Computational Photonics

Professor Salah Obayya, University of Glamorgan, UK Salah Obayya received a BSc in Electronics and Communications Engineering from Mansoura University, Egypt in 1991. Between Oct 1991 and Sept 1996 he worked as an Engineer with the Telecommunications Authority, Egypt. In September 1996, Obayya joined the Department of Electrical, Electronic and Information Engineering, City University London to study for his PhD, in which he developed a novel finite element based full vectorial beam propagation algorithm for the analysis of various photonic devices. Following his PhD, and from Jan 2000 to June 2003, Obayya worked as a Senior Research Fellow at the School of Engineering, City University London. In June 2003, he joined the School of Engineering and Design, Brunel University, UK as a Lecturer, and subsequently became a Senior Lecturer in Oct. 2005. In Sept. 2006 Obayya joined Swansea University as a Reader and moved on to the University of Leeds in July 2007. Obayya is currently Full Professor and Chair in Photonics at the University of Glamorgan where he leads the "Photonics Research Group".

1 Introduction 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