Numerical methods in photonics

 Content: 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