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1 Introduction
) R. X7 e/ [9 M/ a. a1.1 Photonics: the countless possibilities of light propagation
, {& n, @$ {( ]9 L! T2 Q1.2 Modelling photonics
" E# w( W& U' g6 a$ n$ F2 Full-vectorial Beam Propagation Method
9 D) s1 k( E) [0 H2.1 Introduction( a: h1 ?0 A/ _
2.2 Overview of the beam propagation methods
/ B; p9 h9 D( u1 z& a% ^* L! v2.3 Maxwell’s Equations
3 R* t+ C6 f) C3 q! n% C2.4 Magnetic field formulation of the wave equation* x0 D. V/ ?5 F5 g+ d
2.5 Electric field formulation of the wave equation, }. Q% ^( _5 ^* M5 b- l. T
2.6 Perfectly-Matched Layer
4 i9 L! F+ c) S/ [2.7 Finite Element Analysis
4 l0 p0 k" U& p9 C2.8 Derivation of BPM Equations. y+ B j/ d" Q, {3 y) a% [
2.9 Imaginary-Distance BPM: Mode Solver
6 D3 U2 l* P, [6 p1 G3 Assessment of Full-Vectorial Beam Propagation Method U6 ]# p; D, b" l& x6 f
3.1 Introduction0 p8 G5 e+ ]4 b
3.2 Analysis of Rectangular waveguide* Z e( J. \+ [2 [$ a2 p9 T
3.3 Photonic Crystal Fibre
( {! H" l! R, q; h4 R" a3.4 Liquid Crystal Based Photonic Crystal Fibre; ?1 W0 T, G- M( Z* ^1 U, G! S: Z
3.5 Electro-optical Modulators
# Q+ F/ }8 u* H4 o) w3.6 Switches! O+ ?4 ]3 p' S' b4 U
4 Bidirectional Beam Propagation Method h5 h/ f. u3 E, g: I$ z
4.1 Introduction. H* {% S0 ~( k# I$ W
4.2 Optical Waveguide Discontinuity Problem6 \. E4 p; j+ m7 t6 Y5 D' ]
4.3 Finite element analysis of discontinuity problems4 Z4 ]/ y1 _" y5 U8 h' h
4.4 Derivation of Finite Element Matrices
- d* B7 w' I* u( b/ }) d1 k4.5 Application of Taylor’s Series Expansion1 d( t0 A$ E% U& C
4.6 Computation of Reflected, Transmitted and Radiation Waves, c7 u8 q5 O8 V( f3 y
4.7 Optical fiber-facet problem
|0 }! N* L! J1 x) M% U: Y4.8 Finite element analysis of optical fiber facets! d! H& g4 P$ f% w9 ]4 |! i. f4 t
4.9 Iterative analysis of multiple-discontinuities
3 B. c$ M% |( S0 s$ x1 e1 H4.10 Numerical assessment
" l1 Y) E6 f+ g5 Complex-Envelope Alternating-Direction-Implicit Finite Difference Time Domain Method with Assessment q( X' h' S0 f/ b
5.1 Introduction
1 m# r+ j' A n+ T. ?5.2 Maxwell's equations
8 L. O) M7 d+ V: \3 }) e8 p, [5.3 Brief history of Finite Difference Time Domain (FDTD) Method `9 f: u% ]: }; I" u* }
5.4 Finite Difference Time Domain (FDTD) Method$ ~* d% F! o8 G5 I$ U1 {
5.5 -Direction-Implicit FDTD (ADI-FDTD): Beyond the Courant Limit
: H9 p7 V0 ?- C& m5.6 Complex-Envelope ADI-FDTD (CE-ADI-
% N' w% b6 U8 R' c, U% N5 @5.7 Perfectly Matched Layer (PML) Boundary Conditions
; \( `$ m$ W& p/ }5.8 Uniaxal Perfectly Matched Layer (UPML) Absorbing Boundary Condition
2 Q3 @6 t7 K# G) Z0 S, G5.9 PML Parameters% c0 n& \0 q7 y8 B
5.10 PML Boundary Conditions for CE-ADI-FDTD
/ G( V' O: g8 Y' T: e1 c# \/ l$ Z3 T5.11 PhC Resonant Cavities' M! J i- `) l; Y. F
5.12 5x5 Rectangular Lattice PhC Cavity
4 z0 c! |+ g/ i" ~; ]. x; U5.13 Triangular Lattice PhC Cavity8 | \: w. M% I9 M6 S( ]
5.14 Wavelength Division Multiplexing
5 m5 P4 Z* o# P+ m6 X% _6 ?5.15 Conclusions
B/ V6 a; N5 |1 D8 m) r; }6. Finite Volume time Domain (FVTD) Method- V3 C( x+ y) y9 [; {" R! C
6.1 Introduction* M7 `, x( u6 | f, S, }
6.2 Numerical analysis5 q7 X& e2 }3 \
6.3 UPWIND Scheme for the Calculation7 |2 [/ G2 t# _0 n+ I: {
6.4 NON-DIFFUSIVE Scheme for the Flux Calculation) m* L8 ]# S6 O
6.5 2D Formulation of the FVTD Method
- N6 I6 H6 E& W) C# u6.6 Boundary Conditions* `5 X; T' T8 |$ p8 s E8 R
6.7 Nonlinear Optics, d$ v! |3 M9 ]
6.8 Nonlinear Optical Interactions* |% u3 Z: r' q [! y" k _
6.9 Extension of the FDTD Method to Nonlinear Problems
, Z2 b9 I6 J" a# w. v6.10 Extension of the FVTD Method to Nonlinear Problems
7 m4 R+ |: c. n$ C# ]6.11 Conclusions5 z" D; P+ \9 }
7 Numerical Analysis of Linear and Nonlinear PhC Based Devices
2 V% ]& H3 |+ Z$ G0 Y3 F4 I5 {* @7.1 Introduction
8 K8 c# Q' A0 |/ k8 g7.2 FVTD Method Assessment: PhC Cavity
- T2 f* ^0 p. s& W' Z7.3 FVTD Method Assessment: PhC Waveguide
% d. X8 g) x0 V% q7.4 FVTD Method Assessment: PBG T-Branch
+ {! T x. R! G# S) }7.5 PhC Multimode Resonant Cavity
3 ? K% t: S! ^* H; x7.6 FDTD Analysis of Nonlinear Devices
- O( }! p8 z3 B2 i2 O7.7 FVTD Analysis of Nonlinear Photonic Crystal Wires
3 s8 _: u4 S& D; ?7.8 Conclusions
; S/ K* Y8 k/ x: y+ l' b! c3 O8 Multiresolution Time Domain# F5 z( g5 |9 Y. r; o
8.1 Introduction
/ x" Q( }' @/ |. s6 {8.2 MRTD basics
) w6 g# O4 y9 T5 \+ I8.3 MRTD update scheme
, C: v+ S9 y5 `. _8.4 Scaling-MRTD: I% f- P, `' v* S& a* K7 P! U
8.5 Conclusions
3 }/ @' n! q8 x2 E1 m9 MRTD Analysis of PhC-Devices; W9 Q4 D) i$ Y! |3 }7 n
9.1 Introduction6 H& n0 r @0 V$ X( b% j0 P) L
9.2 UPML-MRTD: test and code validation' k+ ` t' _; b' ?
9.3 MRTD vs FDTD for the analysis of linear photonic crystals* K& s* F- q5 E4 l( l& O6 V
9.4 Conclusions+ R0 _' P t3 M0 p4 R6 Y
10 MRTD Analysis of SHG PhC-Devices; n6 L6 E8 j* y( O9 {, X" U
10.1 Introduction
& @$ {' ^8 S& l0 h# J& K" T10.2 Second harmonic generation in optics% ?" w: |& N+ l4 L) a
10.3 Extended S-MRTD for SHG analysis8 g' `2 b/ T* f- g/ Y! z" Q" ~. ]5 W
10.4 SHG in PhC-waveguide
( i5 }, G c7 S3 V% U10.5 Selective SHG in compound PhC-based structures2 {' [* n" v* k2 k# z7 p) \" O4 i
10.6 New design for selective SHG: PhC-microcavities coupling
# {6 W @$ U, O0 A( j6 ]. N10.7 Conclusions
+ F7 R# U, Z( Z& E1 I, Q3 e11 Dispersive Nonlinear MRTD for SHG Applications
0 K- o: R* A2 \; ?11.1 Introduction8 ~8 }, Z& U$ G1 @
11.2 Dispersion analysis$ E7 a+ [: |% b' O: k
11.3 SHG-MRTD scheme for dispersive materials6 |9 ?! ~' i& u; z& F
11.4 Simulation results3 V0 w( k; M* b* i2 E3 _- N
11.5 Conclusions |
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