1st Edition
Numerical Methods in Photonics
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®
Two-Dimensional Waveguides and the Yee Mesh
Exercises
Modeling of Nonlinear Propagation in Waveguides
Introduction
Formalism
Nonlinear Polarization
The Nonlinear Schrödinger 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
Biography
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
