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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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| |

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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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| |

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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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| |

| |

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 | |

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Formulation | |

| |

| |

| |

Numerical Stability Analysis | |

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| |

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Numerical Dispersion Analysis | |

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| |

| |

Lossy Materials | |

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| |

| |

Lossy Screen Example | |

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| |

Split-Field Method, Two Dimensions | |

| |

| |

| |

Formulation | |

| |

| |

| |

Numerical Stability Analysis | |

| |

| |

| |

Numerical Dispersion Analysis | |

| |

| |

| |

Lossy Materials | |

| |

| |

| |

Lossy Screen Example | |

| |

| |

| |

Split-Field Method, Three Dimensions | |

| |

| |

| |

Formulation | |

| |

| |

| |

Numerical Stability Analysis | |

| |

| |

| |

UPML Absorbing Boundary Condition | |

| |

| |

| |

Application of the Periodic FDTD Method | |

| |

| |

| |

Photonic Bandgap Structures | |

| |

| |

| |

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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| |

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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 | |