vii
TABLE OF CONTENTS
CHAPTER
1
2
TITLE
PAGE
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENTS
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
x
LIST OF FIGURES
xi
LIST OF SYMBOLS
xvi
LIST OF APPENDICES
xix
INTRODUCTION
1
1.1
Background of Study
1
1.2
Problem Statement
5
1.3
Objectives of the Study
6
1.4
Research Scope
6
1.5
Significance of the Research
7
LITERATURE REVIEW
9
2.1
Introduction
9
2.2
Historical background
9
2.3
Optical trapping
10
2.4
Ring Resonators
19
viii
3
THEORY
25
3.1
Introduction
25
3.2
Physics of optical tweezers
25
3.3
Types of optical trapping
28
3.3.1 Mie regime
29
3.3.2 Complex region
29
3.3.3 Rayleigh regime
30
3.4
Nonlinearities in optical fibers
36
3.5
Nonlinear response from Kerr effects
37
3.6
Self-phase Modulation
41
3.7
Temporal Soliton
42
3.8
Pulse propagation on optical fiber
44
3.9
Coupled-mode waveguide
46
3.10
Microring resonator
53
3.11
Z-Transform method for single Microring
Resonator configuration
4
54
RESEARCH METHODOLOGY
59
4.1
Introduction
59
4.2
Analytical formulation
60
4.2.1 PANDA ring resonator
60
4.2.2 Double PANDA ring resonator
64
Modelling consideration
73
4.3.1 Introduction
73
4.3.2 Iterative method for single ring
74
4.3
4.3.3 Iterative method for serially-coupled
double ring
5
75
4.3.4 PANDA ring resonator model
76
4.3.5 Double PANDA ring resonator model
80
RESULTS AND DISCUSSION
84
5.1
Introduction
84
5.2
Optical tweezers generated by PANDA
ix
ring resonator system
85
5.3
Coupling coefficients 1 and 2
88
5.4
Coupling coefficients 3 and 4
93
5.5
Ring radii R, RR and RL
98
5.6
Optimized tweezers signals from PANDA
configuration
5.7
Optical trapping by tweezers signals generated
from PANDA system
5.8
103
Optical tweezers generated by double PANDA
ring resonator system
111
5.9
Coupling coefficients 5 and 6
113
5.10
Ring radii R3 and R4
117
5.11
Optimized tweezers signals from double PANDA
configuration
5.12
119
Optical trapping by tweezers signals generated
from double PANDA system
6
102
120
CONCLUSION
126
6.1
Conclusion
126
6.2
Future Work
127
REFERENCES
128
Appendices A-D
143-171
x
LIST OF TABLES
TABLE NO.
5.1
TITLE
PAGE
List of input intensity, output intensity and corresponding
gradient and scattering force components of optical
tweezers signals generated from PANDA system
5.2
108
List of input intensity, output intensity and corresponding
gradient and scattering force components of tweezers
signals generated from double PANDA system
123
xi
LIST OF FIGURES
FIGURE NO.
2.1
TITLE
PAGE
Photograph of different ring resonators configurations
(a) serially coupled double ring (b) serially coupled
triple ring (c) parallel coupled triple ring resonators
3.1
Force vector diagram of a transparent sphere illuminated by
a parallel beam of light with Gaussian intensity profile
3.2
22
27
Light scattering due to dipole moment induced by the
incident light ray
31
3.3
Coupling between two parallel waveguides
47
3.4
Ring resonators coupled to single bus waveguide
53
3.5
Schematic diagram of the light propagation within a
single microring fiber system
54
3.6
Diagram of light propagation within coupling region
55
3.7
Transmission spectrum of single ring resonator system at
throughput port with R=148 m
58
4.1
Schematic diagram of PANDA ring resonator configuration 61
4.2
Schematic diagram of right nanoring on PANDA ring
resonator configuration
62
xii
4.3
Schematic diagram of double PANDA ring resonator
configuration
4.4
Schematic diagram of right nanorings on double
PANDA ring resonator configuration
4.5
82
Procedure to investigate dynamical behaviours of
generated tweezers
5.1
79
Flow chart of simulation/modelling activity for Double
PANDA ring resonator
4.9
76
Flow chart of simulation/modelling activity for PANDA
ring resonator
4.8
70
Schematic diagram of serially coupled double ring
resonator system
4.7
67
Schematic diagram of left nanorings on double
PANDA ring resonator configuration
4.6
65
83
Optical tweezers signals generated by using PANDA system
where (a) input pulse, (b) control signal, (c) to (f) are
circulated signals, (g) throughput and (h) drop port signals
5.2
Results from PANDA ring resonator with different 1
ranging from 0.15, 0.2 to 0.25 and 2 is fixed at 0.1
5.3
90
Output intensity at throughput port, It plotted against 1
and 2 in 3 dimensions for PANDA configuration
5.5
89
Results from PANDA ring resonator with different 2
ranging from 0.75, 0.8 to 0.85 and 1 is fixed at 0.75
5.4
86
91
Output intensity at drop port, Id plotted against 1 and 2
in 3 dimensions for PANDA configuration
92
xiii
5.6
Output tweezers generated at (a) throughput and (b)
drop port of PANDA system with coupling coefficient
3 varies 0.10, 0.15, 0.20, 0.25 and 0.30
5.7
95
Output tweezers generated at (a) throughput and (b)
drop port of PANDA system with coupling coefficient 4
varies 0.10, 0.15, 0.20, 0.25 and 0.30
5.8
96
Peak intensity of the output tweezers signals recorded at
drop port corresponding to values of 3 and 4 ranging
from 0 to 1
5.9
97
Optical tweezers signals generated from different values
of ring radius R recorded at (a) throughput and (b)
drop port of PANDA system
5.10
99
Optical tweezers signals generated from different values
of ring radius RR and RL collected at (a) throughput and
(b) drop port of PANDA system
5.11
Simulation results of tuneable and amplified tweezers
signals generated from PANDA ring resonator
5.12
101
102
Gradient (Fg) and scattering (Fs) force components acting
on gold nanoparticles as a function of axial position at four
different diameters of (a) 5 nm, (b) 10 nm, (c) 15 nm
and (d) 20 nm respectively
5.13
Trapping forces including gradient (Fg) and scattering (Fs)
components as a function of particle size
5.14
102
105
Optical trap stiffness (K) plotted against radius of gold
nanoparticles in water immersion
107
xiv
5.15
Gradient forces, Fg produced from PANDA and multiple
lens systems plotted as a function of input intensity within
the range of 1 to 2 W/m2
5.16
110
Scattering force, Fs produced from PANDA and multiple
lens systems plotted as a function of input intensity within
the range of 1 to 2 W/m2
5.17
110
Optical tweezers signals generated from double PANDA
system where (a) I1, (b) I2, (c) I3 and (d) I4 are circulated
fields while output signals depicted in (e) It and (f) Id
respectively
5.18
112
Output tweezers generated at (a) throughput and (b) drop
port of double PANDA system with 5 varies at 0.10,
0.15, 0.20, 0.25 and 0.30
5.19
114
Output tweezers generated at (a) throughput and (b) drop
port of double PANDA system with 6 varies at 0.25,
0.30, 0.35, 0.40 and 0.45
5.20
115
Peak intensity of the output tweezers signals recorded at
drop port of double PANDA ring resonator system with
respect to coupling coefficients 5 and 6
5.21
116
Optical tweezers signals with different values of ring
radius R3 and R4 generated at (a) throughput and (b)
drop port of the system
5.22
Simulation results of tuneable and amplified tweezers
signals generated from double PANDA ring resonator
5.23
118
119
Gradient (Fg) and scattering (Fs) force components acting
on gold nanoparticles as a function of axial position for
four different diameters of (a) 5 nm, (b) 10 nm, (c) 15 nm
and (d) 20 nm respectively
121
xv
5.24
Trapping forces including gradient (Fg) and scattering (Fs)
components plotted as a function of particle size for
double PANDA system
5.25
Optical trap stiffness (K) plotted against radius of gold nano
particles in water immersion for double PANDA system
5.26
122
122
Gradient forces, Fg produced from double PANDA and
multiple lens systems plotted as a function of input
intensity within the range of 1 to 2 W/m2
5.27
125
Scattering forces, Fs produced from double PANDA and
multiple lens systems plotted as a function of input
intensity within the range of 1 to 2 W/m2
125
xvi
LIST OF SYMBOLS
a
-
Total loss coefficient of the ring waveguide
α
-
Attenuation loss
A
-
Cross sectional area of fiber
Au
-
Aurum
β
-
Unperturbed propagation constant
B
-
Buildup factor
c
-
Speed of light in vacuum
ʗ
-
Coupling constant
Cscat
-
Scattering cross section parameter
CMT
-
Coupled mode theory
d
-
Diameter of the trapped particle
dB
-
Decibel
D
-
Group delay dispersion
E
-
Electric fields
Ein
-
Input signal at input-port
Eadd
-
Control signal at add-port
Et
-
Output signal at throughput-port
Ed
-
Output signal at drop-port
εcore
-
Dielectric constant core fiber
εcladding
-
Dielectric constant cladding fiber
εij
-
Relative permittivity (dielectric constant)
εo
-
Vacuum permittivity
εm
-
Dielectric constant of surrounding medium
εn
-
Dielectric constant of particle
F
-
Finesse
Fs
-
Scattering force
Fg
-
Gradient force
fo
-
Incident frequency
xvii
FSR
-
Free spectral range
FWHM
-
Full width at half maximum
GVD
-
Group velocity dispersion
h
-
Planck’s constant
I
-
Intensity
IDRI
-
Intensity-dependent refractive index
k
-
Wavenumber
km
-
Wavenumber of surrounding medium

-
Coupling coefficient
K
-
Trap stiffness
L
-
Circumference length of center ring
LR
-
Circumference length of the right ring
LL
-
Circumference length of the left ring
m
-
Integer mode number
mo
-
Complex refractive index
n1
-
Real part of refractive index
n2
-
Imaginary part of refractive index
ncore
-
Refractive index of core fiber
ncladding
-
Refractive index of cladding
p
-
Linear momentum
ρ
-
Electric dipole moment
ρf
-
Free charge densities
P
-
Power/Polarizability
PL
-
Linear polarization component
PNL
-
Nonlinear polarization component
Pin
-
Input power
Pout
-
Output power
Q
-
Quality factor
+q
-
Positive charge
-q
-
Negative charge
r
-
Radius of particle
R
-
Radius of center ring
RR
-
Radius of right nanoring
RL
-
Radius of left nanoring
xviii
<S>
-
Time average poynting vector
SHG
-
Second harmonic generation
SPM
-
Self-phase modulation
t
-
Time

-
Pulse duration
T
-
Transmission coefficient
o
-
Vacuum permeability
V
-
Volume
W
-
Watt
ω
-
Angular frequency
x
-
Particle’s displacement
χ
-
Electric susceptibility tensor
XPM
-
Cross-phase modulation
γ
-
Intensity insertion loss coefficient
z-1
-
Z-transform parameter
λ
-
Wavelength
λo
-
Wavelength in free space
∆β1/2
-
Perturbation of propagation constant
∆n
-
Change in refractive index
θ1
-
Angles of incidence
θ2
-
Angles of refraction
ϕ
-
Phase
xix
LIST OF APPENDICES
APPENDIX
TITLE
PAGE
A
Solution of NLSE
143
B
MATLAB R2010a Program: PANDA Ring Resonator
Model
155
MATLAB R2010a Program: Double PANDA Ring
Resonator Model
162
Publications
169
C
D