| |
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| Preface to the Second Edition | |
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| Preface to the First Edition | |
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| Electrodynamics Entering the 21st Century | |
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| Introduction | |
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| The Heritage of Military Defense Applications | |
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| Frequency-Domain Solution Techniques | |
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| Rise of Finite-Difference Time-Domain Methods | |
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| History of FDTD Techniques for Maxwell's Equations | |
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| Characteristics of FDTD and Related Space-Grid Time-Domain Techniques | |
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| Classes of Algorithms | |
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| Predictive Dynamic Range | |
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| Scaling to Very Large Problem Sizes | |
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| Examples of Applications (including Color Plate Section, pages 9-16) | |
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| Radar-Guided Missile | |
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| High-Speed Computer Circuit-Board Module | |
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| Power-Distribution System for a High-Speed Computer Multichip Module | |
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| Microwave Amplifier | |
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| Cellular Telephone | |
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| Optical Microdisk Resonator | |
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| Photonic Bandgap Microcavity Laser | |
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| Colliding Spatial Solitons | |
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| Conclusions | |
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| References | |
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| The One-Dimensional Scalar Wave Equation | |
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| Introduction | |
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| Propagating-Wave Solutions | |
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| Dispersion Relation | |
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| Finite Differences | |
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| Finite-Difference Approximation of the Scalar Wave Equation | |
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| Numerical Dispersion Relation | |
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| Case 1: Very Fine Sampling in Time and Space ([Delta]t [right arrow] 0, [Delta]x [right arrow] 0) | |
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| Case 2: Magic Time-Step (c[Delta]t = [Delta]x) | |
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| Case 3: Dispersive Wave Propagation | |
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| Example of Calculation of Numerical Phase Velocity and Attenuation | |
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| Examples of Calculations of Pulse Propagation | |
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| Numerical Stability | |
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| Complex-Frequency Analysis | |
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| Examples of Calculations Involving Numerical Instability | |
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| Summary | |
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| Order of Accuracy | |
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| Lax-Richtmyer Equivalence Theorem | |
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| Limitations | |
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| References | |
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| Bibliography on Stability of Finite-Difference Methods | |
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| Problems | |
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| Introduction to Maxwell's Equations and the Yee Algorithm | |
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| Introduction | |
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| Maxwell's Equations in Three Dimensions | |
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| Reduction to Two Dimensions | |
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| TM[subscript z] Mode | |
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| TE[subscript z] Mode | |
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| Reduction to One Dimension | |
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| x-Directed, z-Polarized TEM Mode | |
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| x-Directed, y-Polarized TEM Mode | |
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| Equivalence to the Wave Equation in One Dimension | |
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| The Yee Algorithm | |
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| Basic Ideas | |
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| Finite Differences and Notation | |
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| Finite-Difference Expressions for Maxwell's Equations in Three Dimensions | |
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| Space Region With a Continuous Variation of Material Properties | |
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| Space Region With a Finite Number of Distinct Media | |
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| Space Region With Nonpermeable Media | |
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| Reduction to the Two-Dimensional TM[subscript z] and TE[subscript z] Modes | |
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| Interpretation as Faraday's and Ampere's Laws in Integral Form | |
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| Divergence-Free Nature | |
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| Alternative Finite-Difference Grids | |
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| Cartesian Grids | |
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| Hexagonal Girds | |
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| Tetradecahedron/Dual-Tetrahedron Mesh in Three Dimensions | |
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| Summary | |
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| References | |
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| Problems | |
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| Numerical Dispersion and Stability | |
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| Introduction | |
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| Derivation of the Numerical Dispersion Relation for Two-Dimensional Wave Propagation | |
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| Extension to Three Dimensions | |
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| Comparison With the Ideal Dispersion Case | |
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| Anisotropy of the Numerical Phase Velocity | |
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| Sample Values of Numerical Phase Velocity | |
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| Intrinsic Grid Velocity Anisotropy | |
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| Complex-Valued Numerical Wavenumbers | |
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| Case 1: Numerical Wave Propagation Along the Principal Lattice Axes | |
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| Case 2: Numerical Wave Propagation Along a Grid Diagonal | |
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| Example of Calculation of Numerical Phase Velocity and Attenuation | |
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| Example of Calculation of Wave Propagation | |
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| Numerical Stability | |
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| Complex-Frequency Analysis | |
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| Example of a Numerically Unstable Two-Dimensional FDTD Model | |
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| Generalized Stability Problem | |
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| Boundary Conditions | |
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| Variable and Unstructured Meshing | |
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| Lossy, Dispersive, Nonlinear, and Gain Materials | |
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| Modified Yee-Based Algorithms for Improved Numerical Dispersion | |
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| Strategy 1: Center a Specific Numerical Phase-Velocity Curve About c | |
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| Strategy 2: Use Fourth-Order-Accurate Spatial Differences | |
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| Strategy 3: Use Hexagonal Grids | |
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| Strategy 4: Use Discrete Fourier Transforms to Calculate the Spatial Derivatives | |
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| Alternating-Direction-Implicit Time-Stepping Algorithm for Operation Beyond the Courant Limit | |
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| Numerical Formulation of the Zheng/Chen/Zhang Algorithm | |
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| Numerical Stability | |
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| Numerical Dispersion | |
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| Discussion | |
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| Summary | |
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| References | |
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| Problems | |
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| Projects | |
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| Incident Wave Source Conditions | |
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| Introduction | |
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| Pointwise E and H Hard Sources in One Dimension | |
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| Pointwise E and H Hard Sources in Two Dimensions | |
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| Green's Function for the Scalar Wave Equation in Two Dimensions | |
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| Obtaining Comparative FDTD Data | |
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| Results for Effective Action Radius of a Hard-Sourced Field Component | |
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| J and M Current Sources in Three Dimensions | |
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| Sources and Charging | |
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| Sinusoidal Sources | |
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| Transient (Pulse) Sources | |
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| Intrinsic Lattice Capacitance | |
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| Intrinsic Lattice Inductance | |
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| Impact Upon FDTD Simulations of Lumped-Element Capacitors and Inductors | |
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| The Plane-Wave Source Condition | |
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| The Total-Field/Scattered-Field Technique: Ideas and One-Dimensional Formulation | |
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| Ideas | |
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| One-Dimensional Formulation | |
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| Two-Dimensional Formulation of the TF/SF Technique | |
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| Consistency Conditions | |
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| Calculation of the Incident Field | |
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| Illustrative Example | |
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| Three-Dimensional Formulation of the TF/SF Technique | |
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| Consistency Conditions | |
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| Calculation of the Incident Field | |
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| Pure Scattered-Field Formulation | |
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| Application to PEC Structures | |
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| Application to Lossy Dielectric Structures | |
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| Choice of Incident Plane-Wave Formulation | |
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| Waveguide Source Conditions | |
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| Pulsed Electric Field Modal Hard Source | |
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| Total-Field/Reflected-Field Modal Formulation | |
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| Resistive Source and Load Conditions | |
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| Summary | |
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| References | |
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| Problems | |
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| Projects | |
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| Analytical Absorbing Boundary Conditions | |
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| Introduction | |
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| Bayliss-Turkel Radiation Operators | |
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| Spherical Coordinates | |
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| Cylindrical Coordinates | |
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| Engquist-Majda One-Way Wave Equations | |
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| One-Term and Two-Term Taylor Series Approximations | |
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| Mur Finite-Difference Scheme | |
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| Trefethen-Halpern Generalized and Higher Order ABCs | |
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| Theoretical Reflection Coefficient Analysis | |
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| Numerical Experiments | |
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| Higdon Radiation Operators | |
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| Formulation | |
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| First Two Higdon Operators | |
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| Discussion | |
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| Liao Extrapolation in Space and Time | |
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| Formulation | |
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| Discussion | |
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| Ramahi Complementary Operators | |
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| Basic Idea | |
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| Complementary Operators | |
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| Effect of Multiple Wave Reflections | |
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| Basis of the Concurrent Complementary Operator Method | |
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| Illustrative FDTD Modeling Results Obtained Using the C-COM | |
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| Summary | |
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| References | |
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| Problems | |
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| Perfectly Matched Layer Absorbing Boundary Conditions | |
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| Introduction | |
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| Plane Wave Incident Upon a Lossy Half-Space | |
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| Plane Wave Incident Upon Berenger's PML Medium | |
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| Two-Dimensional TE[subscript z] Case | |
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| Two-Dimensional TM[subscript z] Case | |
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| Three-Dimensional Case | |
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| Stretched-Coordinate Formulation of Berenger's PML | |
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| An Anisotropic PML Absorbing Medium | |
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| Perfectly Matched Uniaxial Medium | |
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| Relationship to Berenger's Split-Field PML | |
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| A Generalized Three-Dimensional Formulation | |
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| Inhomogeneous Media | |
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| Theoretical Performance of the PML | |
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| The Continuous Space | |
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| The Discrete Space | |
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| Efficient Implementation of UPML in FDTD | |
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| Derivation of the Finite-Difference Expressions | |
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| Computer Implementation of the UPML | |
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| Numerical Experiments With Berenger's Split-Field PML | |
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| Outgoing Cylindrical Wave in a Two-Dimensional Open-Region Grid | |
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| Outgoing Spherical Wave in a Three-Dimensional Open-Region Lattice | |
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| Dispersive Wave Propagation in Metal Waveguides | |
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| Dispersive and Multimode Wave Propagation in Dielectric Waveguides | |
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| Numerical Experiments With UPML | |
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| Current Source Radiating in an Unbounded Two-Dimensional Region | |
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| Highly Elongated Domains | |
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| Microstrip Transmission Line | |
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| UPML Termination for Conductive Media | |
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| Theory | |
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| Numerical Example: Termination of a Conductive Half-Space Medium | |
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| UPML Termination for Dispersive Media | |
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| Theory | |
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| Numerical Example: Reflection by a Lorentz Medium | |
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| Summary and Conclusions | |
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| References | |
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| Projects | |
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| Near-to-Far-Field Transformation | |
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| Introduction | |
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| Two-Dimensional Transformation, Phasor Domain | |
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| |
| Application of Green's Theorem | |
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| |
| Far-Field Limit | |
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| Reduction to Standard Form | |
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| Obtaining Phasor Quantities Via Discrete Fourier Transformation | |
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| Surface Equivalence Theorem | |
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| Extension to Three Dimensions, Phasor Domain | |
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| Time-Domain Near-to-Far-Field Transformation | |
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| Summary | |
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| References | |
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| Project | |
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| Dispersive and Nonlinear Materials | |
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| Introduction | |
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| Types of Dispersions Considered | |
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| Debye Media | |
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| Lorentz Media | |
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| Piecewise-Linear Recursive Convolution Method, Linear Material Case | |
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| General Formulation of the Method | |
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| Application to Debye Media | |
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| Application to Lorentz Media | |
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| Numerical Results | |
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| Piecewise-Linear Recursive Convolution Method, Nonlinear Dispersive Material Case | |
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| Governing Equations | |
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| General Formulation of the Method | |
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| FDTD Realization in One Dimension | |
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| Numerical Results | |
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| Auxiliary Differential Equation Method, Linear Material Case | |
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| Formulation for Multiple Debye Poles | |
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| Formulation for Multiple Lorentz Pole Pairs | |
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| Numerical Results | |
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| Auxiliary Differential Equation Method, Nonlinear Dispersive Material Case | |
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| Formulation for Multiple Lorentz Pole Pairs, TM[subscript Z] Case | |
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| Numerical Results for Temporal Solitons | |
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| Numerical Results for Spatial Solitons | |
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| Summary and Conclusions | |
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| References | |
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| Problems | |
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| Projects | |
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| Local Subcell Models of Fine Geometrical Features | |
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| Introduction | |
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| Basis of Contour-Path FDTD Modeling | |
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| The Simplest Contour-Path Subcell Models | |
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| Diagonal Split-Cell Model for PEC Surfaces | |
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| Average Properties Model for Material Surfaces | |
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| The Contour-Path Model of the Narrow Slot | |
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| The Contour-Path Model of the Thin Wire | |
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| Locally Conformal Models of Curved Surfaces | |
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| Dey-Mittra Technique for PEC Structures | |
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| Illustrative Results for PEC Structures | |
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| Dey-Mittra Technique for Material Structures | |
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| Maloney-Smith Technique for Thin Material Sheets | |
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| Basis | |
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| Illustrative Results | |
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| Dispersive Surface Impedance | |
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| Maloney-Smith Method | |
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| Beggs Method | |
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| Lee Method | |
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| Relativistic Motion of PEC Boundaries | |
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| Basis | |
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| Illustrative Results | |
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| Summary and Discussion | |
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| References | |
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| Bibliography | |
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| Projects | |
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| Nonorthogonal and Unstructured Grids | |
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| Introduction | |
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| Nonuniform Orthogonal Grids | |
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| Locally Conformal Grids, Globally Orthogonal | |
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| |
| Global Curvilinear Coordinates | |
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| Nonorthogonal Curvilinear FDTD Algorithm | |
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| Stability Criterion | |
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| Irregular Nonorthogonal Structured Grids | |
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| Irregular Nonorthogonal Unstructured Grids | |
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| |
| Generalized Yee Algorithm | |
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| |
| |
| Inhomogeneous Media | |
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| |
| Practical Implementation of the Generalized Yee Algorithm | |
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| A Planar Generalized Yee Algorithm | |
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| |
| Time-Stepping Expressions | |
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| |
| Projection Operators | |
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| |
| Efficient Time-Stepping Implementation | |
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| |
| |
| Examples of Passive-Circuit Modeling Using the Planar Generalized Yee Algorithm | |
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| |
| 32-GHz Wilkinson Power Divider | |
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| 32-GHz Gysel Power Divider | |
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| |
| Signal Lines in an IBM Thermal Conduction Module | |
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| |
| Summary and Conclusions | |
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| References | |
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| Problems | |
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| Projects | |
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| Bodies of Revolution | |
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| Introduction | |
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| Field Expansion | |
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| Difference Equations for Off-Axis Cells | |
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| Ampere's Law Contour Path Integral to Calculate e[subscript r] | |
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| Ampere's Law Contour Path Integral to Calculate e[subscript phi] | |
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| Ampere's Law Contour Path Integral to Calculate e[subscript z] | |
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| |
| Difference Equations | |
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| |
| Surface-Conforming Contour Path Integrals | |
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| Difference Equations for On-Axis Cells | |
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| Ampere's Law Contour Path Integral to Calculate e[subscript z] on the z-Axis | |
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| Ampere's Law Contour Path Integral to Calculate e[subscript phi] on the z-Axis | |
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| |
| Faraday's Law Calculation of h[subscript r] on the z-Axis | |
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| |
| Numerical Stability | |
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| |
| |
| PML Absorbing Boundary Condition | |
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| |
| BOR-FDTD Background | |
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| |
| |
| Extension of PML to the General BOR Case | |
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| Examples | |
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| |
| Application to Particle Accelerator Physics | |
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| |
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| Definitions and Concepts | |
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| Examples | |
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| Summary | |
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| References | |
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| Problems | |
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| Projects | |
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| Analysis of Periodic Structures | |
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| |
| |
| |
| Introduction | |
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| |
| |
| Review of Scattering From Periodic Structures | |
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| |
| |
| Direct Field Methods | |
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| |
| |
| Normal Incidence Case | |
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| |
| |
| Multiple Unit Cells for Oblique Incidence | |
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| |
| |
| Sine-Cosine Method | |
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| |
| |
| Angled-Update Method | |
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| |
| |
| Introduction to the Field-Transformation Technique | |
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| |
| |
| Multiple-Grid Approach | |
| |
| |
| |
| Formulation | |
| |
| |
| |
| Numerical Stability Analysis | |
| |
| |
| |
| Numerical Dispersion Analysis | |
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| |
| |
| Lossy Materials | |
| |
| |
| |
| Lossy Screen Example | |
| |
| |
| |
| Split-Field Method, Two Dimensions | |
| |
| |
| |
| Formulation | |
| |
| |
| |
| Numerical Stability Analysis | |
| |
| |
| |
| Numerical Dispersion Analysis | |
| |
| |
| |
| Lossy Materials | |
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| Lossy Screen Example | |
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| Split-Field Method, Three Dimensions | |
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| Formulation | |
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| Numerical Stability Analysis | |
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| UPML Absorbing Boundary Condition | |
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| Application of the Periodic FDTD Method | |
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| Photonic Bandgap Structures | |
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| Frequency-Selective Surfaces | |
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| Antenna Arrays | |
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| Summary and Conclusions | |
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| Acknowledgments | |
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| References | |
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| Projects | |
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| Modeling of Antennas | |
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| Introduction | |
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| Formulation of the Antenna Problem | |
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| Transmitting Antenna | |
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| Receiving Antenna | |
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| Symmetry | |
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| Excitation | |
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| Antenna Feed Models | |
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| Detailed Modeling of the Feed | |
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| Simple Gap Feed Model for a Monopole Antenna | |
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| Improved Simple Feed Model | |
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| Near-to-Far-Field Transformations | |
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| Use of Symmetry | |
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| Time-Domain Near-to-Far-Field Transformation | |
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| Frequency-Domain Near-Field to Far-Field Transformation | |
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| Plane-Wave Source | |
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| Effect of an Incremental Displacement of the Surface Currents | |
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| Effect of an Incremental Time Shift | |
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| Relation to Total-Field/Scattered-Field Lattice Zoning | |
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| Case Study I: The Standard-Gain Horn | |
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| Case Study II: The Vivaldi Slotline Array | |
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| Background | |
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| The Planar Element | |
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| The Vivaldi Pair | |
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| The Vivaldi Quad | |
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| The Linear Phased Array | |
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| Phased-Array Radiation Characteristics Indicated by the FDTD Modeling | |
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| Active Impedance of the Phased Array | |
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| Near-Field Simulations | |
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| Generic 900-MHz Cellphone Handset in Free Space | |
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| 900-MHz Dipole Antenna Near a Layered Bone-Brain Half-Space | |
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| 840-MHz Dipole Antenna Near a Rectangular Brain Phantom | |
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| 900-MHz Infinitesimal Dipole Antenna Near a Spherical Brain Phantom | |
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| 1,900-MHz Half-Wavelength Dipole Near a Spherical Brain Phantom | |
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| Selected Recent Applications | |
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| Use of Photonic-Bandgap Materials | |
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| Ground-Penetrating Radar | |
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| Antenna-Radome Interaction | |
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| Personal Wireless Communications Devices | |
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| Biomedical Applications of Antennas | |
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| Summary and Conclusions | |
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| References | |
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| Projects | |
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| High-Speed Electronic Circuits With Active and Nonlinear Components | |
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| Introduction | |
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| Basic Circuit Parameters | |
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| Transmission Line Parameters | |
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| Impedance | |
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| S Parameters | |
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| Differential Capacitance Calculation | |
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| Differential Inductance Calculation | |
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| Lumped Inductance Due to a Discontinuity | |
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| Flux / Current Definition | |
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| Fitting Z([omega]) or S([omega]) to an Equivalent Circuit | |
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| Discussion: Choice of Methods | |
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| Inductance of Complex Power-Distribution Systems | |
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| Method Description | |
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| Example: Multiplane Meshed Printed-Circuit Board | |
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| Discussion | |
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| Parallel Coplanar Microstrips | |
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| Multilayered Interconnect Modeling Example | |
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| Digital Signal Processing and Spectrum Estimation | |
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| Prony's Method | |
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| Autoregressive Models | |
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| Pade Approximation | |
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| Modeling of Lumped Circuit Elements | |
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| FDTD Formulation Extended to Circuit Elements | |
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| The Resistor | |
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| The Resistive Voltage Source | |
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| The Capacitor | |
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| The Inductor | |
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| The Diode | |
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| The Bipolar Junction Transistor | |
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| Direct Linking of FDTD and SPICE | |
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| Basic Idea | |
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| Norton Equivalent Circuit "Looking Into" the FDTD Space Lattice | |
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| Thevenin Equivalent Circuit "Looking Into" the FDTD Space Lattice | |
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| Case Study: A 6-GHz MESFET Amplifier Model | |
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| Large-Signal Model | |
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| Amplifier Configuration | |
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| Analysis of the Circuit Without the Packaging Structure | |
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| Analysis of the Circuit With the Packaging Structure | |
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| Summary and Conclusions | |
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| Acknowledgements | |
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| References | |
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| Additional Bibliography | |
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| Projects | |
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| Microcavity Optical Resonators | |
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| Introduction | |
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| Issues Related to FDTD Modeling of Optical Structures | |
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| Optical Waveguides | |
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| Material Dispersion and Nonlinearities | |
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| Macroscopic Modeling of Optical Gain Media | |
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| Theory | |
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| Validation Studies | |
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| Application to Vertical-Cavity Surface-Emitting Lasers | |
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| Passive Studies | |
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| Active Studies | |
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| Microcavities Based on Photonic Bandgap Structures, Quasi One-Dimensional Case | |
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| Microcavities Based on Photonic Bandgap Structures, Two-Dimensional Case | |
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| Microcavity Ring Resonators | |
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| FDTD Modeling Considerations | |
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| Coupling to Straight Waveguides | |
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| Coupling to Curved Waveguides | |
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| Elongated Ring Designs | |
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| Resonances | |
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| Microcavity Disk Resonators | |
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| Resonance Behavior | |
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| Suppression of Higher Order Radial Whispering-Gallery Modes | |
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| Additional FDTD Modeling Studies | |
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| Summary and Conclusions | |
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| References | |
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| Additional Bibliography | |
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| Projects | |
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| Acronyms | |
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| About the Authors | |
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| Index | |