Numerical Methods in Photonics - Gregersen, Niels

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Résumé :
Choosing the appropriate computational method for a photonics problem requires a clear understanding of the pros and cons of the available numerical methods. Numerical Methods in Photonics presents six of the most frequently used methods : FDTD, FDFD, 1+1D nonlinear propagation, modal method, Green's function, and FEM. After an introductory chapter outlining the basics of Maxwell's equations, the book includes self-contained chapters that focus on each of the methods. Each method is accompanied by a review of the mathematical principles on which it is based, along with sample scripts, illustrative examples of characteristic problem solving, and exercises. MATTAB is used throughout the text. This book provides a solid basis to practice writing your own codes. The basic theory is complemented by sets of exercises, which allow you to grasp the essence of the modeling tools.

Sommaire:
Introduction Maxwell's Equations Notation Maxwell's Equations Material Equations Frequency Domain 1D and 2D Maxwell's Equations Wave Equations Waveguides and Eigenmodes FDTD Introduction Numerical Dispersion and Stability Analysis of the FDTD Method Making Your Own 1D FDTD Absorbing Boundary Conditions FDTD Method for Materials with Frequency Dispersion FDTD Method for Nonlinear Materials, Materials with Gain and Lasing Conclusion Exercises References Finite-Difference Modeling of Straight Waveguides Introduction General Considerations Modified Finite-Difference Operators Numerical Linear Algebra in MATLAB(R) Two-Dimensional Waveguides and the Yee Mesh Exercises Modeling of Nonlinear Propagation in Waveguides Introduction Formalism Nonlinear Polarization The Nonlinear Schrodinger Equation Numerical Implementation Exercises The Modal Method Introduction Eigenmodes The 1D Geometry The 2D Geometry Periodic Structures Current Sources Exercises References Green's Function Integral Equation Methods for Electromagnetic Scattering Problems Introduction Theoretical Foundation Green's Function Area Integral Equation Method Green's Function Volume Integral Equation Method Green's Function Surface Integral Equation Method (2D) Construction of Two-Dimensional Green's Functions for Layered Structures Construction of the Periodic Green's Function Reflection from a Periodic Surface Microstructure Iterative Solution Scheme Taking Advantage of the Fast Fourier Transform Further Reading Exercises References Finite Element Method Introduction: Helmholtz Equation in 1D General Scattering Problem in 1D Mathematical Background: Maxwell and Helmholtz Scattering Problems and Their Variational Forms FEM for Helmholtz Scattering in 2D and 3D FEM for Maxwell Scattering in 2D and 3D Exercises