Electromagnetic and Photonic Simulation for the Beginner : : Finite-Difference Frequency-Domain in MATLAB®.

• Author: Rumpf, Raymond C.
• Place / Publishing House: Norwood : : Artech House,, 2022.; {copy}2022.
• Year of Publication: 2022
• Edition: 1st ed.
• Language: English
• Physical Description: 1 online resource (355 pages)

Table of Contents

• 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.