Computational Photonics

1 Introduction1.1 Photonics: the countless possibilities of light propagation1.2 Modelling photonics2 Full-vectorial Beam Propagation Method2.1 Introduction2.2 Overview of the beam propagation methods2.3 Maxwell's Equations2.4 Magnetic field formulation of the wave equation2.5 Electric field formulation of the wave equation2.6 Perfectly-Matched Layer2.7 Finite Element Analysis2.8 Derivation of BPM Equations2.9 Imaginary-Distance BPM: Mode Solver3 Assessment of Full-Vectorial Beam Propagation Method3.1 Introduction3.2 Analysis of Rectangular waveguide3.3 Photonic Crystal Fibre3.4 Liquid Crystal Based Photonic Crystal Fibre3.5 Electro-optical Modulators3.6 Switches4 Bidirectional Beam Propagation Method4.1 Introduction4.2 Optical Waveguide Discontinuity Problem4.3 Finite element analysis of discontinuity problems4.4 Derivation of Finite Element Matrices4.5 Application of Taylor's Series Expansion4.6 Computation of Reflected, Transmitted and Radiation Waves4.7 Optical fiber-facet problem4.8 Finite element analysis of optical fiber facets4.9 Iterative analysis of multiple-discontinuities4.10 Numerical assessment5 Complex-Envelope Alternating-Direction-Implicit Finite Difference Time Domain Method with Assessment5.1 Introduction5.2 Maxwell's equations5.3 Brief history of Finite Difference Time Domain (FDTD) Method5.4 Finite Difference Time Domain (FDTD) Method5.5 -Direction-Implicit FDTD (ADI-FDTD): Beyond the Courant Limit5.6 Complex-Envelope ADI-FDTD (CE-ADI-5.7 Perfectly Matched Layer (PML) Boundary Conditions5.8 Uniaxal Perfectly Matched Layer (UPML) Absorbing Boundary Condition5.9 PML Parameters5.10 PML Boundary Conditions for CE-ADI-FDTD5.11 PhC Resonant Cavities5.12 5x5 Rectangular Lattice PhC Cavity5.13 Triangular Lattice PhC Cavity5.14 Wavelength Division Multiplexing5.15 Conclusions6. Finite Volume time Domain (FVTD) Method6.1 Introduction6.2 Numerical analysis6.3 UPWIND Scheme for the Calculation6.4 NON-DIFFUSIVE Scheme for the Flux Calculation6.5 2D Formulation of the FVTD Method6.6 Boundary Conditions6.7 Nonlinear Optics6.8 Nonlinear Optical Interactions6.9 Extension of the FDTD Method to Nonlinear Problems6.10 Extension of the FVTD Method to Nonlinear Problems6.11 Conclusions7 Numerical Analysis of Linear and Nonlinear PhC Based Devices7.1 Introduction7.2 FVTD Method Assessment: PhC Cavity7.3 FVTD Method Assessment: PhC Waveguide7.4 FVTD Method Assessment: PBG T-Branch7.5 PhC Multimode Resonant Cavity7.6 FDTD Analysis of Nonlinear Devices7.7 FVTD Analysis of Nonlinear Photonic Crystal Wires7.8 Conclusions8 Multiresolution Time Domain8.1 Introduction8.2 MRTD basics8.3 MRTD update scheme8.4 Scaling-MRTD8.5 Conclusions9 MRTD Analysis of PhC-Devices9.1 Introduction9.2 UPML-MRTD: test and code validation9.3 MRTD vs FDTD for the analysis of linear photonic crystals9.4 Conclusions10 MRTD Analysis of SHG PhC-Devices10.1 Introduction10.2 Second harmonic generation in optics10.3 Extended S-MRTD for SHG analysis10.4 SHG in PhC-waveguide10.5 Selective SHG in compound PhC-based structures10.6 New design for selective SHG: PhC-microcavities coupling10.7 Conclusions11 Dispersive Nonlinear MRTD for SHG Applications11.1 Introduction11.2 Dispersion analysis11.3 SHG-MRTD scheme for dispersive materials11.4 Simulation results11.5 Conclusions