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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