Computational Photonics

1.1 Photonics: the countless possibilities of light propagation

1.2 Modelling photonics

2 Full-vectorial Beam Propagation Method

2.1 Introduction

2.2 Overview of the beam propagation methods

2.3 Maxwell’s Equations

2.4 Magnetic field formulation of the wave equation

2.5 Electric field formulation of the wave equation

2.6 Perfectly-Matched Layer

2.7 Finite Element Analysis

2.8 Derivation of BPM Equations

2.9 Imaginary-Distance BPM: Mode Solver

3 Assessment of Full-Vectorial Beam Propagation Method

3.1 Introduction

3.2 Analysis of Rectangular waveguide

3.3 Photonic Crystal Fibre

3.4 Liquid Crystal Based Photonic Crystal Fibre

3.5 Electro-optical Modulators

3.6 Switches

4 Bidirectional Beam Propagation Method

4.1 Introduction

4.2 Optical Waveguide Discontinuity Problem

4.3 Finite element analysis of discontinuity problems

4.4 Derivation of Finite Element Matrices

4.5 Application of Taylor’s Series Expansion

4.6 Computation of Reflected, Transmitted and Radiation Waves

4.7 Optical fiber-facet problem

4.8 Finite element analysis of optical fiber facets

4.9 Iterative analysis of multiple-discontinuities

4.10 Numerical assessment

5 Complex-Envelope Alternating-Direction-Implicit Finite Difference Time Domain Method with Assessment

5.1 Introduction

5.2 Maxwell's equations

5.3 Brief history of Finite Difference Time Domain (FDTD) Method

5.4 Finite Difference Time Domain (FDTD) Method

5.5 -Direction-Implicit FDTD (ADI-FDTD): Beyond the Courant Limit

5.6 Complex-Envelope ADI-FDTD (CE-ADI-

5.7 Perfectly Matched Layer (PML) Boundary Conditions

5.8 Uniaxal Perfectly Matched Layer (UPML) Absorbing Boundary Condition

5.9 PML Parameters

5.10 PML Boundary Conditions for CE-ADI-FDTD

5.11 PhC Resonant Cavities

5.12 5x5 Rectangular Lattice PhC Cavity

5.13 Triangular Lattice PhC Cavity

5.14 Wavelength Division Multiplexing

5.15 Conclusions

6. Finite Volume time Domain (FVTD) Method

6.1 Introduction

6.2 Numerical analysis

6.3 UPWIND Scheme for the Calculation

6.4 NON-DIFFUSIVE Scheme for the Flux Calculation

6.5 2D Formulation of the FVTD Method

6.6 Boundary Conditions

6.7 Nonlinear Optics

6.8 Nonlinear Optical Interactions

6.9 Extension of the FDTD Method to Nonlinear Problems

6.10 Extension of the FVTD Method to Nonlinear Problems

6.11 Conclusions

7 Numerical Analysis of Linear and Nonlinear PhC Based Devices

7.1 Introduction

7.2 FVTD Method Assessment: PhC Cavity

7.3 FVTD Method Assessment: PhC Waveguide

7.4 FVTD Method Assessment: PBG T-Branch

7.5 PhC Multimode Resonant Cavity

7.6 FDTD Analysis of Nonlinear Devices

7.7 FVTD Analysis of Nonlinear Photonic Crystal Wires

7.8 Conclusions

8 Multiresolution Time Domain

8.1 Introduction

8.2 MRTD basics

8.3 MRTD update scheme

8.4 Scaling-MRTD

8.5 Conclusions

9 MRTD Analysis of PhC-Devices

9.1 Introduction

9.2 UPML-MRTD: test and code validation

9.3 MRTD vs FDTD for the analysis of linear photonic crystals

9.4 Conclusions

10 MRTD Analysis of SHG PhC-Devices

10.1 Introduction

10.2 Second harmonic generation in optics

10.3 Extended S-MRTD for SHG analysis

10.4 SHG in PhC-waveguide

10.5 Selective SHG in compound PhC-based structures

10.6 New design for selective SHG: PhC-microcavities coupling

10.7 Conclusions

11 Dispersive Nonlinear MRTD for SHG Applications

11.1 Introduction

11.2 Dispersion analysis

11.3 SHG-MRTD scheme for dispersive materials

11.4 Simulation results

11.5 Conclusions