark, for the transverse

FWHM, the RS diffraction theory shows no remarkable difference (< 6% in the x-direction and

2.1% in the y-direction), in contrast, the Fresnel diffraction theory gives a 52.1% difference.

To prove the flexibility of the new design model, the second GO lens with a longer focal length

has been designed by the new RS model. The focusing performance of the second GO lens has

been simulated by the RS and Fresnel diffraction theory. In this case, the RS diffraction theory

demonstrated its accuracy as expected, in contrast, even the difference of the Fresnel diffraction

theory decrease, it predicts a false focal spot that is far away from the target focal spot.

The new ultrathin flat lens design method can be further applied to design high-performance

flat lenses of arbitrary materials given the NA and focal length requirements, including

metasurfaces or other two-dimensional materials.

59

Chapter 4

Fabrication and characterization of graphene-based ultrathin flat lens

4.1 Introduction

In Chapter 3, we have developed a theoretical model for designing a graphene-based ultrathin

flat lens, the accuracy and simplification of the new model has been demonstrated theoretically.

In this chapter, we will demonstrate lens fabrication and characterization experimentally. The

DLW method reviewed in Chapter 2 has been used to pattern the GO lenses. A homemade

optical system has been used to characterize the focusing quality of the GO lenses. The

experimental results match well with the theoretical predictions. Furthermore, to extend the

practical applications of the graphene-based ultrathin flat lens, we have designed and fabricated

rGO lenses. The design method is similar, of which only the GO zones are changed to the air

zones. And there is a small change in the fabrication, which is that the rGO lens is fabricated

by ablating the rGO films rather than reducing the GO films.

In this chapter, first, the GO lenses designed in Chapter 3 are fabricated. There are two steps

in the fabrication process: GO film fabrication and DLW reduction. The details of the process

are introduced. Then, the rGO lens, which can significantly extend the practical usability of

graphene-based ultrathin flat lenses has been fabricated. There are also two steps of the

fabrication process: rGO film fabrication and DLW ablating. Finally, the focusing quality of

both the GO and rGO lenses is characterized. The experimental results are compared with the

theoretical results. The good matches between them demonstrated the accuracy of our new

ultrathin flat lens design model.

Chapter 4

60

4.2 Fabrication of GO lens

Based on the designed GO lens in Chapter 3, we have fabricated GO lenses by the DLW method.

There are two steps: first, the GO film fabrication. We have two methods to fabricate high-

quality GO films. One is the vacuum filtration method, and the other one is the self-assemble

(SA) method. We choose the proper method based on the experimental requirements; The

second step is to use the DLW pattern to form a GO lens. By controlling the route of the writing

laser, GO lens composed of concentric rings can be fabricated easily.

4.2.1 GO film preparation

Fig. 4- 1. Different thickness GO film measured by AFM. (a) A GO film with ~250 nm

thickness. (b) ~200 nm thickness. (c) 100 nm thickness. (d) 50 nm thickness.

We use the vacuum filtration method to fabricate GO films. The filter we used is a

polyethersulfone membrane with 0.03 μm microspore, and the diameter of it is 47 mm. A GO

suspension had been sonicated for ten minutes before poured into the filtration assembly. By

controlling the GO mass in the suspension, different thicknesses of GO films can be fabricated.

Fig. 4-1 shows the different thickness of GO films on cover glasses measured by an AFM. The

corresponding thicknesses are: (a) ~250 nm; (b) ~200 nm; (c) 100 nm; (d) 50 nm. The vacuum

filtration method is a reasonably quick and simple method to produce films. By controlling the

Chapter 4

61

initial mass of GO in the solution, the thickness of the film can be easily controlled, from a few

micrometres down to several tens of nanometres.

4.2.2 Laser reduction of GO for lens fabrication

Fig. 4- 2. Experimental setup of the laser fabrication system. ES: electronic shutter; BES: beam expanding system; BS1 and BS2: beam splitter; LED: light-emitting diode; Sample:

GO film; OBJ: objective; CCD1 and CCD2: charge-coupled device.

GO reduction is a way to remove oxygen functional groups including hydroxyl, epoxy, and

carboxylic acid groups located on their basal planes and the sheet edges of the GO. With the

removal of oxygen groups [126], three physical properties are changed simultaneously: the

film thickness reduction, the refractive index increase, and the transmission decrease. We use

the DLW method to reduce GO to rGO and pattern the GO lens at the same time. Fig. 4-2 is

the schematic of a laser fabrication system. A low repetition rate femtosecond pulsed laser is

used as the source. The laser pulse is 100 fs, the repetition is 10 kHz, the wavelength is 800

nm. A pair of polarizers are used for the power modulation. An electronic shutter is used to

control the fabrication process. Then, the laser beam is expanded by a lens group. The expanded

laser beam is split by a beam spliter. One beam is collected by a CCD, on which we can check

the quality of the laser beam in a realtime; the other beam is reflected into an objective. The

Chapter 4

62

objective focuses the laser onto the sample, which is the GO film. The reflected beam from the

sample is recollected by the objective and images onto another CCD, of which we can find the

surface of the sample and check the fabrication results. The sample is mounted by a computer-

controlled 3D nanometric piezo stage. Therefore, we can fabricate 3D arbitrary structures,

including the 2D flat lens.

Two GO lenses as described in Chapter 3 have been fabricated. The thickness of the prepared

GO film is 200 nm. Fig. 4-3 shows the AFM images of the two GO lenses. The three rings are

the rGO zones, which are formed by the focused writing laser beam. The thickness difference

between the GO zones and the rGO zones is ~100 nm, as shown in the line profile. This is

because when the GO is reduced to rGO, the thickness decrease to half due to the removal of

the oxygen functional groups. On the other hand, we can find out that the profiles of the rGO

zones are in Gaussian shape. This is caused by the Gaussian shape of the laser focus spot.

Fig. 4- 3. AFM images of the two designed GO lens.

The structure characterizations have proved that the GO lenses we designed have been

fabricated precisely by the DLW method. The next step is to characterize the focusing quality

of the GO lenses and compare them to the previous three theoretical predictions presented in

Chapter 3.

4.2.3 Focusing characterization

Focal spot characterization is one of the most important indicators to evaluate the quality of a

lens. We have set up a system to characterize the focal spot of the graphene-based ultrathin flat

lens. A CCD was used to capture the cross-section of the focal area along the vertical direction

to the lens plane. A Matlab program was used to reconstruct the focal spot of the graphene-

based ultrathin flat lens. The focal spot characterization system is shown in Fig. 4-4. A laser

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source with 633 nm wavelength is used as the incident beam. The beam is expanded to obtain

an approximate plane wave. Then the expanded beam is focused by the graphene-based lens.

An objective with NA equal to 0.8 is used to collect the focused optical field of the lens into a

CCD camera. The objective is mounted by a one dimensional piezo stage which can scan along

the optical axis. Therefore, the cross-section of the focal spot along the optical axis can be

recorded.

Fig. 4- 4. Schematic of the GO lens characterization system. BES: beam expanding system;

OBJ: objective.

The experimentally measured focal intensity distributions of Lens1 in the x-y and x-z planes

and the corresponding theoretical results from the FDTD, RS and Fresnel theoretical

calculations are shown in Fig. 4-5a. It is clear that the theoretical results from the FDTD and

RS methods match reasonably well with the experimental results. On the contrary, the Fresnel

diffraction theory offered a very small focal spot, which is obvious different from the

experimental results. For the detailed comparison, the intensity distribution along the x and z

directions (marked by the black dashed lines in Fig. 4-5a of all results are plotted in Fig. 4-5b

and c, respectively. In Fig. 4-5b, the resulted focal lengths of the experimental measurement,

the FDTD simulation, the RS theoretical results are 3.09 µm, 3.07 μm and 3.11 μm,

respectively. However, the Fresnel theoretical result is 3.48 μm, which is 12.6% different from

the experimental measurement; In Fig. 4-5c, the FWHM of the focal spot along the x and y

directions of the FDTD results are ~0.50 μm (0.79 λ) and ~0.46 μm (0.73 λ), respectively, the

FWHM of the focal spot predicted by the RS diffraction theory is ~0.47 μm (0.74 λ). They

match well with the experimental result, which is 0.51 μm (0.81 λ). However, the FWHM

prediction using the Fresnel diffraction model is only 0.24 μm (0.38 λ), which shows 52.9%

difference from the experimental result. Based on this result, we can conclude that the RS

diffraction theory can predict the focusing process accurately for a high NA lens, in contrast to

the Fresnel diffraction theory, which shows a non-negligible description.

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Fig. 4- 5. Intensity distributions of theoretical and experimental results of Lens1. (a) Intensity distributions in the lateral and axial planes. (b) Intensity distribution along the black dashed lines in the axial planes. (c) Intensity distribution along the black dashed lines parallel to the

x-axis in the lateral planes.

For the Lens2, The results from the experiment, RS and Fresnel theoretical calculations are

shown in Fig. 4-6. It is noticed that the experimental results and the simulation using the RS

diffraction theory again match well. While the focal length calculated by the Fresnel diffraction

theory is significantly different from the others. The FWHMs of the experimental result, the

RS and the Fresnel theoretical calculations are 0.56 μm (0.89λ), 0.54 μm (0.86λ) and 0.50 µm

(0.79λ), respectively. The difference between the experimental result and the RS theoretical

calculation is 3.7%, confirming the high accuracy of the RS diffraction theory as expected.

Meanwhile, the difference between the experimental result and the Fresnel theoretical result is

11.4%. Although the difference for the Fresnel result is still larger than the RS result, it is much

smaller compared with the previous case. The reason is that the effective NA of Lens2 is

smaller (0.71). Whereas, the focal length calculated by the Fresnel theory (10.28 µm) is much

larger than the experimental results (9.14 µm) and that from the RS theory (9.15 µm). In

addition, there is a false focal spot at around 5 μm in the Fresnel diffraction model, which is

not observed in the experiment. Therefore, under such a circumstance, the Fresnel diffraction

theory still fails to give an accurate description of the performance of the GO lens.

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Fig. 4- 6. Intensity distributions of theoretical and experimental results of Lens2. (a) Intensity distributions in the lateral and axial planes. (b) Intensity distributions along the black dashed lines in the axial planes. (c) Intensity distributions along the black dashed lines in the lateral

planes.

Therefore, we have demonstrated that: the design method based on the RS diffraction theory is

able to accurately design GO lenses with arbitrary focal length and diameter without the

optimization process.

The GO lenses fabricated by the DLW method open up new avenues for easily accessible,

highly precise and efficient optical beam manipulations. However, the fact that the GO film

can be easily reduced leads to stability concern for the practical applications of GO lenses.

Because of its high chemical activity and instability, it can be partly reduced to reduced

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graphene oxide (rGO) by many methods [69], even by natural light or heating of less than 200 ℃

[127]. Therefore, solutions need to be developed to mitigate this instability challenge.

4.3 Fabrication of rGO lens

Without protection, the GO films become dark after a few months in the laboratory, which

implies the instability of this GO films even in the ambient environment without considering

the harsh and/or extreme environments, such as aerospace, chemical, and biological

environments. Therefore, the practicability of GO lenses in outdoor environments needs

improvement. On the other hand, GO is highly hydrophilic [57], it readily exfoliates as single

sheets in water, which limits the applied range of GO lens in water, even in the humid

environments, not to say strong acid/alkaline conditions. Additionally, researches have been

reported that as-prepared GO can be dispersed in organic solvents, such as N, N-

dimethylformamide, tetrahydrofuran and ethylene glycol [128-130]. This may limit the

applications of GO devices in biological fields. These limitations need to be properly addressed

before any practical applications of the GO lens can be considered. Therefore, to extend the

practicability of the graphene-based ultrathin lens, we have designed and fabricated a reduce

graphene-based ultrathin flat lens, which is composed of only rGO. Considering the

extraordinary thermal, hydrophobic and other stable chemical properties of rGO [131-135], the

rGO lens is potentially resilient in harsh and/ or extreme environments, such as aerospace,

chemical, and biological environments.

There are two steps for the rGO lens fabrication: rGO film fabrication, and rGO lens fabrication

by ablating regions of the rGO films.

4.3.1 rGO film fabrication

UV light exposure method has been used as a simple and large-scale way to fabricate an rGO

film. According to the experimental experience, the thickness of the GO film decreases to 75%

of the original thickness after the UV light exposure. Therefore, to obtain a 150 nm rGO film,

we transferred a 200 nm GO film on to a glass substrate. Then the GO film was exposed under

the UV light for more than three hours. The UV light reduction setup is shown in Fig. 4-7a.

The UV lamp is Olympus U-UlS100HG, USH-102D, 100 W, 200-600 nm wavelength. Fig. 4-

7b is the rGO film sample on a glass slide. It is obvious that the rGO film is darker than the

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GO film with similar thickness. Fig. 4-7c shows the rGO film with a thickness of ~150 nm.

The insert is the rGO film measured by an AFM.

Fig. 4- 7. rGO film fabrication. (a) The UV light reduction setup for reducing GO to rGO. (b)

The rGO film sample. (c) The thickness measurement of the rGO film by AFM.

4.3.2 Ablating rGO film to fabricate a rGO lens

The design method of an rGO lens is similar to the GO lens design. Here we only use rGO-air

zones to replace GO-rGO zones. We have designed an rGO lens with a focal length of 30 μm.

It has ten rings, the width of the rGO rings is ~ 600 nm, and the radii of the rings are list in Tab.

4-1. The rGO lens fabrication mechanism is that we ablate the rGO films to form air zones by

high power laser. Then an rGO lens is constructed. Therefore, the fabrication of the air zones

is the key point of rGO lens fabrication. In our design, considering that the cross-sections of

the laser fabricated lines are in Gaussian shape, we set the waist radius of the rGO zone to be

around 600 nm. Therefore, to obtain a proper rGO zone, we fabricated a series of lines on an

rGO film with different laser power for the first step. The thickness of the rGO film we used

was ~150 nm, it was prepared by reducing a GO film which was fabricated by the filtration

method. Fig. 4-8a shows an rGO film sample with laser fabricated lines measured by an optical

microscope. Fig. 4-8b and c are parts of the line samples measured by an AFM, the

corresponding laser power is 30 and 60 μw, respectively. The profiles along the white dashed

lines provide us the thickness and linewidths of the laser fabricated lines.

Tab. 4- 1. Radii of the rGO lens rings designed with 30-μm-focal length, unit: μm. a1 a2 a3 a4 a5 a6 a7 a8 a9 a10

4.45 7.71 9.96 11.82 13.45 14.93 16.30 17.59 18.81 19.98

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Fig. 4- 8. Laser fabricated lines in rGO film. (a) Under microscopy. (b) AFM image of rGO lines fabricated with a laser power of 30 μw. (c) AFM image of rGO lines fabricated with a

laser power of 60 μw.

We used an objective with an NA equal to 0.85 to focus the writing laser. By changing the laser

power, we have obtained the relationship between the linewidths and the laser writing power,

as shown in Fig. 4-9a. At the same time, we also studied the same relationship when the rGO

is prepared based on a GO film fabricated by the SA method, as shown in Fig. 4-9b. There was

a quite interesting phenomenon, for the rGO film fabricated with filtrated GO film, the

linewidth increases as the laser power increases within a certain range, however, for the rGO

film fabricated with the SA GO film, the linewidth is nearly unchanged with a certain range of

the laser power. On the other hand, we noticed that the largest linewidth of the first rGO film

is larger than the second rGO film even its laser writing power is smaller than the latter. The

potential reason is that the added PDDA decreases the thermal conductivity of the second rGO

film, which plays an important way during the reduction process of the GO film. The linewidth

unchanged character of the second rGO film provides the possibility to fabricate a graphene-

based lens conveniently and with high precision.

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Fig. 4- 9. Relationship between linewidths and laser writing power. (a) For the rGO prepared base on a GO film fabricated by the filtration method. (b) For the rGO prepared base on a GO

film fabricated by the SA method.

Considering the smallest interval between the rings, which is ~1.17 μm (between ring a9 and

a10), we chose the laser writing power at 55 μw. After ablating the unwanted rGO film, we

fabricated the designed rGO lens. Fig. 4-10a shows the rGO lens under the transmission optical

microscope (50×). The black rings are rGO, which can be distinguished clearly. Fig. 4-9b is

the topographic profile of the rGO lens measured by a 3D optical profiler. One can see the

approximate Gaussian profile of each rGO ring in the bottom cross-sectional profile in Figure

4-9(b), which is attributed to the Gaussian-shaped focal spot of the writing laser.

Fig. 4- 10. rGO ultrathin flat lens. (a) Transmission optical microscopic image of an rGO lens. (b) Topographic profile of the rGO ultrathin flat lens measured by an optical profiler

and the cross-sectional profile marked by the white dashed line in (b).

4.3.3 Focusing characterization

Same as the experimental method in Section 4.2.3, we have characterized the focal quality of

the rGO lens. The focusing intensity distributions are shown in Fig. 4-10. To decrease the

calculation time of the RS model, we only calculate the intensity on the axes, which decreases

the calculation time to seconds. In Fig. 4-10a and b, a pretty good focal spot has been obtained

experimentally. In Fig. 4-10c, the designed focal length, which is 30 μm, has been realized,

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and the experimental and theoretical results match well. In Fig. 4-10d, the FWHM of the

theoretical and experimental results is ~0.52 and 0.56±0.07 (0.88λ) μm, respectively. The

difference between them is ~7%, considering the resolution of the CCD, the experimental result

proves the accuracy of the theoretical model. Therefore, both the accuracy and flexibility of

our design model and theoretical simulation have been demonstrated by the experimental

measurements of the rGO lens.

Fig. 4- 11. Intensity distributions in the focal area. (a) Intensity distribution in the y-z plane of

the experimental results. (b) Intensity distribution in the x-y plane of the experimental results. (c) Intensity distributions along the black dashed lines in the axial planes. (c) Intensity

distributions along the black dashed lines in the lateral planes.

4.4 Chapter summary

By taking full advantage of the DLW method, we have fabricated both the GO and GO/air lens.

The structure characterizations by AFM and 3D optical profiler verified the high resolution and

fabrication of these lenses. Based on the simple and efficient DLW method, we can also

fabricate large-scale ultrathin flat lens with high resolution for imaging, which can extremely

enlarge the application range of our graphene-based ultrathin flat lens.

The focal qualities of both the GO and rGO lenses have been characterized by a homemade

optical system. The design flexibility of the RS method has been demonstrated by both GO and

rGO lenses with desired focal lengths and NAs. The accuracy of our design methods has been

verified both experimentally and by the FDTD simulation. The theoretical and experimental

results show that the RS diffraction theory is able to accurately calculate the focusing process

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of GO lenses with arbitrary NA and focal lengths with a high speed and efficiency. Therefore,

the demonstrated RS method is expected to find broad applications in designing and analyzing

other ultrathin flat lenses, including metasurface lenses and lenses made of other 2D materials.

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Chapter 5

Harsh environment tests of the rGO lens

5.1 Introduction

Ultrathin flat lenses provide [19, 21, 50, 136, 137] revolutionary solutions for lenses. And they

offer compact designs for myriads of nanophotonics and integrated photonic systems. Due to

the thin structure, ultra-lightweight, high focusing performance and the capability of achieving

chromatic aberration compensation [138] in a broad spectral range [138-143], it has a great

potential to replace conventional bulky lenses in many applications for different conditions,

such as aerospace, chemical, and biological surroundings. Therefore, one or a few

environmental factors such as extremely high/low temperatures, bio-chemicals, corrosive

chemicals, strong UV radiation, plasma radiation, AO, or high vacuum have to be considered

when using an ultrathin flat lens. The ultrathin flat lenses should survive and maintain their

outstanding performance under those harsh conditions with low maintenance. Constructing

materials are one of the most important basements for the ultrathin flat lens to preserve their

structural and performance stability. However, most ultrathin flat lenses, including metalens

[19], super-oscillatory lens [144] and plasmonic lens [145, 146] are made of metal or

semiconductor materials that are unstable in these harsh environments. Therefore, the

applications of these ultrathin flat lenses in harsh environments may be limited.

Based on the extraordinary thermal and chemical stabilities of rGO [82, 131-135, 147, 148],

the rGO lens is potentially resilient in various harsh environments, such as strong acid/alkaline

solutions, extremely high/low temperature, strong UV radiation, plasma radiation, AO and high

vacuum.

In this chapter, we discuss the performance of the rGO lenses in LEO, strong acid and alkaline,

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and biochemical conditions. The conceptual drawings of these applications are shown in Fig.

5-1.

Fig. 5- 1. Applications of rGO flat lenses in different environmental scenarios. (a) Imaging

optical element for a satellite in aerospace. (b) Observing strong acid/alkaline chemical reactions. (c) Biophotonic microfluidic devices.

First, the LEO space environment has been simulated in the lab, 200 ℃ heating, liquid nitrogen

(-196 ℃), vacuum and atomic oxygen radiation have been carried out onto the rGO lenses.

Then, the strong corrosive condition has been simulated. H2SO4 solution with PH=0 and KOH

solution with PH=14 were used to test the acid-base resistance [149-151] of the rGO lenses.

Finally, phosphate-buffered saline (PBS) [152-154] was used to imitate the physiological

condition. After each test, both the surface morphology and the focusing performance was

studied. We use focal intensity distributions as a benchmark to identify the tiny change of the

rGO lenses and verify the harsh environment stability with high accuracy.

5.2 Low Earth orbit environment test

Ultrathin and ultra-lightweight rGO lenses are expected to replace the current bulky lens system.

In this way, the overall weight of the satellite can be significantly reduced, which largely saves

the launching cost of the satellite. In the aerospace application as shown in Fig. 5-1a, the rGO

lens is potential exposed to extreme heat and cold cycles, strong UV radiation, ultra-high

vacuum, AO, and high energy radiation [155-157]. Testing and characterization of the rGO

lenses exposed to these extreme conditions can provide data to enable the manufacturing of

long-life reliable rGO lenses used on Earth as well as in the sophisticated satellite and

spacecraft components. According to the NASA standard [158], we have tested and

characterized the rGO lenses under UV radiation, extreme heat and cold cycles, ultra-high

vacuum and AO radiation, respectively. The results show that the rGO lens can maintain intact

under all LEO conditions except for the long-term AO radiation.

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5.2.1 Ultraviolet radiation

To simulate the strong UV radiation environment, a UV light has been used as the UV radiation

source. The type of UV light is Olympus U-UlS100HG, USH-102D, 100 W, 200-600 nm

wavelength. The schematic of the UV radiation experiment setup can be referred to in Fig. 4-

7a, the UV light is focused by a lens to increase the energy density, and the sample is located

in the focus of the lens. We fabricated a few rGO lenses by a laser ablation method, which has

been discussed in Chapter 4. Before the UV radiation experiment, we have characterized the

focal spots of these rGO lenses. Then, the rGO lenses were exposed to the focused UV light

for 24 hours. Fig. 5-2 shows the comparisons of experimental results between the original and

UV radiated rGO lenses. Fig. 5-2a is the microscopic image of the rGO lenses, there is no

obvious damage on the rGO lenses after UV radiation treating. Figs. 5-2b and c are the intensity

distributions on the lateral and axial planes of the focal spots. We can see the rGO lenses

preserve their good focal qualities. More exact comparisons are shown in Figs. 5-2d and e, Fig.

5-2d gives the intensity distributions along the black dashed line in Fig. 5-2b. The FWHM of

the original and UV radiated rGO lens is 0.56±0.07 and 0.57±0.07 μm, respectively.

Considering the experimental error, there is no degradation after 24 hours of UV radiation. Fig.

5-2e gives the intensity distributions along the black dashed line in Fig. 5-2c, there is almost

no change of the focal length (which is 30 μm), and even the detailed intensity distribution

matches well. Therefore, we conclude that the rGO lenses maintain their focusing

performances after 24 hours of UV radiation.

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Fig. 5- 2. UV radiation test of rGO lenses. (a) rGO lenses under microscopy before and after 24 hours of UV radiation. (b) Intensity distributions on the lateral plane of the focal spots. (c) Intensity distributions on the axial plane of the focal spots. (d) Intensity distributions along the black dashed lines in the axial planes. (e) Intensity distributions along the black dashed

lines in the lateral planes.

5.2.2 Extreme heat and cold

Extreme heat and cold cycle is another feature of the LEO environment, as out and in of

sunlight, the degree a material experiences in LEO variates from -120 ̊ C to +120 ̊ C [158, 159].

To simulate this situation, liquid nitrogen has been used to obtain an extremely cold condition,

which is ~-196 ˚C [160]. And a vacuum oven has been used to obtain high-heat condition. The

rGO lens sample we used is the same sample used in the UV radiation experiment. The sample

was immersed in the liquid nitrogen for 1 hour, as shown in Fig. 5-3a, during the experiment,

we add liquid nitrogen every 10 minutes to ensure that the sample is fully immersed in the

liquid nitrogen. After the extreme cold test, we measured the focusing performances of the rGO

lenses. Then, the extreme heat experiment was carried on with the same sample. An oven, as

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shown in Fig. 5-3b has been used to provide the high-temperature condition. The rGO lenses

were baked for 24 hours at 200 °C in the vacuum oven. After the extreme heat test, we measured

the focusing performances of the rGO lenses. The results are shown in Fig. 5-4. In Fig. 5-4a,

microscopic images of the rGO lenses from the original and after extreme temperature tests are

exhibited. No obvious physical damage can be found. In Fig. 5-4b and c, intensity distributions

on the lateral and axial planes of the focal spots are compared among the original, extreme cold

and heat tested rGO lenses. We can see the rGO lenses maintain their good focal qualities after

both extreme cold and heat tests. More exact comparisons are shown in Figs. 5-4d and e, Fig.

5-4d gives the intensity distributions along the black dashed lines in Fig. 5-4b. The FWHM of

the focal spot from the original, extreme cold and heat tortured rGO lens is 0.56±0.07,

0.56±0.07 and 0.55±0.07 μm, respectively. Considering the experimental error, there is almost

no change after 1 hour of -196 ˚C and 24 hours of 200 ˚C treatments. Fig. 5-4e gives the

intensity distributions along the black dashed lines in Fig. 5-4c, the focal length change is

between 30 to 30.1 μm with ±0.1 μm experimental error, and the difference among the detailed

intensity distribution is negligible. Therefore, we can conclude that the extreme cold and heat

has an ignorable impact on the focusing quality of the rGO lenses.

Fig. 5- 3. Extreme cold and heat experiments. (a) rGO lenses immersed in liquid nitrogen. (b)

The vacuum oven for extreme heat experiment.

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Fig. 5- 4. The Extreme cold and heat tests of rGO lenses. (a) rGO lenses under microscopy

before and after experiments. (b) Intensity distributions on the lateral plane of the focal spots. (c) Intensity distributions on the axial plane of the focal spots. (d) Intensity distributions along the black dashed lines in the axial planes. (e) Intensity distributions along the black

dashed lines in the lateral planes.

5.2.3 Ultra-high vacuum

Ultra-high vacuum is another feature of the LEO environment. The pressure in LEO space is

around 10-3~10-6 Pa [156, 158], which will cause outgassing. The volatile release from

materials leads to structure distortion, surface contamination, and material properties change,

which will affect the functions of the applications. Therefore, research about the ultra-high

vacuum effect on rGO lens must be studied. According to the NASA standard [158], the sample

should be thermal vacuum baked for 24 hours at 100 ˚C. As shown in Fig. 5-5, A C-PVO-25

precise digital vacuum drying oven from LABEC has been used to provide the experimental

situation. The pressure is 0.01 Pa, the temperature is 100 ˚C, the same rGO lens sample used

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in the previous experiments has been baked in this condition for 24 hours. After the experiment,

we measured the focusing performances of the rGO lenses, the whole results are shown in Fig.

5-6. In Fig. 5-6a, microscopic images of the rGO lenses of the original and after ultra-high

vacuum tests are exhibited. There is no obvious physical damage on the rGO lens surface. In

Figs. 5-6b and c, intensity distributions on the lateral and axial planes of the focal spots are

compared between the original and ultra-high vacuum tested rGO lenses. We can find the rGO

lenses preserve their good focal qualities after 24 hours ultra-high vacuum test. More exact

comparisons are shown in Figs. 5-6d and e, Figs. 5-6d gives the intensity distributions along

the black dashed lines in Fig. 5-6b. The FWHM of the focal spot from the original and ultra-

high vacuum treated rGO lens is 0.56±0.07 and 0.57±0.07 μm, respectively. Considering the

experimental error, there is almost no change after 24 hours test of the ultra-high vacuum. Fig.

5-6e gives the intensity distributions along the black dashed lines in Fig. 5-6c, both focal length

change is 30 μm with ±0.1 μm experimental error, and the difference among the detailed

intensity distribution is negligible. Therefore, we can conclude that the rGO lenses maintain

their high-quality focal performance after the ultra-high vacuum test.

Fig. 5- 5. The digital vacuum drying oven in the experiment.

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Fig. 5- 6. The ultra-high vacuum tests of rGO lenses. (a) rGO lenses under microscopy before

and after experiments. (b) Intensity distributions on the lateral plane of the focal spots. (c) Intensity distributions on the axial plane of the focal spots. (d) Intensity distributions along the black dashed lines in the axial planes. (e) Intensity distributions along the black dashed

lines in the lateral planes.

5.2.4 Atomic oxygen radiation

AO is one of the most hazardous component in LEO for most carbon-based materials [156]. It

will lead to the degradation of materials, in turn, result in the defunctionalization of the

applications work in LEO. The AO particles are produced when the molecular oxygen is

reacted with UV radiation in the LEO environment. The density of AO is approximately

2~8×109 atom/cm3 at about 300 km altitude [161], On the other hand, because of the orbital

velocity, which is ~8 km/s, the kinetic energy of AO particle is approximate 5.2 eV. Therefore,

we can calculate the flux range of AO [162], which is approximately from 1014 to 1015

atoms/cm2s. As shown in Fig. 5-7a, a Samco RIE-101iPH has been used to generate oxygen

plasma to simulate the AO radiation. Fig. 5-7b is the schematic of the AO radiation process on

the rGO lenses, the AO particles pump onto the rGO lenses with proper velocity.

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Fig. 5- 7. rGO lens treated by AO radiation. (a) The reactive ion etching equipment (b) Scheme of AO radiation. (c) Thickness changes with the increase of AO radiation time.

In the experiment, the pressure in the plasma chamber was 0.37 Pa, the gas composition ratio

of oxygen to argon (O2: Ar) was 2:8; the power of radio-frequency plasma source was 200 W

to obtain the ~9.77×1013 atom/cm3; the bias power was 30 W to give AO particles 5.2 eV

kinetic energy. Five independent samples have been used in this experiment include the first

sample used in the former experiments. They were used for 5, 15, 30, 45 and 60 s AO radiation,

separately. According to the ratio of the density being simulated, 1 second in the experiment

corresponds to 5.5 hours in the LEO condition. The rGO lens was completely removed from

the substrate and lost focusing function after 60 s, which means the lifetime of the rGO lens

under the AO condition is about 13 days in the LEO condition. Considering the potential

damage on the rGO lenses from AO radiation. Actually, these experiments were carried out at

the last, also after the following strong corrosive and biochemical environment experiments.

During each experiment, we measured the thicknesses of the samples by an AFM and measured

the optical focusing performance of these rGO lenses. Fig. 5-7c shows the thickness changes

with different AO radiation time. The thickness of the rGO lenses decreases as the AO

treatment time increases. The fit line is a second-order polynomial, which means the thickness-

decrease rate increases with AO treatment time prolongs. On the other hand, the etching of

rGO lenses is quite uniform, which offers the potential of the rGO lenses to maintain the focal

spots before all the rGO layers were removed. In Fig. 5-8a, microscopic images of the original

and after AO radiated rGO lenses are exhibited, we can find out that the etching of rGO lenses

is very uniform that no obvious physical damage on the rGO lens surface can be found even

the thicknesses of them change. In Fig. 5-8b and c, intensity distributions on the lateral and

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axial planes of the focal spots are compared between the original and the AO radiated rGO

lenses. We can find the rGO lenses maintain their good focal qualities before they are

completely etched off by the AO radiation. More exactly comparisons are shown in Fig. 5-8d

and e. Fig. 5-8d gives the intensity distributions along the black dashed lines in Fig. 5-8b. The

FWHMs of the focal spots from the original and different time AO radiation treated rGO lenses

are 0.56, 0.54, 0.52, 0.54 and 0.51 μm, respectively, with 0.07 μm experimental error. The last

four FWHMs correspondings to the 5, 15, 30 and 45 s AO radiation. Therefore, in the lateral

plane of the focal spot, there is no obvious change after different times of AO radiation. Fig.

5-8e gives the intensity distributions along the black dashed lines in Fig. 5-8c, the focal length

change from 30 to 30.2 μm with ±0.1 μm experimental error, and the differences among the

detailed intensity distributions are negligible. Therefore, the rGO lenses maintain their focusing

performance in the axial plane. In conclusion, the rGO lenses maintain their focal qualities

before totally etched off by the AO radiation. However, to achieve a longer lifetime of the rGO

lens, one simple potential solution is to increase the thickness of the rGO lens. But for long

period aerospace applications, it is better to cover the rGO lenses to protect especially from the

AO condition or simply to replace the worn-out rGO lenses with new ones due to its low cost.

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Fig. 5- 8. The AO radiation experiment of rGO lenses. (a) rGO lenses under microscopy

before and after experiments. (b) Intensity distributions on the lateral plane of the focal spots. (c) Intensity distributions on the axial plane of the focal spots. (d) Intensity distributions along the black dashed lines in the axial planes. (e) Intensity distributions along the black

dashed lines in the lateral planes.

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5.3 Strong corrosive environment

Benefit by the ultrathin nature of the rGO lens, it is potential to integrate the rGO lenses with

chemical containers. These applications can be used to in-situ observe the localized chemical

reaction or acquire spectral information of a limited amount of chemicals. However, most of

the chemical reactions involve strong acid/alkaline solution, as shown in Fig. 5-1b. And the

observing process may last for a long period of time. Therefore, it is important to understand

the performance stability of the rGO lens under such circumstances for a relatively long period

of time. Fig. 5-9 is the schematic of the strong acid/alkaline tolerance test. A PH test paper is

used to measure the PH value of the acid/alkaline solution. The rGO lenses are immersed in

the solution. In this section, we have measured the focusing performance of our rGO lenses

after the strong acid/alkaline treatments. The final results demonstrate the stability of the rGO

lenses under strong corrosive environments.

Fig. 5- 9. Scheme of strong acid/alkaline tolerance tests.

5.3.1 Strong acid condition

In this strong acid tolerance test, we used the same sample of rGO lens, which was used in the

previous experiments. The strong acid solution is prepared by adding 2.7 ml concentrated

sulphuric acid (98%) into 1 L pure water. As shown in Fig. 5-10, the PH value of the acid

solution is 0. The sample has been immersed in the acid solution for 7 days at the room

temperature. After the acid tolerance test, we characterized the rGO lens, the results are shown

in Fig. 5-11. Fig. 5-11a is the microscopic image of the rGO lenses, there is no obvious damage

on the rGO lenses after the acid solution experiment. Figs. 5-11b and c are the intensity

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84

distributions on the lateral and axial planes of the focal spots. The high-quality focus of the

rGO lens remains. More exactly comparisons are shown in Figs. 5-11d and e, Fig. 5-11d gives

the intensity distributions along the black dashed lines in Fig. 5-11b. The FWHM of the original

and after acid tortured rGO lens is 0.56±0.07 and 0.59±0.07 μm, respectively. Considering the

experimental error, there is almost no degradation after immersed in the sulphuric acid solution

for 7 days. Fig. 5-11e gives the intensity distributions along the black dashed lines in Fig. 5-3c,

there is no change of the focal length, which is 30 μm, and even the detailed intensity

distribution matches well. Therefore, we conclude that the focusing performance of the rGO

lenses is stable after 7 days of strong acid torture.

Fig. 5- 10. rGO lenses in acid solution (PH=0).

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85

Fig. 5- 11. The strong acid tolerance test of rGO lenses. (a) rGO lenses under a microscope.

(b) Intensity distributions on the lateral plane of the focal spots. (c) Intensity distributions on the axial plane of the focal spots. (d) Intensity distributions along the black dashed lines in the axial planes. (e) Intensity distributions along the black dashed lines in the lateral planes.

5.3.2 Strong alkaline condition

Fig. 5- 12. rGO lenses in acid solution (PH=0).

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86

Fig. 5- 13. The strong alkaline tolerance test of rGO lenses. (a) rGO lenses under a

microscope. (b) Intensity distributions on the lateral plane of the focal spots. (c) Intensity distributions on the axial plane of the focal spots. (d) Intensity distributions along the black

dashed lines in the axial planes. (e) Intensity distributions along the black dashed lines in the lateral planes.

The strong alkaline solution is prepared by dissolving 5.6 g potassium hydroxide in 1 L pure

water. As shown in Fig. 5-12, the PH value of the acid solution is 14. We used the same rGO

lens sample in this strong alkaline tolerance test. The sample has been immersed in the alkaline

solution for 7 days at the room temperature. After the alkaline tolerance test, we characterized

the rGO lens, the results are shown in Fig. 5-13. Fig. 5-13a is the microscopic image of the

rGO lenses, there is no obvious damage on the rGO lenses after the alkaline tolerance test. Figs.

5-13b and c are the intensity distributions on the lateral and axial planes of the focal spots.

From the figures, we can say the high-quality focus of the rGO lens remains. More exactly

comparisons are shown in Figs. 5-13d and e, Fig. 5-13d gives the intensity distributions along

the black dashed lines in Fig. 5-13b. The FWHM of the original and after alkaline tortured rGO

lens is 0.56±0.07 and 0.60±0.07 μm, respectively. Considering the experimental error, there is

almost no degradation of the focal performance after immersed in a potassium hydroxide

solution for 7 days. Fig. 5-13e gives the intensity distributions along the black dashed lines in

Fig. 5-13c, there is no observable change of the focal length, which is 30 μm, and even the

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87

detailed intensity distribution matches well. Therefore, we conclude that the focusing

performance of the rGO lenses is stable after 7 days of strong alkaline torture.

5.4 Biochemical environment

Fig. 5- 14. rGO lens in PBS solution.

Biochemical research is another field that the rGO lens can be applied. The ultrathin rGO flat

lenses can be integrated into microfluidic devices as biophotonic applications to observe

samples such as cells, as illustrated in Figure 5-1(c). To imitate the biological environment of

the human body, one commonly used solution is the PBS [152-154], which is a water-based

salt solution containing disodium hydrogen phosphate, sodium chloride and, in some

formulations, potassium chloride, and potassium dihydrogen phosphate. The buffer helps to

maintain a constant PH (PH=7.5±0.1). The PBS solution we used is P5368-10PAK from Sigma

Aldrich. The experimental exhibition is shown in Fig. 5-14, the PH value is 7.5. During the

experiment, the same rGO lens sample was immersed in the PBS solution for 24 hours at 37

˚C. After the experiment, we characterized the rGO lens, the results are shown in Fig. 5-15.

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88

Fig. 5- 15. The biological workable test of rGO lenses. (a) rGO lens under a microscope. (b) rGO lens measured by the 3D optical profiler. (c) Intensity distributions on the lateral plane

of the focal spots. (d) Intensity distributions on the axial plane of the focal spots. (e) Intensity distributions along the black dashed lines in the axial planes. (f) Intensity distributions along

the black dashed lines in the lateral planes.

Fig. 5-15a is the image of the rGO lens under a microscope. There is no obvious damage on

the surface of the rGO lens. Furthermore, we used the 3D profiler to measure the surface profile

of the rGO lenses. Fig. 5-15b is one of the surface profiles, the detailed profile along the white

dashed line is plotted in the inset. It proves that after all these harsh environment tests except

the AO radiation, the physical structures of the rGO lenses show no degradation. Figs. 5-15c

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89

and d are the intensity distributions on the lateral and axial planes of the focal spots. From the

figures, we can say the high-quality focus of the rGO lens remains. More exactly comparisons

are shown in Figs. 5-15e and f, Fig. 5-15e gives the intensity distributions along the black

dashed lines in Fig. 5-15c. The FWHM of the original and biochemical tested rGO lens is

0.56±0.07 and 0.54±0.07 μm, respectively. Fig. 5-15f gives the intensity distributions along

the black dashed lines in Fig. 5-15d. The focal length changes from 30 to 30.1 μm with 0.1 μm

experimental error, and the detailed intensity distributions along the z-axis match well.

Therefore, considering the experimental error, there is no degradation of the focal performance

after immersed in PBS solution for 24 hours at 37 ˚C, which means the rGO lens is workable

for the biological field.

5.5 Chapter summary

In this chapter, we test the performance stability of the rGO lens in different working

environments, such as LEO, strong corrosive chemical and biochemical environments. For

these environments, we test the UV radiation, extreme heat and cold cycle, ultra-high vacuum

and AO radiation, which corresponding to the characteristics of the LEO environment. And we

test the strong acid/alkaline corrosion, which responding to the strong corrosive chemical

environments. Finally, we imitate the biological environment to test the performance stability

of the rGO lens. We use both the physical structure and focal intensity distributions as

benchmarks to identify the tiny change of the rGO lenses and verify the harsh environment

stability of the rGO lens. Our results show that there is no obvious deterioration in the surface

morphology of the rGO lenses, and the extraordinary focusing performances of them are almost

unaffected in almost all of these circumstances except for the long-term AO radiation direct

exposure. Nevertheless, with proper protection against AO radiation, the rGO lens can be safely

applied in the aerospace environment.

The graphene lenses have extraordinary environmental stability and can maintain high-level

structural integrity and outstanding focusing performance under different test conditions. Thus

it opens tremendous practical application opportunities for ultrathin flat lenses. Therefore, we

have demonstrated a resilient ultrathin flat lens that can be readily applied in multiple harsh

environments, in particular where harsh environments and low maintenance are required for

example strong corrosive chemical condition or biochemical condition without any protection.

90

Chapter 6

Fibre endoscope with Graphene-based lens

6.1 Introduction

Fibre endoscope is an efficient and robust tool that is widely used in various kinds of fields,

such as the industrial, military, especially the medical field. Due to the mechanical flexibility

and compact size of optical fibres, endoscopes are able to in-site image areas with minimal

invasion, which are hard to reach for a conventional optical microscope. The employment of

endoscopes in all kinds of fields help to save costs and increase efficiency dramatically.

However, with the development of human life and scientific researches, endoscopes are unable

to satisfy the new requirements gradually. First, the size of the commercial endoscope is too

large, which limits its application scenarios tremendously, especially with the development of

integration and miniaturization in modern society. Second, the resolution of the existing

endoscope is too low, about a few micrometres, which is far below the high-resolution

requirements in practical applications. Third, the imaging speed is low, which limits the real-

time imaging capability. Researchers have proposed and developed a variety of methods to

solve these challenges. But each of them has its own disadvantages. For examples, the lens

group fabricated on the fibre tip [109] as presented in Chapter 2, it increases the resolution of

the endoscope, but it also increases the fabrication difficulty and the complexity of an

endoscope; The image reconstruction [163-165] method can realize the miniaturization of the

endoscopy, but it is limited in resolution.

A new endoscope, which is of high resolution, miniaturization, easy fabrication is eagerly to

be designed and developed. Graphene-based lenses have a number of advantages, such as high

resolution, broadband, ultra-lightweight, nanometre thickness, and easy fabrication, and high

potential for integration with optical components to change or optimize their functionalities,

Chapter 6

91

such as conventional optical lenses, fibre tips, and on-chip optical systems. Therefore, it is

potentially to design a new type of endoscope based on the graphene-based ultrathin flat lenses.

In this chapter, we explore the possibility of a graphene ultrathin lens based endoscope design.

The first part is the theory: the fibre modes and the design of an on fibre tip GO lens are deduced;

Then the theoretical design results are introduced. The second part is the experiments: first, the

GO lens is fabricated directly on the fibre tip. Then, the focusing quality of the on fibre tip GO

lens is characterized. The experimental and theoretical results match well, which is the first

demonstration of a workable endoscope prototype based on graphene lens.

6.2 On fibre tip graphene lens design

In chapter 3, we derived the graphene-based lens design method based on the RS diffraction

theory. The following experimental results in Chapter 4 have demonstrated the accuracy of our

design method. However, for the on fibre tip graphene-based lens, as the incident beam is from

fibre, the incident light is different from the former case, which is a plane wave incidence.

Therefore, we have to derivate the formula again especially for the case of an on fibre tip

graphene-based lens by considering the optical modes from a fibre. In this section, the fibre

modes calculation method will be introduced first. Then, a simple design method for the

fundamental mode is derived. Finally, the theoretical design results are exhibited.

6.2.1 Fibre modes

Fig. 6- 1. The schematic of a standard step-indexed optical fibre.

The schematic of a standard step-indexed optical fibre is shown in Fig. 6-1. n1 and n2 represent

the refractive index of the fibre core and cladding, respectively, a is the radius of the fibre core.

There is no current and free charge in the fibre, and we also consider that the fibre is linear and

isotropic dielectric. We assume that there is no loss in the fibre and the dielectric variation

Chapter 6

92

∇ε ≈ 0. Therefore, for a monochromatic wave with a wavelength λ in vacuum, we can simplify

the vectorial Maxwell equations, and derive the scalar Helmholtz equation for electric field E:

∇2𝐸 + 𝑘2𝐸 = 0, (6-1)

where k=nk0, k0=2π/λ. The magnetic field follows the same Helmholtz equation, but we will

not discuss it here. Considering the condition that ∇ε ≈ 0, only the electric field component Ez

satisfies the scalar Helmholtz equation Eq. 6-1. Therefore, under the cylindrical-coordinate

system, as in Fig. 6-1, it can be simplified and expanded as:

𝜕2𝐸𝑧

𝜕𝑟2+1

𝑟

𝜕𝐸𝑧

𝜕𝑟+

1

𝑟2𝜕2𝐸𝑧

𝜕𝜑2+𝜕2𝐸𝑧

𝜕𝑧2+ 𝑘2𝐸𝑧 = 0. (6-2)

As the optical fibre is cylindrically symmetric, Ez is a periodic function of azimuth angle φ; On

the other hand, the fibre modes should be stable when they propagate along the z-axis, therefore,

Ez is harmonic along the z-axis. We assume the transmission constant is β. Based on the method

of separation of variables, we can directly give the general form of Ez:

𝐸𝑧(𝑟, 𝜑, 𝑧) = 𝐸𝑧(𝑟)𝑒𝑗(𝜑−𝛽𝑧), (6-3)

where l=0,1,2⋯. Substitute Eq. 6-3 into Eq. 6-2, we obtain the Bessel’s equation:

𝑑2𝐸𝑧(𝑟)

𝑑𝑟2+𝑑𝐸𝑧(𝑟)

𝑟𝑑𝑟+ (𝑘2 − 𝛽2 −

𝑙2

𝑟2) 𝐸𝑧(𝑟) = 0 (6-4)

Now, the analysis of the electromagnetic field in the fibre is to resolve the Bessel’s equation.

We bring in three dimensionless parameters: transverse propagation constants u, w and

normalized frequency V, and they satisfy

𝑢2 = 𝑎2(𝑘02𝑛1

2−𝛽2) (0≤r≤a);

𝑤2 = 𝑎2(𝛽2 − 𝑘02𝑛2

2) (r≥a);

𝑉 = √𝑢2 + 𝑤2 = 𝑎𝑘0√𝑛12 − 𝑛2

2. (6-5)

Therefore, Eq. 6-4 can be decomposed into two equations:

𝑑2𝐸𝑧(𝑟)


𝑟𝑑𝑟+ (

𝑢2

𝑎2−

𝑙2

𝑟2) 𝐸𝑧(𝑟) = 0 (0≤r≤a); (6-6a)

𝑑2𝐸𝑧(𝑟)


𝑟𝑑𝑟− (

𝑤2

𝑎2+

𝑙2

𝑟2)𝐸𝑧(𝑟) = 0 (r≥a). (6-6b)

Chapter 6

93

According to the process of solving Bessel’s equation, we use the boundary conditions that the

electromagnetic field Ez is a finite real number when r = 0, it is zero when r tends to be infinity,

and it is continuous when r=a. Therefore the mode field can be expressed as

𝐸𝑧 = 𝐴𝐽𝑙(𝑢𝑟

𝑎)𝑒𝑗(l𝜑−𝛽𝑧) (0≤r≤a); (6-7a)

𝐸𝑧 = 𝐵𝐾𝑙(𝑤

𝑎)𝑒𝑗(l𝜑−𝛽𝑧) (r≥a). (6-7b)

Where A and B are constants; 𝐽𝑙 represents the lth order Bessel’s function; 𝐾𝑙 represents the lth

order modified Bessel’s function. From Eq. 6-7a and b, we know that the values of u, w and β

decide the electromagnetic field of the fibre modes. Therefore, the fibre mode formula

derivations become solving the value of u, w and β. By using the boundary condition that the

electromagnetic field is continuous at r=a, we can obtain the characteristic equation of β:

[𝐽′𝑙(𝑢)

𝑢𝐽𝑙(𝑢)+

𝐾′𝑙(𝑤)

𝑤𝐾𝑙(𝑤)] [𝑛1

2 𝐽′𝑙(𝑢)

𝑢𝐽𝑙(𝑢)+ 𝑛2

2 𝐾′𝑙(𝑤)

𝑤𝐾𝑙(𝑤)] = (

𝑙𝛽

𝑘0)2

(𝑛22 1

𝑢2+ 𝑛1

2 1

𝑤2)2. (6-8)

For most fibres, the refractive index difference Δ between the fibre core and cladding is very

small, for example, Δ=0.01. Therefore, to simplify the solution, a weakly guiding

approximation is introduced, which is

Δ ≪ 1; 𝑛12 ≈ 𝑛22; 𝑘12 ≈ 𝑘22 ≈ β2. (6-9)

where Δ=𝑛12−𝑛2

2

2𝑛12 , k1 and k2 are the wave vector in the fibre core and cladding, respectively.

The characteristic equation can be simplified to: 𝐽′𝑙(𝑢)

𝑢𝐽𝑙(𝑢)+

𝐾′𝑙(𝑤)

𝑤𝐾𝑙(𝑤)= ±𝑙( 1

𝑢2+

1

𝑤2). (6-10)

When l=0, there is transverse electric filed TE0n or transverse magnetic mode TM0n, the

corresponding characteristic equation is:

𝐽′0(𝑢)

𝑢𝐽0(𝑢)+

𝐾′0(𝑤)

𝑤𝐾0(𝑤)= 0. (6-11)

There is a unified form of Eq. 6-10 and Eq. 6-11:

𝑢𝐽𝑚+1(𝑢)

𝐽𝑚(𝑢)=

𝑤𝐾𝑚+1(𝑤)

𝐾𝑚(𝑤) or 𝑢𝐽𝑚−1(𝑢)

𝐽𝑚(𝑢)=

−𝑤𝐾𝑚−1(𝑤)

𝑤𝐾𝑚(𝑤). (6-12)

Eq. 6-12 is the characteristic equation of the linearly polarized modes LPmn, and the two

equations are equal. The relationship between m and j is expressed in Eq. 6-13. n represents

the number of the roots of the corresponding mth order Bessel’s function.

Chapter 6

94

𝑚 = {

1𝑇𝐸𝑎𝑛𝑑𝑇𝑀𝑚𝑜𝑑𝑒𝑠𝑗 + 1𝐸𝐻𝑚𝑜𝑑𝑒𝑗 − 1𝐻𝐸𝑚𝑜𝑑𝑒

. (6-13)

The simple scalar characteristic equation, as given in Eq. 6-12 has been used to obtain the value

of β, and the corresponding LPmn mode has been calculated. All these data are calculated by a

MATLAB program. Fig. 6-2a shows the relationship between V and β/k0 for mode LP01 and

LP02, the range of β/k0 is between n1 and n2. As we know V is decided by parameters a, n1 and

n2, given by Eq. 6-5. Therefore, for a known step-indexed fibre, we can calculate the value of

V, then we can obtain the value of β, which means the values of u and w are known, given by

Eq. 6-5. Then, the electric mode filed can be expressed by Eq. 6-7a and b. For a fibre with

n1=1.46242, n2=1.45742, a=4.2 μm, and the incident wavelength is 0.632 μm, we have

simulated the electric field modes of the corresponding mode, as shown in Fig. 6-2b, the electric

fields have been normalized.

Fig. 6- 2. The LP01 and LP02 modes in the standard step-indexed fibre. (a) β/k0 versus V. (b)

The corresponding electric field modes.

In general, the subscript m of LPmn indicates the number of the maximum pairs along the

peripheral direction. When m=0, as shown in Fig. 6-2b, there is no maximum pair along the

peripheral direction. The subscript n indicates the number of the maximum pairs along the fibre

Chapter 6

95

diameter. There are one and two maximum pairs, respectively, in Fig 6-2b. With the same

parameters, we have simulated for LP11 and LP21, as shown in Fig. 6-3. Along the peripheral

direction, there are one and two pairs of maximums, respectively. Along the fibre diameter,

there is one maximum pair.

Fig. 6- 3. The LP11 and LP21 modes in the standard step-indexed fibre. (a) β/k0 versus V. (b)

The corresponding electric field modes.

We noticed that for mode LP11, it is odd symmetry. Considering the symmetry of our graphene-

based lens, potentially there exists no focal spot. This characteristic provides the mode

modulation of the on fibre tip graphene-based lens.

The electric field modes are the key parameters for the design and simulation of the on fibre

tip graphene-based lens. It is the incident electric filed for the on fibre tip graphene-based lens.

The design method derivation will be introduced in the next section.

Chapter 6

96

6.2.2 Design of graphene oxide lens for the fundamental mode

Fig. 6- 4. The schematic of a GO lens on a step-indexed fibre.

The schematic of an on fibre tip GO lens is shown in Fig. 6-4. The GO lens covers all the fibre

core to enable a high efficiency. According to the accurate lens design in Chapter 3, we can get

the intensity distribution on the r2-θ2 plane directly:

𝑈2(𝑟2, 𝜃2, 𝑧) =1

2𝜋∫ ∫ 𝑈′1(𝑟1, 𝜃1)(−𝑖𝑘 −

∞

0

2𝜋

0

1

√𝑧2+𝑟12+𝑟2


)exp(−𝑖𝑘√𝑧2+𝑟1

2+𝑟22−2𝑟1𝑟2cos(𝜃1−𝜃2))

𝑧2+𝑟12+𝑟2

2−2𝑟1𝑟2cos(𝜃1−𝜃2)z𝑟1𝑑𝑟1𝑑𝜃1, (6-14)

where 𝑈′1(𝑟1, 𝜃1) is

𝑈′1(𝑟1, 𝜃1) =

{

𝐽𝑚(

𝑢𝑟1𝑎)

𝐽𝑚(𝑢)(0 ≤ 𝑟1 ≤ 𝑎)

𝐾𝑚(𝑤𝑟1𝑎)

𝐾𝑚(𝑤)(𝑟1 ≥ 𝑎)

, (6-15)

m is the subscript of LPmn.

We only consider the intensity distribution on the z-axis, namely r2=0. Therefore, the

integration of the field distribution along the z-axis is:

𝑈2(𝑧, 𝜃1) =1

2𝜋∫ ∫ 𝑈1′(𝑟1, 𝜃1)

∞

0

2𝜋

0(−𝑖𝑘 −

1

√𝑧2+𝑟12)exp(−𝑖𝑘√𝑧2+𝑟1

2))

𝑧2+𝑟12 𝑧𝑟1𝑑𝑟1𝑑𝜃1. (6-16)

Given the fact that the amplitude modulation contributes much more than the phase modulation,

we only consider the amplitude modulation. For a point F on the z-axis, the distance between

it and the fibre tip plane is f. The field distribution at point F is:

Chapter 6

97

𝑈2(𝑓, 𝜃1) =1

2𝜋∫ ∫ 𝑈1′(𝑟1, 𝜃1)

∞

0

2𝜋

0(−𝑖𝑘 −

1

√𝑓2+𝑟12)exp(−𝑖𝑘√𝑓2+𝑟1

2))

𝑓2+𝑟12 𝑧𝑟1𝑑𝑟1𝑑𝜃1. (6-17)

Therefore, the intensity distribution 𝐼2(𝑓, 𝜃1) at point F is:

𝐼2(𝑓, 𝜃1) = 𝑎𝑏𝑠[𝑈2(𝑓, 𝜃1)]2. (6-18)

With a known f, 𝐼2(𝑓, 𝜃1) is decided by r1 only, which means the integral range of r1 decides

the field value at point F. Therefore, the periodic-like change of the intensity I2(R) (this has

been discussed in Chapter 3.) predicts the ring radii of the GO lens with the known focal length

f, where R is a variable represents r1. The extremes of I2(R) indicate the ring positions that

contribute to the constructive interferences to the intensity I2(R). A Matlab program has been

used to find out these ring positions.

6.2.3 Design results

Tab. 6- 1. Radii of the rings for the GO lens. a1 a2 a3

Radii 1 (μm) 1.27 2.15 3.01 Radii 2 (μm) 1.42 2.31 3.08

The radii of our designed on fibre tip GO lens is list in Tab. 6-1. The first radii group is based

on a fibre with a 6 μm diameter core. The theoretical results are shown in Fig. 6-5, the incident

wavelength is 0.633 μm. Fig. 6-5a and b show the axial and lateral planes of the focal spot. A

good focal spot is predicated. Fig. 6-5c and d are the details along the black dashed lines in Fig.

6-5a and b. The focal length is 1.71 μm as shown in Fig. 6-5c, the FWHM along the x-axis is

0.49 μm (0.77 λ).

Chapter 6

98

Fig. 6- 5. Theoretical design results of the first on fibre tip GO lens. (a) Intensity distributions

in the axial plane. (b) Intensity distributions in the lateral plane. (c) Intensity distributions along the black dashed lines in the axial planes. (d) Intensity distributions along the black

dashed lines parallel to the x-axis in the lateral planes.

However, as the fibre is not a single-mode fibre for 0.633 μm wavelength, there is a mismatch

between the experimental and theoretical results. This will be discussed in the next section.

Because of the mismatch, we designed another on fibre tip GO lens and fabricated it on a

single-mode fibre for 0. 633 μm wavelength (630HP from Thorlabs). The designed radii are

listed in the second group of Tab. 6-1. The Intensity distributions are shown in Fig. 6-6. Fig.

6-6a and b show the axial and lateral plane of the focal spot, a good focal spot was predicated.

Fig. 6-6c and d are the details along the black dashed lines in Fig. 6-6a and b. The focal length

is 1.91 μm as shown in Fig. 6-6c, the FWHM along the x-axis is 0.49 μm (0.77 λ), as shown in

Fig. 6-6d.

Chapter 6

99

Fig. 6- 6. Theoretical design results for the correctional on fibre tip GO lens. (a) Intensity distributions in the axial plane. (b) Intensity distributions in the lateral plane. (c) Intensity

distributions along the black dashed lines in the axial planes. (d) Intensity distributions along the black dashed lines parallel to the x-axis in the lateral planes.

We also have designed a few on fibre tip GO lenses with longer focal lengths. The numbers of

the rings are dozens. But here only the first ten radii are listed in Tab. 6-2.

Tab. 6- 2. Radii of the rings for the GO lens. a1 a2 a3 a4 a5 a6 a7 a8 a9 a10

Radii 1(μm) 6.81 10.56 13.58 17.59 19.42 21.10 22.68 24.18 25.60 26.96 Radii 2(μm) 9.62 14.88 18.72 21.91 24.70 27.22 29.54 31.70 33.74 35.67

The Intensity distributions corresponding to the first radii group in Tab. 6-2 are shown in Fig.

6-7. Fig. 6-7a and b show the axial and lateral plane of the focal spot. A good focal spot can be

predicated. Fig. 6-7c and d are the details along the black dashed lines in Fig. 6-7a and b. The

focal length is 50 μm as shown in Fig. 6-7c, the FWHM along the x-axis is 0.42 μm (0.66 λ),

as shown in Fig. 6-67d. We also have simulated the designed on fibre tip GO lens of the second

radii group in Tab. 6-2, but only the details were plotted to simplify our simulation. As shown

in Fig. 6-7e, the focal length is 100 μm, and the FWHM along the x-axis is 0.41 μm (0.65 λ),

as shown in Fig. 6-7d. We found that with the focal length increases, the FWHM keeps small,

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which means, the on fibre tip GO lenses with long focal lengths maintain their high resolution

in theory.

Fig. 6- 7. Theoretical design results for the on fibre tip GO lenses with longer focal lengths (50 μm and 100 μm). (a) Intensity distributions in the axial plane for the GO lens with a 50 μm focal length. (b) Intensity distributions in the lateral plane for the GO lens with a 50 μm focal length. (c) Intensity distributions along the black dashed lines in the axial planes. (d)

Intensity distributions along the black dashed lines parallel to the x-axis in the lateral planes. (e) Intensity distributions along the black dashed lines in the axial planes for the GO lens with a 100 μm focal length. (f) Intensity distributions along the black dashed lines parallel to the x-

axis in the lateral planes for the GO lens with a 100 μm focal length.

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6.3 Fabrication of the GO lens on the fibre tip

Fig. 6- 8. Cut fibre tip under a microscope. (a) Side profile of a cut fibre. (b) The surface of

the cut fibre.

Fig. 6- 9. GO film transfer on naked fibre tips. (a) Holes mode for naked fibre. (b) GO film

transferred on the surface of the hole measured by a microscope. (c) Microscope image of the holes after the GO film was transferred onto the fibre tip. (d) The surface of the cut fibre with

GO film.

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The first step of the on fibre tip GO lens fabrication is a flat tip fibre preparation. We used a

fibre cleaver (F-CLX-8 from Newport) to cut the fibre. Flat and clean fibre tips have been

achieved, the side profile of the cut fibre is shown in Fig. 6-8a. The naked surface of the fibre

tip is shown in Fig.6-8b. Then, the second step is the transfer of a GO film onto the fibre tips.

The GO film was fabricated by the vacuum filtration method. Fig. 6-9a is a hole mould

fabricated by the CO2 laser cutting system. The diameters of the holes are slightly larger than

the diameter of the naked fibre. We transferred the GO film onto the mould firstly. Fig. 6-9b is

the microscopic image of the GO film on the surface of a hole. Then we threaded the cut fibre

carefully from the other side of the hole. The GO film was then transferred onto the fibre tip.

To increase the success rate, it is better to keep the GO film moist before it is transferred onto

the fibre tip. Fig. 6-9c is the hole after the GO film was transferred onto the fibre tip. Fig. 6-9d

is the surface of the cut fibre with a GO film. This process decreases the difficulty to transfer

GO film onto a naked fibre tip. However, as the fibre is too small, the success rate is low. On

the other hand, as the naked fibre is very fragile, the prepared naked fibre is potentially broken

at any step. Therefore, we chose a fibre with an FC/PC connector, which decreases our

experimental difficulty tremendously.

The GO film was peeled off from the substrate by immersing it into a container with water or

ethanol, then with the help of a pair of tweezer, the GO film can be easily transferred onto the

fibre tip with the FC/PC connector. Fig. 6-10a shows the fibre with an FC/PC connector. Fig.

6-10b shows the surface of the fibre with FC/PC connector, the size of this surface is much

larger than the naked fibre. Fig. 6-10c shows the fibre surface with the GO film.

Fig. 6- 10. GO film preparation on a fibre tip with FC/PC connector. (a) A fibre with an

FC/PC connector. (b) The surface of the fibre tip. (c) The surface of the fibre tip with a GO film.

After the fibre tip was integrated with a GO film, the fibre was fixed into the sample stage of

the DLW system (the schematic is shown in Fig. 4-6). A homemade holder has been fabricated

by cutting plastic with a CO2 laser cutting system. Fig. 6-11a shows the plastic holder, there is

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a GO film on the fibre tip. To locate the core of the fibre, a beam was coupled into the fibre

from the other end of the fibre. Fig. 6-11b shows the cross-section of the fibre, a clear

fundamental mode can be observed with the microscopic setup in the DLW system. The red

dashed line is a mark to indicate the profile of the focused laser spot on the sample. Therefore,

by matching the fundamental mode area and the circular mark, we can locate the core of the

fibre precisely.

Fig. 6- 11. Locating of the fibre core. (a) Homemade fibre holder for the DLW system. (b)

The fundamental mode and the circle mark.

According to the experimental experience of fabricating GO lenses on a substrate of cover glass,

the laser power was set to 10 μw, the fabrication speed is 30 μm/s. Fig. 6-12 shows the on fibre

tip GO lens under a microscope. Fig. 6-12a is the on fibre tip GO lens without a coupled beam,

Fig. 6-12b is the on fibre tip GO lens with a coupled beam, it is clear that the GO lens matches

well with the fundamental mode.

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Fig. 6- 12. GO lens fabrication on a fibre tip. (a) On fibre tip GO lens without the coupling beam. (b) On fibre tip GO lens with the coupling beam.

We also fabricated a large GO lens on a fibre tip with a core diameter equal to 100 μm, Fig. 6-

13 is the microscopic image of this GO lens. However, due to the mode crosstalk, the

experimental results show that there is no focal spot. This will be discussed in the next section.

Fig. 6- 13. Large GO lens on a fibre with a 100 μm core diameter.

6.4 Focusing characterization

We have fabricated a few on fibre tip GO lenses, then the on fibre tip GO lenses have been

characterized with a homemade characterization system, as shown in Fig. 6-14. A 633 nm laser

beam is coupled into the fibre through a lens, the output beam from the other distal end of the

fibre with the GO lens is collected by a 100x objective, then recorded by a computer. Through

the scanning of the objective along the optical axis, the images of the focal spot can be recorded.

Then a MATLAB program is used to reconstruct the 3D image of the focal spot.

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Fig. 6- 14. Schematic of the on fibre tip GO lens characterization system. 3D: three

dimensional. PC: personal computer.

The theoretical and experimental results for the first GO lens we designed are shown in Fig. 6-

15, it was fabricated on a fibre with a ~6-μm-diameter fibre core. A focal spot has been

observed, the focal length is 1.71 μm (Fig. 6-15c), and the FWHM on the x-axis is 0.54 μm

(0.87 λ) (Fig. 6-15d). However, the detailed intensity distributions of the experimental and

theoretical results along the z-axis are mismatched. The reason is that the fibre we used is not

a single-mode fibre for 0.633 um wavelength. Therefore, not only the fundamental mode but

also the high order modes take part in the diffraction. We have simulated the intensity

distribution of different fibre modes to prove our suspicion. To simplify the simulation, we

only give the intensity distributions along the z-axis. Fig. 6-16 shows the simulation results for

different fibre modes. We found that, for a GO lens, different fibre mode shows different

diffraction result. For example, for mode LP21, there is hardly any focusing phenomenon. The

odd symmetry of the electric field of mode LP11 leads to destructive interference. For mode

LP02, it shows a groove at the location were mode LP01 shows a focal spot. Therefore, our first

result shows an elongated focal spot on the z-axis.

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Fig. 6- 15. Comparison of theoretical and experimental results for the first on fibre tip GO lens. (a) Intensity distributions in the axial plane. (b) Intensity distributions in the lateral

plane. (c) Intensity distributions along the black dashed lines in the axial planes. (d) Intensity distributions along the black dashed lines parallel to the x-axis in the lateral planes.

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Fig. 6- 16. The diffraction distributions on the z-axis of the first four fibre modes.

Therefore, we designed another GO lens for a ~630 nm single-mode fibre (630 HP from

Thorlabs) and fabricated it by the DLW method. The results are shown in Fig. 6-17. The

intensity distributions in the y-z planes of the experimental and theoretical results are shown in

Fig. 6-17a. There is a clear focal spot, which proves the focusing ability of our on fibre tip GO

lens. Fig. 6-17b shows the intensity distributions in the x-y planes. A good circular focal spot

is shown. More details are shown in Fig. 6-17c and d, the line figures are the intensity

distributions along the black dashed lines in Fig. 6-17a and b. It is clear that the experimental

results match well with the theoretical results. First, the focal length of the experimental results

is 1.92 μm, and the theoretical prediction is 1.91 μm. The difference is ignorable. Second, the

FWHM along the x-axis of the experimental result is 0.55 μm (0.87λ). The corresponding

theoretical result is 0.49 μm (0.77 λ). The difference between the theoretical and experimental

results is 10.9%. Considering the experimental error, the difference is acceptable. Therefore,

the experimental results prove our theoretical predictions and demonstrate the first focusing

performance of an on fibre tip graphene lens.

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Fig. 6- 17. Theoretical and experimental results comparison for the correctional on fibre tip GO lens. (a) Intensity distributions in the axial plane. (b) Intensity distributions in the lateral plane. (c) Intensity distributions along the black dashed lines in the axial planes. (d) Intensity

distributions along the black dashed lines parallel to the x-axis in the lateral planes.

Furthermore, we have tried to fabricate a long focal length GO lens on a fibre with a large core

diameter. However, as we discussed before, the different modes have an impact on the focal

spot. On the other hand, the interference of the coupled laser shows a huge disturb on the focus.

Currently, based on the single-mode fibre in hand, the longest focal length we have obtained is

4.8 μm. As the fundamental mode size of a single-mode fibre is the most important factor to

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determine the upper limit of the focal length, single-mode fibres with large core diameters can

be used, such as photonic crystal fibre.

6.5 Chapter summary

In this chapter, the theoretical design method of an on fibre tip GO lens has been derivated.

The on fibre tip GO lenses have been fabricated by the DLW method. The experimental results

match well with the theoretical predictions.

First, based on the wave optics theory, the electric field modes in a step-indexed fibre have

been derivated. Based on the Matlab program, the numerical simulation provides the

relationship between the lengthways propagation constant β of the fibre with the normalized

frequency V. Given a known fibre, the value of V is certain, then we can obtain the value of β.

With the value of β, we can calculate the transverse propagation constant u and w. According

to Eq. 6-7a and b, we can obtain the electric field modes in the fibre.

For the on fibre tip GO lens, the electric field modes are the incident beam. Therefore,

borrowing the design theory in Chapter 3, we can design an on fibre tip GO lens directly. We

have designed a few on fibre tip GO lenses with the fundamental mode as the incident beam is

the. The theoretical results demonstrate the focusing ability of the on fibre tip GO lenses. In

the same way, this theory is also applicable to an on fibre tip rGO lens.

Based on the designed on fibre tip GO lens, we have fabricated a few samples. However, we

found the focal spot is elongate in the z-direction. More theoretical simulates prove that it is

because of the other modes existing in the multimode fibre. Therefore, we fabricated another

on fibre tip GO lens on a single-mode fibre with a new design, the experimental results match

well with the theoretical results.

To obtain an on fibre tip GO lens with a long focal length, we have designed a few GO lenses

for fibres with a large core diameter. However, there is no focusing phenomenon in

experiments. The interference of the laser beam and the many modes in the fibre are the reasons

for these results. To overcome this problem, an SLM can be introduced to control the electric

field on the fibre tip.

In conclusion, we have demonstrated the focusing ability of the on fibre tip GO lens

experimentally and theoretically. The next step is to obtain a scanning imaging by our on fibre

tip GO lens.

110

Chapter 7

Conclusion and outlook

7.1 Conclusion of this thesis

In this thesis, an accurate design method for ultrathin flat graphene-based lenses has been

developed. The experimental results have confirmed the accuracy of this new method. An rGO

lens has been designed and fabricated, which are stable in aerospace, chemical, and biological

et al harsh environments. Furthermore, the accurate design method has been applied to the on

fibre tip graphene-based lenses, which could potentially work as endoscopes. Based on the

design, on fibre tip GO lenses have been fabricated, and the experimental results match well

with the theoretical predictions. The detailed achievements are summarized as follows:

1. A design method based on the RS diffraction theory has been developed. The new design

method is able to accurately design ultrathin flat lenses with arbitrary focal length and

diameter without the optimization process. The new design method has been compared

with the Fresnel model design method, which is only applicable for low NA lenses

satisfying the paraxial condition. For a high NA GO lens we targeted, the largest ring

positions difference between the two design results is ~13.9 %. And the resulted focal

length difference is approximate 9.1%. Based on the designed GO lenses, theoretical results

have been simulated by the Fresnel diffraction theory, RS diffraction theory and FDTD.

The match between the RS and the FDTD results have demonstrated the accuracy of our

new design method. For the FWHMs along the x and y directions, the differences between

the RS and FDTD results are less than 6% in the x-direction and 2.1% in the y-direction.

For the focal length, the difference between the RS and FDTD results is ~1.1%. On the

other hand, a significant difference can be identified in the Fresnel theoretical results. The

FWHMs difference is ~ 52.1%, the focal length difference is ~13.3%, Therefore, the

Fresnel diffraction theory failed to accurately predict the focusing performance of the high

NA GO lenses.

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2. Furthermore, the design flexibility of the RS method has been demonstrated by two GO

lenses with desired focal lengths and NAs. Also, the experimental fabrication of GO lenses

by the DLW method and the point spread function characterization of the GO lens have

verified the accuracy of our new design method. The theoretical and experimental results

show that: the new design method based on the RS diffraction theory is able to design a

targeted GO lens accurately, and the RS diffraction theory is able to accurately calculate

the focusing process of GO lenses with arbitrary NA and focal lengths with high speed and

efficiency. Therefore, the demonstrated RS method is expected to find broad applications

in designing and analyzing other ultrathin flat lenses, including metasurface lenses and

lenses made of other 2D materials.

3. Considering the harsh environments in practical applications, rGO lenses designed by the

new method have been fabricated by direct laser ablating method. The performance

stability of the rGO ultrathin flat lenses has been tested in a number of harsh environments

according to the requirements of diverse applications. The harsh environments include LEO

conditions, strong corrosive chemical and biochemical conditions. To simulate these

conditions, the rGO lenses have been exposed to UV light for 24 hours; heated to 200 ˚C

for 24 hours; immersed in liquid nitrogen for 1 hour; baked in ultra-vacuum at 100 ˚C for

24 hours; immersed in strong acid solution (PH=0) for 7 days; immersed in strong alkaline

solution (PH=14) for 7 days; immersed in PBS solution for 24 hours; exposed to AO

radiation for 45 s. The measured results after each torture of these conditions show that

there is no measurable deterioration in either the surface morphology or the highly sensitive

focusing performance of the rGO lens in almost all of the circumstances except for the

long-term AO radiation direct exposure. Nevertheless, with proper protection against AO

radiation, the rGO lenses can be safely applied in the aerospace environment. The

encouraging results suggest that rGO is a promising ultra-stable material potentially useful

for a variety of practical circumstances, in particular where harsh environments and low

maintenance are required for example strong corrosive chemical condition or biochemical

condition without any protection.

4. On fibre tip graphene-based lenses have been designed by using the new design method

with different incident fields. A GO lens designed for a single-mode fibre has been

fabricated by the DLW method. The experimental results match well with the theoretical

prediction. Subwavelength FWHM (0.87 λ, incident wavelength is 0.633 μm) of the focal

spots have been obtained. The results have proved the potential usage of the GO lens in an

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112

endoscope configuration. Furthermore, the theoretical results show that, with large

diameters of the single modes, on fibre tip GO lenses with long focal lengths are able to be

designed, and the FWHMs of the focal spots can maintain their subwavelength scales.

These results preliminarily demonstrated the capability of the GO lens can be potentially

used as an endoscope with high resolution, miniaturization, and easy fabrication.

Furthermore, considering the resilience of the rGO lenses, being able to function in harsh

environments will be one of the most important benefits of the new endoscope.

In conclusion, based on the new design method, high NA graphene-based lenses are able to be

designed in a great simplicity and efficiency. Combing with the DLW method, the scalable

fabrication of graphene-based lenses are able to be realized. In addition, by taking full

advantage of the physical and chemical properties of graphene-based materials, the resilience

to harsh environments of the graphene-based lenses has been demonstrated. This further

enhances the applicable ranges of the graphene-based lens. Furthermore, the design and

fabrication of on fibre tip GO lens have opened up and demonstrated the practical applications

of the graphene-based ultrathin flat lens. The practical value of the graphene-based ultrathin

flat lens is enormous, more effort should be devoted to this area to ensure the full potential is

realized.

7.2 Outlook and future work

The research work presented in this thesis can be further extended and exploited. The following

points are some key areas to be further studied and will provide profound knowledge and may

lead to practical applications of the ultrathin flat graphene-based lenses.

1. Design of aberration-free graphene-based ultrathin flat lenses. Usually, a conventional

aberration-free lens requires complex optimization and fabrication, such as special

structures or multi-lenses, which leads to the bulky volume and complicated structures. The

ultrathin flat graphene-based lenses focus light by the diffraction mechanism. It is thus

possible to design aberration-free graphene-based lenses by taking full advantages of the

amplitude and phase modulations or introducing gradual phase modulations. The

aberration-free graphene-based lens can be designed and fabricated, which makes it highly

competitive to replace the conventional lens in the optic system, especially in the integrated

nano-photonic systems.

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2. Considering the hydrophilicity of the GO film, it is inapplicable to use the GO lens to work

as the endoscope. The rGO lens is a better choice to replace the GO lens to work in harsh

environments, as we have discussed. Therefore, the fabrication of rGO lens onto the fibre

tip to work as an endoscope should be studied. In addition, an on fibre tip graphene-based

lens with a long focal length should be designed and fabricated. As we mentioned in

Chapter 6, the experimental results are limited by the model crosstalk and the interference

of the incident laser beam. An SLM should be introduced to control the electric field

distribution in the multimode fibre, and then control the focal spot length and the focus

location. To acquire a high-resolution image, the scanning imaging system should be

designed and set up. The first step is to design a scanning imaging system with the on fibre

tip rGO lens as a light source and an objective lens to collect the signal. The on fibre tip

GO lens could work as both light source and signal collection element in the scanning

imaging system. These researches will advance the practical usability of the endoscope

with graphene-based lenses.

3. Based on the new compact endoscopes, more integrated imaging systems can be set up and

studied, such as the optical coherence tomography system, the fluorescence lifetime

imaging system, and the second and third harmonic generation imaging system.

In conclusion, owing to the multiple advantages of ultrathin, high resolution, ultralight-weight,

broadband, and unique physical and chemical properties, more effort is urgently needed to be

devoted to the research of the graphene-based lenses and their applications.

114

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Publications of the author

Journal papers

Cao, Guiyuan, Han Lin, Scott Fraser, Xiaorui Zheng, Blanca Del Rosal, Zhixing Gan, Shibiao

Wei, Xiaosong Gan, and Baohua Jia. "Resilient graphene ultrathin flat lens in aerospace,

chemical, and biological harsh environment." ACS applied materials and interfaces (2019).

Cao, Guiyuan, Xiaosong Gan, Han Lin, and Baohua Jia. "An accurate design of graphene oxide

ultrathin flat lens based on Rayleigh-Sommerfeld theory." Opto-Electronic Advances 1, no. 07

(2018): 180012.

Zhou, Chunhua, Guiyuan Cao, Zhixing Gan, Qingdong Ou, Weijian Chen, Qiaoliang Bao,

Baohua Jia, and Xiaoming Wen. "Spatially modulating the fluorescence color of mixed-halide

perovskite nanoplatelets through direct femtosecond laser writing." ACS applied materials and

interfaces 11, no. 29 (2019): 26017-26023.

Gan, Zhixing, Weijian Chen, Lin Yuan, Guiyuan Cao, Chunhua Zhou, Shujuan Huang,

Xiaoming Wen, and Baohua Jia. "External stokes shift of perovskite nanocrystals enlarged by

photon recycling." Applied Physics Letters 114, no. 1 (2019): 011906.

Gan, Zhixing, Xiaoming Wen, Weijian Chen, Chunhua Zhou, Shuang Yang, Guiyuan Cao,

Kenneth P. Ghiggino, Hua Zhang, and Baohua Jia. "The Dominant Energy Transport Pathway

in Halide Perovskites: Photon Recycling or Carrier Diffusion?." Advanced Energy

Materials (2019): 1900185.

Du, Zhenmin, Chengyang Hu, Guiyuan Cao, Han Lin, Baohua Jia, Sigang Yang, Minghua

Chen, and Hongwei Chen. "Integrated wavelength beam emitter on silicon for 2-dimensional

optical scanning." IEEE Photonics Journal (2019).

Conferences

Cao, Guiyuan, Han Lin, Xiaosong Gan, and Baohua Jia. "A fiber tip graphene oxide lens

towards fiber optic endoscope application." In Frontiers in Optics, pp. FM4C-2. Optical

Society of America, 2019.

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