Numerical Methods in Photonics  book cover
1st Edition

Numerical Methods in Photonics

ISBN 9781138074699
Published November 22, 2017 by CRC Press
362 Pages 96 B/W Illustrations

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Book Description

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.

Table of Contents


Maxwell’s Equations


Maxwell’s Equations

Material Equations

Frequency Domain

1D and 2D Maxwell’s Equations

Wave 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


General Considerations

Modified Finite-Difference Operators

Numerical Linear Algebra in MATLAB®

Two-Dimensional Waveguides and the Yee Mesh


Modeling of Nonlinear Propagation in Waveguides



Nonlinear Polarization

The Nonlinear Schrödinger Equation

Numerical Implementation


The Modal Method



The 1D Geometry

The 2D Geometry

Periodic Structures

Current Sources



Green’s Function Integral Equation Methods for Electromagnetic Scattering Problems


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



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


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Andrei V. Lavrinenko, Technical University of Denmark, Kongens Lyngby
Jesper Lægsgaard, Technical University of Denmark, Kongens Lyngby
Niels Gregersen, Technical University of Denmark, Kongens Lyngby
Frank Schmidt, Zuse Institute, Berlin, Germany
Thomas Søndergaard, Aalborg University, Denmark


"… 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