362 pages | 96 B/W Illus.
Simulation and modeling using numerical methods is one of the key instruments in any scientific work. In the field of photonics, a wide range of numerical methods are used for studying both fundamental optics and applications such as design, development, and optimization of photonic components. Modeling is key for developing improved photonic devices and reducing development time and cost.
Choosing the appropriate computational method for a photonics modeling 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 in which it is based, along with sample scripts, illustrative examples of characteristic problem solving, and exercises. MATLAB® is used throughout the text.
This book provides a solid basis to practice writing your own codes. The theoretical formulation is complemented by sets of exercises, which allow you to grasp the essence of the modeling tools.
"… useful to students and researchers who want to have a deeper understanding of the methods commonly used in computational electromagnetics. After addressing the basic principles, this book provides the readers with the details and mathematical/numerical framework of commonly used methods including FDTD, finite element, Green’s function, and modal. It then goes on to more advanced topics such as modelling nonlinear materials and materials with gain. This book is a useful addition to the library of any research university."
—C T Chan, Hong Kong University of Science and Technology
1D and 2D Maxwell’s Equations
Waveguides and Eigenmodes
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
Finite-Difference Modeling of Straight Waveguides
Modified Finite-Difference Operators
Numerical Linear Algebra in MATLAB®
Two-Dimensional Waveguides and the Yee Mesh
Modeling of Nonlinear Propagation in Waveguides
The Nonlinear Schrödinger Equation
The Modal Method
The 1D Geometry
The 2D Geometry
Green’s Function Integral Equation Methods for Electromagnetic Scattering Problems
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
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