i OPTICAL BISTABILITY IN MOBIUS MICRORING RESONATOR AHMAD FAKHRURRAZI BIN ...

36 Pages·2017·0.81 MB·English

i
OPTICAL BISTABILITY IN MOBIUS MICRORING RESONATOR
AHMAD FAKHRURRAZI BIN AHMAD NOORDEN
A thesis submitted in fulfilment of the
requirements for the award of the degree of
Doctor of Philosophy (Physics)
Faculty of Science
Universiti Teknologi Malaysia
MAY 2015
iii

Dedicated with my deepest love and affection to
my family
For their supports and blessings

To all my friends specially Nurul Faridah
For their motivational support
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ACKNOWLEDGEMENT

First and foremost, all praise to Allah, the Almighty, the Benevolent for His
blessing and guidance, for giving me the inspiration to embark on this project and
instilling in me the strength to see that this research becomes reality. Many people
have contributed to the creation and completion of this research. I would like to
express my gratitude to all those who have helped in one way or another in the
planning, brainstorming, writing, editing stages, and discussion for this research. I
would like to specially thank to my supervisor Prof. Dr. Jalil Bin Ali for his
continued guidance and support for this research and contributing in stimulating
suggestions and encouragement, help me to coordinate this research.

I would also like to express my sincere gratitute to my friends especially Dr.
Mehdi, Dr. Kasyif, Dr. Safwan, Dr. Suzairi, Dr. Ong, Dr. Najmee, Azam, Sufi,
Helmi, Nina and Fairuz for their research experiences and knowledges sharing and
support in the field of nanophotonics research. They have created a very warm and
friendly working atmosphere within the laboratory. I would also like to thank the
scientific research officer, Mr. Abdul Rashid for his assistance.

A special thanks to my family. Words cannot express how grateful I am to
my mother, and father for all of the motivational support during my struggle. Your
prayer for me help to sustain me thus far. I would also like to thank all of my friends
who supported me in writing, and incented me to strive towards my goal. At the end
I would like express appreciation to my best friend Nurul Faridah who was always
be my support in the moments when there was no one to answer my queries.
v

ABSTRACT

Optical bistability is one of the nonlinear properties that produce an essential
light control which contributes in various photonics applications such as all-optical
switching and optical memory. In this thesis, bistability behavior of optical signals
generated in microring resonator (MRR) systems using bright soliton input pulses
with 1.55 μm wavelength is studied. The generation of the bistable signals is
mathematically analyzed through the transfer matrix analysis and simulated by the
MATLAB software version 2014a. The behavior of the propagated input pulses in
terms of intensity and phase shift is investigated for different configurations
including All-pass MRR, Add-drop MRR and PANDA MRR systems. Three novel
Mobius MRR configurations consist of All-pass Mobius MRR, Add-drop Mobius
MRR and PANDA Mobius MRR configurations are proposed and the light treatment
through Mobius MRR systems is analytically studied and compared with
conventional MRR systems. For determining the effect of physical parameters such
as ring radius, control power variation and coupling coefficients on the output pulse,
the optical hysteresis loops of bistable signals are generated via silicon-on-insulator
nonlinear MRR configurations. The analyses of the results are conducted by
calculating the output switching power, input threshold power and hysteresis width
of bistable loop for radius variation from 1 μm to 6 μm with an increment of 1 μm,
change of coupling coefficient from 0.4 to 0.9 with increment of 0.1 and variation of
controlled power from 50 mW to 100 mW with increment of 10 mW. It is found that
small coupling coefficients enhance the hysteresis width and output switching power
of optical bistable loops. The value of output switching power obtained at the output
port of Add-drop Mobius MRR is 30.26 mW which is higher than those obtained
from All-pass Mobius and PANDA Mobius MRR configurations. The threshold
powers of the All-pass Mobius, Add-drop Mobius and PANDA Mobius
configurations for on switching operations are obtained as 20.59 mW, 31.39 mW and
25.19 mW respectively. It is found that, optimization of the Mobius MRR system
can be conducted by increasing the external radius of Mobius ring waveguide and
decreasing the coupling coefficient with implementation of the high control power.
In this work, the Mobius configurations are introduced as a convenient compact
design to generate optical bistability in comparison with conventional configurations
of nonlinear MRR system.
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ABSTRAK

Optik dwikestabilan adalah salah satu daripada sifat-sifat tak linear yang
menghasilkan kawalan cahaya penting yang menyumbang dalam pelbagai kegunaan
fotonik seperti semua-pensuisan optik dan memori optik. Dalam tesis ini, tingkah
laku dwikestabilan isyarat optik yang dihasilkan dalam sistem pengalun cincin mikro
(MRR) menggunakan denyut input soliton cerah dengan panjang gelombang 1.55
μm telah dikaji. Penjanaan isyarat dwistabil dianalisis secara matematik melalui
analisis matriks pindahan dan disimulasikan dengan perisian MATLAB versi 2014a.
Kelakuan denyut input rambatan dikaji dari segi keamatan dan anjakan fasa untuk
susunan yang berbeza termasuk sistem MRR lepasan-semua, MRR penambah-jatuh
dan MRR PANDA. Tiga susunan MRR Mobius baru terdiri daripada susunan MRR
Mobius lepasan-semua, MRR Mobius penambah-jatuh dan MRR Mobius PANDA
dicadangkan dan rawatan cahaya melalui sistem MRR Mobius dikaji secara analitik
dan dibandingkan dengan sistem MRR konvensional. Untuk menentukan kesan
parameter fizikal seperti perubahan jejari cincin, kuasa kawalan dan pekali
gandingan denyut output, gelung histerisis optik isyarat dwistabil telah dihasilkan
melalui susunan MRR tak linear silikon-atas-penebat. Analisis keputusan dilakukan
dengan pengiraan kuasa pesuisan output, kuasa ambang input dan lebar gelung
histerisis dwistabil untuk perubahan jejari daripada 1 μm hingga 6 μm dengan
kenaikan 1 μm, perubahan pekali gandingan daripada 0.4 kepada 0.9 dengan
kenaikan 0.1 dan perubahan kuasa kawalan daripada 50 mW kepada 100 mW
dengan kenaikan 10 mW. Ia didapati bahawa pekali gandingan kecil meningkatkan
lebar histerisis dan kuasa pensuisan output gelung optik dwistabil. Nilai kuasa
pensuisan output diperolehi di port output MRR Mobius penambah-jatuh ialah 30.26
mW yang mana lebih tinggi daripada susunan MRR Mobius lepasan-semua dan
MRR Mobius PANDA. Kuasa ambang susunan Mobius lepasan-semua, Mobius
penambah-jatuh dan Mobius PANDA untuk operasi pensuisan terpasang diperoleh
masing-masing sebagai 20.59 mW, 31.39 mW dan 25.19 mW. Ia didapati bahawa,
pengoptimuman sistem Mobius MRR boleh dilakukan dengan meningkatkan jejari
luar pemandu-gelombang cincin Mobius, dan mengurangkan pekali gandingan
dengan pelaksanaan kuasa kawalan yang tinggi. Dalam kerja ini, susunan Mobius
diperkenalkan sebagai reka bentuk padat yang mudah untuk menjana dwikestabilan
optik berbanding dengan susunan konvensional pada sistem MRR tak linear.
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TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENT iv
ABSTRACT v
ABSTRAK vi
TABLE OF CONTENTS vii
LIST OF TABLES x
LIST OF FIGURES xii
LIST OF ABBREVIATIONS xvii
LIST OF SYMBOLS xviii
LIST OF APPENDICES xxi

1 INTRODUCTION 1
1.1 Research Background 1
1.2 Problem Statement 2
1.3 Research Objectives 3
1.4 Research Scope 4
1.5 Research Significance 5
1.6 Thesis Outline 5

2 LITERATURE REVIEW OF OPTICAL BISTABILITY 7
2.1 Introduction 7
2.2 Optical Bistability Switching 7
2.3 Optical Bistability in MRR 19
viii

3 THEORY OF OPTICAL BISTABILITY 25
3.1 Introduction 25
3.2 Nonlinear Response of Optical Fiber 25
3.3 Nonlinear Refraction 28
3.4 Self-phase Modulation 29
3.5 Group Velocity Dispersion 30
3.6 Temporal Optical Soliton 32
3.7 Microring Resonator 37
3.8 Mobius Resonator Configuration 38
3.9 Coupling Theory 43
3.10 Transfer Matrix Analysis 50
3.11 Optical Bistability 52

4 RESEARCH METHODOLOGY 58
4.1 Introduction 58
4.2 Mathematical Computation of Optical Fields
in MRR 59
4.2.1 All-pass Type MRR Configurations 59
4.2.2 Add-drop Type MRR Configurations 65
4.2.3 PANDA Type MRR Configurations 71
4.3 Modelling of Microring Resonator System 79
4.3.1 Modelling of All-pass MRR 80
4.3.2 Modelling of Add-drop MRR 84
4.3.3 Modelling of PANDA MRR 88

5 RESULTS AND DISCUSSIONS 91
5.1 Introduction 91
5.2 Analysis of Optical Bistability in All-pass Type
MRR Configurations 92
5.2.1 Analysis of Output Power of All-pass
and All-pass Mobius MRR 93
ix

5.2.2 Optical Hysteresis Operating in All-pass
and All-pass Mobius Configurations 96
5.2.3 Parametric Effects of Optical Bistability in
All-pass Type MRR Configurations 101
5.3 Analysis of Optical Bistability in Add-drop Type
MRR Configurations 110
5.3.1 Analysis of Output Power of Add-drop Filter
and Add-drop Mobius MRR 110
5.3.2 Optical Hysteresis Operating in Add-drop
and Add-drop Mobius MRR
Configurations 113
5.3.3 Parametric Effects of Optical Bistability in
Add-drop Type MRR Configuration 118
5.4 Analysis of Optical Bistability in PANDA Type
MRR Configurations 129
5.4.1 Analysis of Output Power of PANDA
and PANDA Mobius MRR 129
5.4.2 Optical Hysteresis Operating in PANDA and
PANDA Mobius MRR Configurations 133
5.4.3 Parametric Effects of Optical Bistability in
PANDA Type MRR Configuration 141
5.5 Optimization and Switching of Optical Bistability in
Mobius-Type MRR 164

6 CONCLUSION 171
6.1 Conclusion 171
6.2 Future Work 173

REFERENCES 174
Appendices A-D 184 - 208
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LIST OF TABLES

TABLE NO. TITLE

PAGE
5.1 The threshold powers, output switch powers, and
hysteresis widths of the optical bistability loops at
output port, point 1, and point 2 for the All-pass
Mobius configuration 100

5.2 List of threshold powers, output switch powers, and
hysteresis widths of the optical bistability loops with
variation of radius, and coupling for All-pass and All-
pass Mobius configurations 108

5.3 List of threshold powers, output switch powers, and
hysteresis widths of the optical bistability loops with
variation of control power for All-pass and All-pass
Mobius configurations 109

5.4 The threshold powers, output switch powers, and
hysteresis widths of the optical bistability loops at
output ports, point 1, point 2, point 3 and point 4 for
the Add-drop filter ADF and Add-drop Mobius ADM
configurations. 117

5.5 Threshold powers, output switching powers ΔP ,
switch
and hysteresis width W for Add-drop Mobius and
hys
Add-drop filter configurations as a function of radius,
coupling coefficients and control powers. 128

5.6 Threshold powers, output switch powers, and
hysteresis widths of the optical bistability loops for
optical power at output port, point 1, 2, 3, and 4 of All-
pass and All-pass Mobius configurations 140

5.7 List of threshold powers, output switch powers, and
hysteresis widths of the optical bistability loops with
variation of radius for PANDA and PANDA Mobius
configurations 160
xi

5.8 List of threshold powers, output switch powers, and
hysteresis widths of the optical bistability loops with
variation of coupling coefficient for PANDA and
PANDA Mobius configurations 161

5.9 List of threshold powers, output switch powers, and
hysteresis widths of the optical bistability loops with
variation of control power for PANDA and PANDA
Mobius configurations 162

5.10 Optimized Mobius types MRR configurations
properties 168