Computational Photonics

This book explores the state-of-the art in computational modelling techniques for photonic devices In this book, the author provides a comprehensive coverage of modern numerical modelling techniques for designing photonic devices for use in modern optical telecommunications systems. In addition the book presents the state-of-the-art in computational photonics techniques, covering methods such as full-vectorial finite-element beam propagation, bidirectional beam propagation, complex-envelope alternative direction implicit finite difference time domain, multiresolution time domain, and finite volume time domain. The book guides the reader through the concepts of modelling, analysing, designing and optimising the performance of a wide range of photonic devices by building their own numerical code using these methods. Key Features: Provides a thorough presentation of the state-of-the art in computational modelling techniques for photonics Contains broad coverage of both frequency- and time-domain techniques to suit a wide range of photonic devices Reviews existing commercial software packages for photonics Presents the advantages and disadvantages of the different modelling techniques as well as their suitability for various photonic devices Shows the reader how to model, analyse, design and optimise the performance of a wide range of photonic devices by building their own numerical code using these methods Accompanying website contains the numerical examples representing the numerical techniques in this book, as well as several design examples (wiley.com/go/obayya_computational) This book will serve as an invaluable reference for researchers, optical telecommunications engineers, engineers in the photonics industry. PhD and MSc students undertaking courses in the areas of photonics and optical telecommunications will also find this book of interest.

This book explores the state-of-the art in computationalmodelling techniques for photonic devicesIn this book, the author provides a comprehensive coverage ofmodern numerical modelling techniques for designing photonicdevices for use in modern optical telecommunications systems. Inaddition the book presents the state-of-the-art in computationalphotonics techniques, covering methods such as full-vectorialfinite-element beam propagation, bidirectional beam propagationcomplex-envelope alternative direction implicit finite differencetime domain, multiresolution time domain, and finite volume timedomain. The book guides the reader through the concepts ofmodelling, analysing, designing and optimising the performance of awide range of photonic devices by building their own numerical codeusing these methods.Key Features:* Provides a thorough presentation of the state-of-the art incomputational modelling techniques for photonics* Contains broad coverage of both frequency- and time-domaintechniques to suit a wide range of photonic devices* Reviews existing commercial software packages forphotonics* Presents the advantages and disadvantages of the differentmodelling techniques as well as their suitability for variousphotonic devices* Shows the reader how to model, analyse, design and optimise theperformance of a wide range of photonic devices by building theirown numerical code using these methods* Accompanying website contains the numerical examplesrepresenting the numerical techniques in this book, as well asseveral design examples (href="wiley.com/go/obayya_computational">wiley.com/go/obayya_computational)This book will serve as an invaluable reference for researchersoptical telecommunications engineers, engineers in the photonicsindustry. PhD and MSc students undertaking courses in the areas ofphotonics and optical telecommunications will also find this bookof interest.

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