Computational methods for electromagnetic and optical systems

Includes bibliographical references and index.

Machine generated contents note: 1.1.Introduction -- 1.2.Fourier Series and Its Properties -- 1.3.Fourier Transform -- 1.4.Hankel Transform -- 1.5.Discrete Fourier Transform -- 1.6.Review of Eigenanalysis -- Problems -- References -- 2.1.Introduction -- 2.2.Transfer Function for Propagation -- 2.3.Split-Step Beam Propagation Method -- 2.4.Beam Propagation in Linear Media -- 2.4.1.Linear Free-Space Beam Propagation -- 2.4.2.Propagation of Gaussian Beam through Graded Index Medium -- 2.5.Beam Propagation through Diffraction Gratings: Acoustooptic Diffraction -- 2.6.Beam Propagation in Kerr-Type Nonlinear Media -- 2.6.1.Nonlinear Schrodinger Equation -- 2.6.2.Simulation of Self-Focusing Using Adaptive Fourier and Fourier-Hankel Transform Methods -- 2.7.Beam Propagation and Coupling in Photorefractive Media -- 2.7.1.Basic Photorefractive Physics -- 2.7.2.Induced Transmission Gratings -- 2.7.3.Induced Reflection Gratings and Bidirectional Beam Propagation Method -- 2.8.z-Scan Method -- 2.8.1.Model for Beam Propagation through PR Lithium Niobate -- 2.8.2.z-Scan: Analytical Results, Simulations, and Sample Experiments -- Problems -- References -- 3.1.Introduction -- 3.2.Maxwell's Equations -- 3.3.Constitutive Relations: Frequency Dependence and Chirality -- 3.3.1.Constitutive Relations and Frequency Dependence -- 3.3.2.Constitutive Relations for Chiral Media -- 3.4.Plane Wave Propagation through Linear Homogeneous Isotropic Media -- 3.4.1.Dispersive Media -- 3.4.2.Chiral Media -- 3.5.Power Flow, Stored Energy, Energy Velocity, Group Velocity, and Phase Velocity -- 3.6.Metamaterials and Negative Index Media -- 3.6.1.Beam Propagation in NIMs -- 3.7.Propagation through Photonic Band Gap Structures: The Transfer Matrix Method -- 3.7.1.Periodic PIM-NIM Structures -- 3.7.2.EM Propagation in Complex Structures -- Problems -- References -- 4.1.Introduction -- 4.2.State Variable Analysis of an Isotropic Layer -- 4.2.1.Introduction -- 4.2.2.Analysis -- 4.2.3.Complex Poynting Theorem -- 4.2.4.State Variable Analysis of an Isotropic Layer in Free Space -- 4.2.5.State Variable Analysis of a Radar Absorbing Layer -- 4.2.6.State Variable Analysis of a Source in Isotropic Layered Media -- 4.3.State Variable Analysis of an Anisotropic Layer -- 4.3.1.Introduction -- 4.3.2.Basic Equations -- 4.3.3.Numerical Results -- 4.4.One-Dimensional k-Space State Variable Solution -- 4.4.1.Introduction -- 4.4.2.k-Space Formulation -- 4.4.3.Ground Plane Slot Waveguide System -- 4.4.4.Ground Plane Slot Waveguide System, Numerical Results -- Problems -- References -- 5.1.Introduction -- 5.2.H-Mode Planar Diffraction Grating Analysis -- 5.2.1.Full-Field Formulation -- 5.2.2.Differential Equation Method -- 5.2.3.Numerical Results -- 5.2.4.Diffraction Grating Mirror -- 5.3.Application of RCWA and the Complex Poynting Theorem to E-Mode Planar Diffraction Grating Analysis -- 5.3.1.E-Mode RCWA Formulation -- 5.3.2.Complex Poynting Theorem -- 5.3.2.1.Sample Calculation of PuWE -- 5.3.2.2.Other Poynting Theorem Integrals -- 5.3.2.3.Simplification of Results and Normalization -- 5.3.3.Numerical Results -- 5.4.Multilayer Analysis of E-Mode Diffraction Gratings -- 5.4.1.E-Mode Formulation -- 5.4.2.Numerical Results -- 5.5.Crossed Diffraction Grating -- 5.5.1.Crossed Diffraction Grating Formulation -- 5.5.2.Numerical Results -- Problems -- References -- 6.1.Introduction to Photorefractive Materials -- 6.2.Dynamic Nonlinear Model for Diffusion-Controlled PR Materials -- 6.3.Approximate Analysis -- 6.3.1.Numerical Algorithm -- 6.3.2.TE Numerical Simulation Results -- 6.3.3.TM Numerical Simulation Results -- 6.3.4.Discussion of Results from Approximate Analysis -- 6.4.Exact Analysis -- 6.4.1.Finite Difference Kukhtarev Analysis -- 6.4.2.TM Numerical Simulation Results -- 6.5.Reflection Gratings -- 6.5.1.RCWA Optical Field Analysis -- 6.5.2.Material Analysis -- 6.5.3.Numerical Results -- 6.6.Conclusion -- Problems -- References -- 7.1.Introduction -- 7.2.Rigorous Coupled Wave Analysis Circular Cylindrical Systems -- 7.3.Rigorous Coupled Wave Analysis Mathematical Formulation -- 7.3.1.Introduction -- 7.3.2.Basic Equations -- 7.3.3.Numerical Results -- 7.4.Anisotropic Cylindrical Scattering -- 7.4.1.Introduction -- 7.4.2.State Variable Analysis -- 7.4.3.Numerical Results -- 7.5.Spherical Inhomogeneous Analysis -- 7.5.1.Introduction -- 7.5.2.Rigorous Coupled Wave Theory Formulation -- 7.5.3.Numerical Results -- Problems -- References -- 8.1.Introduction -- 8.2.RCWA Bipolar Coordinate Formulation -- 8.2.1.Bipolar and Eccentric Circular Cylindrical, Scattering Region Coordinate Description -- 8.2.2.Bipolar RCWA State Variable Formulation -- 8.2.3.Second-Order Differential Matrix Formulation -- 8.2.4.Thin-Layer, Bipolar Coordinate Eigenfunction Solution -- 8.3.Bessel Function Solutions in Homogeneous Regions of Scattering System -- 8.4.Thin-Layer SV Solution in the Inhomogeneous Region of the Scattering System -- 8.5.Matching of EM Boundary Conditions at Interior-Exterior Interfaces of the Scattering System -- 8.5.1.Bipolar and Circular Cylindrical Coordinate Relations -- 8.5.2.Details of Region 2 (Inhomogenous Region) Region 3 (Homogenous Interior Region) EM Boundary Value Matching -- 8.5.3.Region 0 (Homogenous Exterior Region) Region 2 (Inhomogenous Region) EM Boundary Value Matching -- 8.5.4.Details of Layer-to-Layer EM Boundary Value Matching in the Inhomogeneous Region -- 8.5.5.Inhomogeneous Region Ladder-Matrix -- 8.6.Region 1 Region 3 Bessel-Fourier Coefficient Transfer Matrix -- 8.7.Overall System Matrix -- 8.8.Alternate Forms of the Bessel-Fourier Coefficient Transfer Matrix -- 8.9.Bistatic Scattering Width -- 8.10.Validation of Numerical Results -- 8.11.Numerical Results, Examples of Scattering from Homogeneous and Inhomogeneous Material Objects -- 8.12.Error and Convergence Analysis -- 8.13.Summary, Conclusions, and Future Work -- Problems -- Appendix 8.A -- Appendix 8.B -- References -- 9.1.Introduction -- 9.2.Case Study I: Fourier Series Expansion, Eigenvalue and Eigenfunction Analysis, and Transfer Matrix Analysis -- 9.3.Case Study II: Comparison of KPE BA, BC Validation Methods, and SV Methods for Relatively Small Diameter Scattering Objects -- 9.4.Case Study III: Comparison of BA, BC, and SV Methods for Gradually, Stepped-Up, Index Profile Scattering Objects -- 9.5.Case Study IV: Comparison of BA, BC, and SV Methods for Mismatched, Index Profile, Scattering Objects -- 9.6.Case Study V: Comparison of BA, BC, and SV Methods for Gradually, Stepped-Up, Index Scattering Objects with High Index Core -- 9.7.Case Study VI: Calculation and Convergence Analysis of EM Fields of an Inhomogeneous Region Material Object Using the SV Method, Δepsilon = 1, α = 5.5, Λ = 0, Example -- 9.8.Case Study VII: Calculation and Convergence Analysis of EM Fields of an Inhomogeneous Region Material Object Using the SV Method, Δepslon = 0.4, α = 5.5, Λ = 0 Example -- 9.9.Case Study VIII: Comparison of Homogeneous and Inhomogeneous Region Bistatic Line Widths -- 9.10.Case Study IX: Conservation of Power Analysis -- Appendix 9.A: Interpolation Equations.

"This text introduces and examines a variety of spectral computational techniques - including k-space theory, Floquet theory and beam propagation - that are used to analyze electromagnetic and optical problems. The book also presents a solution to Maxwell's equations from a set of first order coupled partial differential equations"--Provided by publisher.