vii
TABLE OF CONTENTS
CHAPTER
1
2
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
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
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
4
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
RESEARCH METHODOLOGY
58
4.1
Introduction
58
4.2
Mathematical Computation of Optical Fields
in MRR
4.3
5
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
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
RESULTS AND DISCUSSIONS
91
5.1
Introduction
91
5.2
Analysis of Optical Bistability in All-pass Type
MRR Configurations
5.2.1
92
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
5.2.3
96
Parametric Effects of Optical Bistability in
All-pass Type MRR Configurations
5.3
101
Analysis of Optical Bistability in Add-drop Type
MRR Configurations
5.3.1
110
Analysis of Output Power of Add-drop Filter
and Add-drop Mobius MRR
5.3.2
110
Optical Hysteresis Operating in Add-drop
and Add-drop Mobius MRR
Configurations
5.3.3
113
Parametric Effects of Optical Bistability in
Add-drop Type MRR Configuration
5.4
118
Analysis of Optical Bistability in PANDA Type
MRR Configurations
5.4.1
129
Analysis of Output Power of PANDA
and PANDA Mobius MRR
5.4.2
129
Optical Hysteresis Operating in PANDA and
PANDA Mobius MRR Configurations
5.4.3
133
Parametric Effects of Optical Bistability in
PANDA Type MRR Configuration
5.5
Optimization and Switching of Optical Bistability in
Mobius-Type MRR
6
141
164
CONCLUSION
171
6.1 Conclusion
171
6.2 Future Work
173
REFERENCES
Appendices A-D
174
184 - 208
x
LIST OF TABLES
TABLE NO.
TITLE
PAGE
5.1
5.2
5.3
5.4
5.5
5.6
5.7
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
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 Allpass Mobius configurations
108
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
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
Threshold powers, output switching powers ΔPswitch,
and hysteresis width Whys for Add-drop Mobius and
Add-drop filter configurations as a function of radius,
coupling coefficients and control powers.
128
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 Allpass and All-pass Mobius configurations
140
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
5.9
5.10
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
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
Optimized
properties
168
Mobius
types
MRR
configurations
xii
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
The relation between induced polarization P and electric
field E
26
Schematics illustration of optical pulse with dispersive
and SPM
33
3.3
All-pass microring resonator configuration
38
3.4
Add-drop ring resonator configuration
38
3.5
Schematics diagram of Mobius strip
39
3.6
Photograph of Mobius wire resonator comprise of 5.715
cm radius with 3.175 cm vertical height of aluminum
cavity
40
3.7
Schematics diagram of Mobius resonator
40
3.8
Schematics diagram of transmission line comprised of
inductors and capacitors components in rectangular loop
arrangement
41
Schematics Mobius and ring resonator with the periodic
elements of LC electrical circuit
41
Schematic diagram of fabrication process of microring
waveguide in Mobius shape
42
3.11
Coupling between two parallel waveguides
44
3.12
Schematics diagram of transfer matrix method
51
3.13
Fabry-Perot interferometer with the unidirectional
nonlinear cavity
54
The detuning of optical input source without increment
of intensity
55
3.1
3.2
3.9
3.10
3.14
xiii
3.15
The output versus input intensity curve with zero phase
detuning
56
The output versus input intensity curve with low phase
detuning
56
The output versus input intensity curve with high phase
detuning
57
4.1
Schematics diagram of All-pass MRR system
60
4.2
Schematic diagram of All-pass Mobius configuration
63
4.3
Schematics diagram of Add-drop MRR system
66
4.4
Schematics diagram of Add-drop Mobius ring resonator
69
4.5
PANDA configuration of MRR system
71
4.6
Propagation of electric field approaching the PANDA
right side ring waveguide
73
Propagation of electric field approaching the PANDA
left side ring waveguide
73
4.8
Schematics diagram of PANDA Mobius ring resonator
75
4.9
Right-side ring coupled to the centre PANDA Mobius
configuration
77
Left-side ring coupled to the centre PANDA Mobius
configuration
77
The modelling process of All-pass and All-pass Mobius
configuration of MRR system
83
The modelling process of Add-drop and Add-drop
Mobius configuration of MRR system
87
The modelling process of PANDA and PANDA Mobius
configuration of MRR system
90
5.1
Optical Bright soliton signal spectrum
93
5.2
The optical power spectrum of all-pas and All-pass
Mobius configuration, (a) and (b) are the power of
circulated field at point 1 and point 2 respectively, c) is
the output power of the microring system
95
Hysteresis loop of optical bistability behavior on All-
97
3.16
3.17
4.7
4.10
4.11
4.12
4.13
5.3
xiv
pass and All-pass Mobius configuration MRR system
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
i) Schematic diagram All-pass and All-pass Mobius of
ii)Circulated power at point 1 a) and 2 b) plotted with
respect to input power
98
The input-output power relation of radius variation in
All-pass configuration Ri where i= 1μm, 2μm, 3μm,
4μm, 5μm, and 6μm.
102
The output-to-input power relation of coupling
coefficients variation κi where i=0.4, 0.5, 0.6, 0.7, 0.8,
and 0.9
105
The output-to-input relation with the increment of input
power Pin (in=50mW, 60mW, 70mW, 80mW, 90mW,
and 100mW) variation
107
Optical powers generated at through (a) and drop (b)
port of ADF and Add-drop-Mobius configurations
111
Optical circulation powers in ADF and ADM
configurations at point 1, 2, 3, and 4 as (a) to (d)
respectively
112
Hysteresis loop of optical bistability generated by using
ADF and ADM configuration
114
Optical hysteresis loop of circulating power of ADF and
ADM configurations
116
Output-to-input power relation of radius variation in
ADF and ADM configurations Ri where i= 1μm, 2μm,
3μm, 4μm, 5μm, and 6μm
119
The output-to-input power relation of coupling
coefficients variation κi in ADF and ADM
configurations where i = 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9
122
i) The output-to-input power relation of control power
Pc variation in ADF and ADM configurations. ii) The
hysteresis loop of the bistable signal in ADM MRR.
126
Optical transmission spectrum generated at output (a)
and drop (b) ports of PANDA and PANDA M
configurations
130
Optical circulation powers in PANDA and PANDAMobius configurations at point 1, 2, 3, and 4 as (a) to (d)
respectively
132
xv
5.17
5.18
5.19
5.20
5.21
5.22
5.23
5.24
5.25
5.26
5.27
The output port optical power versus the input power in
PANDA and PANDA M configuration
134
Circulation power hysteresis i) diagram of PANDA and
PANDA M circulation point ii) Input-output power
relation of circulating power at point 1,2,3 and 4
136
Optical bistability in increase of main ring radius
PANDA configuration a) schematics of PANDA
configuration with radius variation of 6 μm to 7μm b)
Input-output power relation for 6 μm and c) Inputoutput power relation for 7 μm
142
Output-to-input
power
relation
of
PANDA
configuration with radius variation for 6 μm, 7 μm, 8
μm, 9 μm, 10 μm, and 11 μm a) to f).
143
Optical bistability in increase of main ring radius
PANDA Mobius configuration a) schematics of
PANDA Mobius configuration with radius variation of
6 μm to 7μm b) Input-output power relation for 6 μm
and c) Input-output power relation for 7 μm
145
Output-to-input power relation of PANDA Mobius
configuration with radius variation for 6 μm, 7 μm, 8
μm, 9 μm, 10 μm, and 11 μm
146
Output-to-input power relation of a) PANDA Mobius
and b) PANDA configurations with 0.4 and 0.5 coupling
coefficients
150
Output-to-input power relation of PANDA and PANDA
Mobius configurations with coupling coefficients
variation for 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9
151
PANDA control power variation i) schematic diagram
of PANDA configurations with control power variation
of 50mW to 60mW, ii) Input-output power relation with
50mW and 60mW power variation
153
PANDA Mobius control power variation i) schematic
diagram of PANDA Mobius configurations with control
power variation of 50mW to 60mW, ii) Input-output
power relation with 50mW and 60mW power variation
155
Output-to-input power relation of PANDA and PANDA
Mobius configurations with coupling coefficients
variation for 50 mW, 60 mW, 70 mW, 80 mW, 90 mW,
and 100 mW
157
xvi
5.28
5.29
5.30
The output port optical power versus the input power for
All-pass, Add-drop, and PANDA types MRR
configuration
165
The switching operation of optical bistability hysteresis
loop using All-pass Mobius MRR configuration
166
Optical bistability from the simulated All-pass Mobius
MRR, experimental data of conventional All-pass MRR,
and finite-element-method (FEM) simulation of single
MRR system.
169
xvii
LIST OF ABBREVIATIONS
MRR
-
Microring Resonator
FDTD
-
Finite-Different-Time-Domain
SPR
-
Surface Palsmon Resonance
VCSEL
-
Vertical Cavity Surface Emitting Laser
EDF-FBG
-
Erbium Doped Fiber-Fiber Bragg Grating
FBG
-
Fiber Bragg Grating
SMFPLD
-
Single Mode of Fabry Perot Laser Diode
EIR
-
Induced Reflection Effect
WGM
-
Whispering Gallery Mode
NLC
-
Nematic Liquid Crystal
PHI
-
Photo Induced Isotropic
ICP
-
Inductively Plasma Coupled
SEM
-
Scanning Electron Microscopy
All-pass M
-
All-pass Mobius
Add-drop M
-
Add-drop Mobius
PANDA M
-
PANDA Mobius
xviii
LIST OF SYMBOLS
ε0
-
Electric vacuum permittivity
χ
-
Electric susceptibility
α
-
Attenuation loss
P
-
Polarization
PNL
-
Nonlinear polarization
c
-
Speed of light
n
-
Internal refractive index
ω0
-
Angular frequency
E
-
Electric field
Po
-
Nonlinear angular frequency
t
-
Propagation time
Χ(i)
-
ith order of susceptibility
χeff
-
Effective susceptibility
n0
-
Linear refractive index
k0
-
Wavenumber
L
-
Propagation length
I
-
Intensity
𝜙L
-
Linear phase shift
𝜙NL
-
Nonlinear phase shift
λ
-
Wavelength
β
-
Propagation constant
T
-
Pulse propagation time
vg
-
Group velocity
β2
-
Group velocity dispersion parameter
ΔT
-
Pulse spreading time
LD
-
Dispersion length
xix
T0
-
Pulse width
A
-
Pulse amplitudes
a(t,z)
-
Pulse envelope
f(x,y)
-
Spatial structure of optical field
β(ω)
-
Phase constant
βnl
-
Nonlinear phase constant
βl
-
Linear phase constant
Io
-
Pulse propagation time
z
-
Pulse propagation distance in z direction
LNL
-
Nonlinear length
η0
-
Wave impedance
In
-
Current amplitude
N
-
Number of ladder circuit
L’
-
Inductance
C’
-
Capacitance
M
-
Mutual impedance
k
-
Wavevector
n2’
-
Waveguide 2 refractive index
n1
-
Waveguide 1 refractive index
μo
-
Vacuum permeability
S1
-
Complex amplitude
u
-
Wave amplitude function
C21
-
Coupling coefficient waveguide 1 to 2
iS
-
Cross coupling parameter
C
-
Self-coupling parameter
T’
-
Transmission coefficient
R’
-
Reflection coefficient
𝜙H
-
High negative detuning
𝜙L
-
Low negative detuning
𝜙0
-
Centre detuning
κi
-
Coupling coefficient at coupling region i
n2
-
Nonlinear index
Aeff
-
Effective area
xx
Ei
-
Electric field at i position
Eim
-
Electric field at i position for Mobius resonator
ξi
-
Phase shift for i radius
𝛾i
-
Propagation loss at coupling region i
Aeff
-
Effective area
xxi
LIST OF APPENDICES
APPENDIX
TITLE
PAGE
A
All-pass and All-pass Mobius Coding
184
B
Add-drop and Add-drop Mobius Coding
192
C
PANDA and PANDA Mobius Coding
197
D
Threshold Determination Graph
208