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1 Introduction0 b) O7 @5 K2 Y$ [' s& d: g
1.1 Photonics: the countless possibilities of light propagation
( s! c0 ]' T T, c1.2 Modelling photonics& d% N; d0 F# E* Z; ?" u0 ~
2 Full-vectorial Beam Propagation Method1 P- t% F2 q2 ]
2.1 Introduction2 k% {$ F! q* R* E
2.2 Overview of the beam propagation methods1 }' Z8 E8 M/ K n- ~( r
2.3 Maxwell’s Equations1 n' |) r* B4 O2 S2 F
2.4 Magnetic field formulation of the wave equation
0 D ?, l6 r6 v( R1 x( m2.5 Electric field formulation of the wave equation |3 i) x8 R) o* w* U8 u3 b
2.6 PeRFectly-Matched Layer
0 |# j6 u4 y& F2.7 Finite Element Analysis
9 M' _: K' n& q, W% |+ u4 G2.8 Derivation of BPM Equations" S. f1 A- L& E$ Z, `" ^* m, e
2.9 Imaginary-Distance BPM: Mode Solver$ ^, L& I. q& I: A/ k* v
3 Assessment of Full-Vectorial Beam Propagation Method4 s) n" b6 |+ L* K* r
3.1 Introduction
" C' v7 W% u& P5 P+ N3.2 Analysis of Rectangular waveguide
, l0 W1 B5 e3 `' y! ?8 i3.3 Photonic Crystal Fibre" k a% `& [5 d3 e" {, Y
3.4 Liquid Crystal Based Photonic Crystal Fibre
3 k' \1 l A0 e4 u& x3.5 Electro-optical Modulators7 w( S( \$ w2 Z& A6 q6 ]9 N' ~
3.6 Switches4 [; W3 a! S3 J7 M2 C4 W
4 Bidirectional Beam Propagation Method
; h; Z C1 M+ D# N4.1 Introduction- r9 {) @; ]. A+ a( }( h# |* ~
4.2 Optical Waveguide Discontinuity Problem
2 R W/ A' \0 ^( ~+ {/ S3 c" q( W9 v6 }4.3 Finite element analysis of discontinuity problems, R1 ^! K1 c. N& g& S1 `& {
4.4 Derivation of Finite Element Matrices
% G7 E3 S( B+ ]7 _" D4.5 Application of Taylor’s Series Expansion/ U6 J& \8 w- o5 B4 q
4.6 Computation of Reflected, Transmitted and Radiation Waves
. ?. B7 i0 D. Y0 y; C$ d4.7 Optical fiber-facet problem& b) g: |. q* \, v
4.8 Finite element analysis of optical fiber facets
* S9 C( f4 f7 M) D, t7 b( O4.9 Iterative analysis of multiple-discontinuities8 ~$ B: X+ {3 G* u. o Q
4.10 Numerical assessment
0 j$ c- N7 z# t% _- S5 Complex-Envelope Alternating-Direction-Implicit Finite Difference Time Domain Method with Assessment) y7 {; c8 x* ]7 x' l! h
5.1 Introduction/ S& G! x" o+ M, H
5.2 Maxwell's equations
, v5 q/ ]$ t+ o! |5.3 Brief history of Finite Difference Time Domain (FDTD) Method, c A% J# l" p: `0 {
5.4 Finite Difference Time Domain (FDTD) Method4 U7 J; s6 j: L& a) J, r( p
5.5 -Direction-Implicit FDTD (ADI-FDTD): Beyond the Courant Limit* M1 E: `. A7 Q; W+ q0 }+ Q( X o
5.6 Complex-Envelope ADI-FDTD (CE-ADI-
$ r( \; n. c, {" Y5.7 Perfectly Matched Layer (PML) Boundary Conditions* m6 \0 J. z6 ?% ?& [
5.8 Uniaxal Perfectly Matched Layer (UPML) Absorbing Boundary Condition
$ V/ z3 u; j3 V3 o) j' Y* b) y4 E5.9 PML Parameters
: Q: b" g9 O! G2 q0 [5.10 PML Boundary Conditions for CE-ADI-FDTD
( g* [' n6 S" L+ Z0 o5 q5.11 PhC Resonant Cavities7 u' U3 Y, a P( K M9 z2 W6 a
5.12 5x5 Rectangular Lattice PhC Cavity+ _$ |8 G+ o# S4 U2 K3 Y6 X
5.13 Triangular Lattice PhC Cavity+ V5 R* i! o& l4 S
5.14 Wavelength Division Multiplexing1 w3 D5 Q, [3 Z i( ?
5.15 Conclusions+ w' }5 K6 K# Q3 i$ N5 h' t8 ]6 j
6. Finite Volume time Domain (FVTD) Method
/ |3 e% H' ?8 V% T/ o4 ~& K6.1 Introduction
6 l- l! _/ j/ s* c6.2 Numerical analysis
u' ^1 J$ {: G8 i5 M+ ?6.3 UPWIND Scheme for the Calculation
9 O6 o) ?( J+ O3 e: V6.4 NON-DIFFUSIVE Scheme for the Flux Calculation
) ~5 J0 s; G5 T' [* f7 k/ z" a6.5 2D Formulation of the FVTD Method1 F8 ]6 k0 a0 b. ]' c! d( @
6.6 Boundary Conditions
5 I b( |% r+ \8 a1 l# ]# U6.7 Nonlinear Optics. t) y, s% Y$ ^8 y4 Y
6.8 Nonlinear Optical Interactions/ v- a# J, _- a; I! B+ ]
6.9 Extension of the FDTD Method to Nonlinear Problems
( U* v; n4 d! ^( v+ o3 C, ~0 }6.10 Extension of the FVTD Method to Nonlinear Problems
' X1 `5 X {. H5 t0 \) L# @6.11 Conclusions! y% L0 D$ O/ f4 v% K
7 Numerical Analysis of Linear and Nonlinear PhC Based Devices
9 H. d8 }7 Z4 Q2 s7.1 Introduction
6 E+ \$ H C2 [& m0 H Y7.2 FVTD Method Assessment: PhC Cavity/ z) I8 s# d! j7 c, w0 r& l
7.3 FVTD Method Assessment: PhC Waveguide; Y$ ^! _7 ?. L% G) }+ z9 |8 t
7.4 FVTD Method Assessment: PBG T-Branch" Q/ |0 b- O( t) h- V4 \' p$ G
7.5 PhC Multimode Resonant Cavity
; V5 [2 E% a- }! z7.6 FDTD Analysis of Nonlinear Devices
+ }& R, Z1 p+ s& H2 T6 a6 K3 F7.7 FVTD Analysis of Nonlinear Photonic Crystal Wires( P& S6 y6 ~/ E; R
7.8 Conclusions& u8 V2 G% m) n4 J9 n: h& r
8 Multiresolution Time Domain% ~) K. m7 D4 p, _
8.1 Introduction4 d/ o- A6 H3 ~; j) q
8.2 MRTD basics. W3 D# A- Y f; D, P3 i
8.3 MRTD update scheme3 P1 H. N' M2 o- H8 E
8.4 Scaling-MRTD" N; m7 C8 ?9 ^+ P! m
8.5 Conclusions+ K K: z5 {. M/ T( G9 ]
9 MRTD Analysis of PhC-Devices
' ~5 C( c" Q4 p9 @( P- `1 P6 y; k7 J9.1 Introduction, N' ?4 { G5 {5 I d# M" J: u& s
9.2 UPML-MRTD: test and code validation8 G8 A" @" |' y) o9 K, l! M/ d
9.3 MRTD vs FDTD for the analysis of linear photonic crystals$ w" [4 r! b2 n
9.4 Conclusions
# r3 Z; S1 Y+ X9 }( Q9 Y10 MRTD Analysis of SHG PhC-Devices
2 `6 U: X$ V0 y7 t+ `- z10.1 Introduction) R4 G3 m* h2 y4 M
10.2 Second hARMonic generation in optics
, O! V. n ~1 \ f; X0 F# `10.3 Extended S-MRTD for SHG analysis( S6 R( k$ Y4 E
10.4 SHG in PhC-waveguide) m9 n" I; c, N4 n. [* h
10.5 Selective SHG in compound PhC-based structures/ F. k% L6 ?9 t+ N, e! p
10.6 New design for selective SHG: PhC-microcavities coupling" q+ F( g6 g- x ~! {
10.7 Conclusions0 A8 [* s* j8 n0 {
11 Dispersive Nonlinear MRTD for SHG Applications
* @; N3 g+ O% G2 A11.1 Introduction
- N$ m* R" X. m5 c* G9 t11.2 Dispersion analysis
# @) v6 D- H4 o! ]/ G0 e% F, B11.3 SHG-MRTD scheme for dispersive materials( @8 l+ Z* e: q' X3 _' l, P
11.4 Simulation results
0 _2 y" z/ H& y# o9 r# H# u: q11.5 Conclusions |
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