Intro -- Electromagnetic and Photonic Simulation for the Beginner: Finite-Difference Frequency-Domain in MATLAB® -- Contents -- Foreword -- Preface -- Introduction -- Chapter 1 MATLAB Preliminaries -- 1.1 Basic Structure of an FDFD Program in MATLAB -- 1.1.1 MATLAB Code for Ideal Structure of a Program -- 1.2 MATLAB and Linear Algebra -- 1.2.1 Special Matrices -- 1.2.2 Matrix Algebra -- 1.3 Setting Up a Grid in MATLAB -- 1.3.1 MATLAB Array Indexing -- 1.3.2 Parameters Describing a Grid in MATLAB -- 1.3.3 Calculating the Grid Parameters -- 1.4 Building Geometries onto Grids -- 1.4.1 Adding Rectangles to a Grid -- 1.4.2 The Centering Algorithm -- 1.4.3 The Meshgrid -- 1.4.4 Adding Circles and Ellipses to a Grid -- 1.4.5 Grid Rotation -- 1.4.6 Boolean Operations -- 1.5 Three-Dimensional Grids -- 1.6 Visualization Techniques -- 1.6.1 Visualizing Data on Grids -- 1.6.2 Visualizing Three-Dimensional Data -- 1.6.3 Visualizing Complex Data -- 1.6.4 Animating the Fields Calculated by FDFD -- Reference -- Chapter 2 Electromagnetic Preliminaries -- 2.1 Maxwell's Equations -- 2.2 The Constitutive Parameters -- 2.2.1 Anisotropy, Tensors, and Rotation Matrices -- 2.2.2 Rotation Matrices and Tensor Rotation -- 2.3 Expansion of Maxwell's Curl Equations in Cartesian Coordinates -- 2.4 The Electromagnetic Wave Equation -- 2.5 Electromagnetic Waves in LHI Media -- 2.5.1 Wave Polarization -- 2.6 The Dispersion Relation for LHI Media -- 2.7 Scattering at an Interface -- 2.7.1 Reflectance and Transmittance -- 2.8 What is a Two-Dimensional Simulation? -- 2.9 Diffraction from Gratings -- 2.9.1 The Grating Equation -- 2.9.2 Diffraction Efficiency -- 2.9.3 Generalization to Crossed Gratings -- 2.10 Waveguides and Transmission Lines -- 2.10.1 Waveguide Modes and Parameters -- 2.10.2 Transmission Line Parameters -- 2.11 Scalability of Maxwell's Equations.

2.12 Numerical Solution to Maxwell's Equations -- References -- Chapter 3 The Finite-Difference Method -- 3.1 Introduction -- 3.2 Finite-Difference Approximations -- 3.2.1 Deriving Expressions for Finite-Difference Approximations -- 3.2.2 Example #1-Interpolations and Derivatives from Three Points -- 3.2.3 Example #2-Interpolations and Derivatives from Two Points -- 3.2.4 Example #3-Interpolations and Derivatives from Four Points -- 3.3 Numerical Differentiation -- 3.4 Numerical Boundary Conditions -- 3.4.1 Dirichlet Boundary Conditions -- 3.4.2 Periodic Boundary Conditions -- 3.5 Derivative Matrices -- 3.6 Finite-Difference Approximation of Differential Equations -- 3.7 Solving Matrix Differential Equations -- 3.7.1 Example-Solving a Single-Variable Differential Equation -- 3.8 Multiple Variables and Staggered Grids -- 3.8.1 Example-Solving a Multivariable Problem -- References -- Chapter 4 Finite-Difference Approximation of Maxwell's Equations -- 4.1 Introduction to the Yee Grid Scheme -- 4.2 Preparing Maxwell's Equations for FDFD Analysis -- 4.3 Finite-Difference Approximation of Maxwell's Curl Equations -- 4.4 Finite-Difference Equations for Two-Dimensional FDFD -- 4.4.1 Derivation of E Mode Equations When Frequency Is Not Known -- 4.4.2 Derivation of H Mode Equations When Frequency Is Not Known -- 4.4.3 Derivation of E Mode Equations When Frequency Is Known -- 4.4.4 Derivation of H Mode Equations When Frequency Is Known -- 4.5 Derivative Matrices for Two-Dimensional FDFD -- 4.5.1 Derivative Matrices Incorporating Dirichlet Boundary Conditions -- 4.5.2 Periodic Boundary Conditions -- 4.5.3 Derivative Matrices Incorporating Periodic Boundary Conditions -- 4.5.4 Relationship Between the Derivative Matrices -- 4.6 Derivative Matrices for Three-Dimensional FDFD -- 4.6.1 Relationship Between the Derivative Matrices.

4.7 Programming the YEEDER2D() Function in MATLAB -- 4.7.1 Using the yeeder2d() Function -- 4.8 Programming the YEEDER3D() Function in MATLAB -- 4.8.1 Using the yeeder3d() Function -- 4.9 The 2× Grid Technique -- 4.10 Numerical Dispersion -- References -- Chapter 5 The Perfectly Matched Layer Absorbing Boundary -- 5.1 The Absorbing Boundary -- 5.2 Derivation of the UPML Absorbing Boundary -- 5.3 Incorporating the UPML into Maxwell's Equations -- 5.4 Calculating the UPML Parameters -- 5.5 Implementation of the UPML in MATLAB -- 5.5.1 Using the addupml2d() Function -- 5.6 The SCPML Absorbing Boundary -- 5.6.1 MATLAB Implementation of calcpml3d() -- 5.6.2 Using the calcpml3d() Function -- References -- Chapter 6 FDFD for Calculating Guided Modes -- 6.1 Formulation for Rigorous Hybrid Mode Calculation -- 6.2 Formulation for Rigorous Slab Waveguide Mode Calculation -- 6.2.1 Formulation of E Mode Slab Waveguide Analysis -- 6.2.2 Formulation of H Mode Slab Waveguide Analysis -- 6.2.3 Formulations for Slab Waveguides in Other Orientations -- 6.2.4 The Effective Index Method -- 6.3 Implementation of Waveguide Mode Calculations -- 6.3.1 MATLAB Implementation of Rib Waveguide Analysis -- 6.3.2 MATLAB Implementation of Slab Waveguide Analysis -- 6.3.3 Animating the Slab Waveguide Mode -- 6.3.4 Convergence -- 6.3.5 MATLAB Implementation for Calculating SPPs -- 6.4 Implementation of Transmission Line Analysis -- References -- Chapter 7 FDFD for Calculating Photonic Bands -- 7.1 Photonic Bands for Rectangular Lattices -- 7.2 Formulation for Rectangular Lattices -- 7.3 Implementation of Photonic Band Calculation -- 7.3.1 Description of MATLAB Code for Calculating Photonic Band Diagrams -- 7.3.2 Description of MATLAB Code for Calculating IFCs -- References -- Chapter 8 FDFD for Scattering Analysis -- 8.1 Formulation of FDFD for Scattering Analysis.

8.1.1 Matrix Wave Equations for Two-Dimensional Analysis -- 8.2 Incorporating Sources -- 8.2.1 Derivation of the QAAQ Equation -- 8.2.2 Calculating the Source Field fsrc(x,y) -- 8.2.3 Calculating the SF Masking Matrix Q -- 8.2.4 Compensating for Numerical Dispersion -- 8.3 Calculating Reflection and Transmission for Periodic Structures -- 8.4 Implementation of the FDFD Method for Scattering Analysis -- 8.4.1 Standard Sequence of Simulations for a Newly Written FDFD Code -- 8.4.2 FDFD Analysis of a Sawtooth Diffraction Grating -- 8.4.3 FDFD Analysis of a Self-Collimating Photonic Crystal -- 8.4.4 FDFD Analysis of an OIC Directional Coupler -- References -- Chapter 9 Parameter Sweeps with FDFD -- 9.1 Introduction to Parameter Sweeps -- 9.2 Modifying FDFD for Parameter Sweeps -- 9.2.1 Generic MATLAB Function to Simulate Periodic Structures -- 9.2.2 Main MATLAB Program to Simulate the GMRF -- 9.2.3 Main MATLAB Programs to Analyze a Metal Polarizer -- 9.3 Identifying Common Problems in FDFD -- References -- Chapter 10 FDFD Analysis of Three-Dimensional and Anisotropic Devices -- 10.1 Formulation of Three-Dimensional FDFD -- 10.1.1 Finite-Difference Approximation of Maxwell's Curl Equations -- 10.1.2 Maxwell's Equations in Matrix Form -- 10.1.3 Interpolation Matrices -- 10.1.4 Three-Dimensional Matrix Wave Equation -- 10.2 Incorporating Sources into Three-Dimensional FDFD -- 10.3 Iterative Solution for FDFD -- 10.4 Calculating Reflection and Transmission for Doubly Periodic Structures -- 10.5 Implementation of Three-Dimensional FDFD and Examples -- 10.5.1 Standard Sequence of Simulations for a Newly Written Three-Dimensional FDFD Code -- 10.5.2 Generic Three-Dimensional FDFD Function to Simulate Periodic Structures -- 10.5.3 Simulation of a Crossed-Grating GMRF -- 10.5.4 Simulation of a Frequency Selective Surface.

10.5.5 Parameter Retrieval for a Left-Handed Metamaterial -- 10.5.6 Simulation of an Invisibility Cloak -- References -- Appendix A -- A.1 Best Practices for Building Devices onto Yee Grids -- A.2 Method Summaries -- List of Acronyms and Abbreviations -- About the Author -- Index.