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1 Introduction" ^9 {9 H; _% ^7 x3 M9 \
1.1 Photonics: the countless possibilities of light propagation
0 E& f( [( ~5 V1 t; d1.2 Modelling photonics
! s$ A$ K# H w2 Full-vectorial Beam Propagation Method
6 Y; g9 L: e% G; k2.1 Introduction7 c% L4 M: g9 c1 \2 ]
2.2 Overview of the beam propagation methods F* f+ s7 A+ R2 y
2.3 Maxwell’s Equations3 c: w0 L1 O9 G
2.4 Magnetic field formulation of the wave equation b, }# ?9 H4 m- g2 U* T
2.5 Electric field formulation of the wave equation$ L, m0 f$ N/ `4 e
2.6 Perfectly-Matched Layer( I" I. x3 P% j" q( X
2.7 Finite Element Analysis$ Z5 X& b9 B1 Q6 T9 u6 X4 [
2.8 Derivation of BPM Equations
' S6 [& C; t" ?2.9 Imaginary-Distance BPM: Mode Solver
$ r0 u$ w5 x2 p ]7 C' k3 Assessment of Full-Vectorial Beam Propagation Method2 m; h, G6 t, ?( P& M& o
3.1 Introduction& g$ I( o+ a. ]. Q
3.2 Analysis of Rectangular waveguide! ]( z2 b2 k0 b4 C/ w1 ]0 J# ^
3.3 Photonic Crystal Fibre6 X) q' Z, E- S8 @
3.4 Liquid Crystal Based Photonic Crystal Fibre
5 j6 ~; e7 e0 h3.5 Electro-optical Modulators
) b# N0 X. a/ W9 k5 h( D3.6 Switches
& W( b# @# j% O: T4 Bidirectional Beam Propagation Method
2 @4 g# }6 J* r! Y5 u. [4.1 Introduction
$ _6 D1 M1 ^8 ^% S- L4.2 Optical Waveguide Discontinuity Problem
' B2 L% O" I# ~; D4.3 Finite element analysis of discontinuity problems$ N+ b G1 m# i. W- T4 U, `
4.4 Derivation of Finite Element Matrices
" W2 x& _( ?/ o* L. z4.5 Application of Taylor’s Series Expansion7 d! j& b' S" f& h4 g' ?8 ]
4.6 Computation of Reflected, Transmitted and Radiation Waves
" }( f8 U1 |" i/ H4.7 Optical fiber-facet problem
( j X- I& b+ |6 v, R4.8 Finite element analysis of optical fiber facets
; m% |. Z6 g& d2 H0 ?) w4.9 Iterative analysis of multiple-discontinuities. u- @' ^0 V8 K4 G% H
4.10 Numerical assessment
6 y# t3 ]8 j. K8 A/ ^1 V5 Complex-Envelope Alternating-Direction-Implicit Finite Difference Time Domain Method with Assessment
& z1 W5 m+ o+ C9 Q6 O1 T; U8 S5.1 Introduction! z3 J# ]4 {. g6 N
5.2 Maxwell's equations: j' Q: S$ m* ^4 h
5.3 Brief history of Finite Difference Time Domain (FDTD) Method
# p& P& |' c+ [/ V1 {5.4 Finite Difference Time Domain (FDTD) Method9 R8 u' O1 q, s4 S- v& \) L( f2 q
5.5 -Direction-Implicit FDTD (ADI-FDTD): Beyond the Courant Limit8 U A1 S5 ?& i
5.6 Complex-Envelope ADI-FDTD (CE-ADI-2 r+ n; ~, T' ~0 L" N' I
5.7 Perfectly Matched Layer (PML) Boundary Conditions4 t D" \9 U, p a' X
5.8 Uniaxal Perfectly Matched Layer (UPML) Absorbing Boundary Condition
+ L. ?" |+ c) h7 ]5.9 PML Parameters
" e* H7 U+ w+ Q( ]5.10 PML Boundary Conditions for CE-ADI-FDTD
/ N4 r, Y7 J" t; C. ^( T5.11 PhC Resonant Cavities( R, d3 N/ }3 l' S- V# ^% @
5.12 5x5 Rectangular Lattice PhC Cavity
) B# _9 d; `5 T/ ~5.13 Triangular Lattice PhC Cavity
; S9 J# ]" ?7 C/ g( R6 e9 G5.14 Wavelength Division Multiplexing
7 q N: w/ z9 V( P+ g( i0 b+ m9 |! E5.15 Conclusions/ r- G" y. d! W! g& \
6. Finite Volume time Domain (FVTD) Method- P/ k. [% K4 F
6.1 Introduction7 v# F3 s% y# b# ~( @# y0 f
6.2 Numerical analysis
# Z! E8 N% H4 o5 X6.3 UPWIND Scheme for the Calculation
5 y, S/ D' x/ `3 A# g" h o6.4 NON-DIFFUSIVE Scheme for the Flux Calculation
! X% b$ G) j7 W) b: Q9 ]. p. d6.5 2D Formulation of the FVTD Method
# j9 l- T6 W2 b# m1 M; n; x6.6 Boundary Conditions
8 v6 S4 s+ \( O! E/ {9 l6 h, E9 ~/ h6.7 Nonlinear Optics
& V6 M8 s2 I& ?3 z+ N0 f6.8 Nonlinear Optical Interactions6 a% K3 ?7 _. v! ]6 n
6.9 Extension of the FDTD Method to Nonlinear Problems
8 A4 ^, |: O% m7 F7 ?6.10 Extension of the FVTD Method to Nonlinear Problems3 |- v1 w( I4 i" T- [; d4 X
6.11 Conclusions
5 \# A! {, \9 b1 ?1 b8 E4 t# K: U7 Numerical Analysis of Linear and Nonlinear PhC Based Devices: d# R2 M# B' d, c! K# i. B' i
7.1 Introduction! A) N( \$ e) k" I- u& i* i# ?
7.2 FVTD Method Assessment: PhC Cavity
1 j0 V. q$ S0 U/ |% p1 n7.3 FVTD Method Assessment: PhC Waveguide( W6 Y: n3 }4 H- M$ o. f9 k- |, `
7.4 FVTD Method Assessment: PBG T-Branch
3 a( t, e% O; L$ I) P, U4 l9 M) h1 d7.5 PhC Multimode Resonant Cavity9 L- }0 R8 C2 k q7 {
7.6 FDTD Analysis of Nonlinear Devices
" \. D+ x- j4 o7.7 FVTD Analysis of Nonlinear Photonic Crystal Wires
( `: Y1 [: W7 ^7 J8 g7.8 Conclusions
( z$ h% j% E v0 }5 f: s8 Multiresolution Time Domain3 p6 H& u5 z# [) Q2 v
8.1 Introduction: k3 G9 y6 v" h& l0 u; t( y
8.2 MRTD basics
7 B% _$ ~4 d6 o" c2 ^. a8 l8.3 MRTD update scheme
3 `1 N2 y2 x6 ^: Q% b$ {3 v8.4 Scaling-MRTD
m" P( N5 _1 g: Q7 ?, O- F/ G8.5 Conclusions
: d& N+ ?% s. s0 [7 Y9 MRTD Analysis of PhC-Devices: }0 [' S2 r: S0 U B/ l. v' K
9.1 Introduction8 D0 `$ J. K* [5 U5 {
9.2 UPML-MRTD: test and code validation
! O s* R# g8 a4 H! b5 h5 Q; n9.3 MRTD vs FDTD for the analysis of linear photonic crystals
. w' U! W6 h6 O X9.4 Conclusions
, P8 }7 Z. [. M1 d% x2 y7 x10 MRTD Analysis of SHG PhC-Devices, E: _) r& u5 W" y
10.1 Introduction
- f* }8 Z, h8 I2 L# W10.2 Second harmonic generation in optics9 a g3 x4 y7 e) F. B
10.3 Extended S-MRTD for SHG analysis: [+ i: w8 @5 D5 B i" ~# Q
10.4 SHG in PhC-waveguide
! f7 b# F% P; B% T3 H0 |8 i7 @! ?10.5 Selective SHG in compound PhC-based structures
3 N, F- {/ j( _% U10.6 New design for selective SHG: PhC-microcavities coupling
- h7 |$ |4 j [& K10.7 Conclusions& U1 R& x: V- T n
11 Dispersive Nonlinear MRTD for SHG Applications
, e8 c) u* }7 e; n# |1 [' m* T11.1 Introduction# a. w; {1 U9 {3 i
11.2 Dispersion analysis
3 b: e. t2 }* W( @6 O& R. O11.3 SHG-MRTD scheme for dispersive materials5 c* R, t5 ]) S6 _: R5 s
11.4 Simulation results
9 K! _: {5 T$ n) F# w& K. S( _11.5 Conclusions |
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