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Allen Taflove.3rd.Computational Electrodynamics FDTD 文字版125M

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Allen Taflove.3rd.Computational Electrodynamics FDTD精简版125M
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Computational Electrodynamics 封面.jpg

Computational Electrodynamics
The Finite-Difference Time-Domain Method
Third Edition
Allen T af10ve
Susan C. Hagness

Contents
Preface to the Third Edition XIX
Electrodynamics Entering the 21st Century
l.l Introduction
1.2 The Heritage of MiIitary Defense AppIications
1.3 Frequency-Domain Solution Techniques
1.4 Rise of Finite-Difference Time-Domain Methods
1.5 History of FDTD Techniques for Maxwell's Equations
1.6 Characteristics of FDTD and Related Space-Grid Time-Domain Techniques
1.6.1 Classes of AIgorithms
1.6.2 Predictive Dynamic Range
1.6.3 ScaIing to Very Large Problem Sizes
1. 7 Examples of Applications
1.7.1 Impulsive Around-the-World Extremely Low-Frequency Propagation
1.7.2 Cellphone Radiation Interacting with the Human Head
1.7.3 Early-Stage Detection of Breast Cancer Using an Ultrawidebar>d Microwave Radar
1.7.4 Homing Accuracy of a Radar-Guided Missile
1.7.5 Electromagnetic Wave Vulnerabil 山es of a MiIitary Jet Plane
1.7.6 Millimeter-Wave Propagation in a Defect-Mode Electromagnetic Bandgap Structure
1.7.7 Photonic Crystal Microcavity Laser
1.7.8 Photonic Crystal Cross-Waveguide Switch
1.8 ConcI usions
References
1
2 The One-Dimensional Scalar Wave Equation
2.1 Introduction
2.2 Propagating-Wave Solutions
2.3 Dispersion Relation
2.4 Finite Differences
2.5 Finite-Difference Approximation of the Scalar Wave Equation
2.6 Numerical Dispersion Relation
2.6.1 Case 1: Very Fine SampIing in Time and Space
2.6.2 Case 2: Magic Time-Step
2.6.3 Case 3: Dispersive Wave Propagation
2.6.4 Example of Calculation of Numerical Phase Velocity and Attenuation
2.6.5 Examples of Calculations of Pulse Propagation
2.7 Numerical Stability
2.7.1 Complex-Frequency Analysis
2.7.2 Examples of Calculations Involving Numerical Instability
2.8 Summary
Appendix 2A: Order of Accuracy
2A.1 Lax-Richtmyer Equivalence Theorem
2A.2 Limitations
References
Selected Bibliography on Stability of Finite-Difference Methods
Problems
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vi Computational Electrodynamics: The Finite-Difference Time-Domain Method
3 Introduction to Maxwell's Equations and the Yee Algorithm
Allen Tajlove and Jamesina Simpson
3.1 Introduction
3.2 Maxwell's Equations in Three Dimensions
3.3 Reduction to Two Dimensions
3.3.1 TM Mode z
3.3.2 TE Mode z
3.4 Reduction to One Dimension
3.4.1 x-Directed, z-Polarized TEM Mode
3.4.2 x-Directed, y-Polarized TEM Mode
3.5 Equivalence to the Wave Equation in One Dimension
3.6 The Yee AIgorithm
3.6.1 Basic Ideas
3.6.2 Finite Differences and Notation
3.6.3 Finite-Difference Expressions for Maxwell' s Equations in Three Dimensions
3.6.4 Space Region with a Continuous Variation of Material Properties
3.6.5 Space Region with a Finite Number of Distinct Media
3.6.6 Space Region with Nonpe 口neable Media
3.6.7 Reduction to the Two-Dimensional TM, and TE, Modes
3.6.8 Interpretation as Faraday's and Ampere's Laws in Integral Form
3.6.9 Divergence-Free Nature
3.7 Altemative Finite-Difference Grids
3.7.1 Cartesian Grids
3.7.2 Hexagonal Grids
3.8 Emerging Application: Gridding the Planet Earth
3.8.1 Background
3.8.2 The Latitude-Longitude Space Lattice
3.8.3 The Geodesic (Hexagon-Pentagon) Grid
3.9 Summary
References
Problems

lll
4 Numerical Dispersion and Stability 107
4.1 Introduction 107
4.2 Derivation of the Numerical Dispersion Relation for Two-Dimensional Wave Propagation 107
4.3 Extension to Three Dimensions 110
4.4 Comparison with the Ideal Dispersion Case 111
4.5 Anisotropy of the Numerical Phase Velocity 111
4.5.1 Sample Values of Numerical Phase Velocity III
4.5.2 Intrinsic Grid Velocity Anisotropy 116
4.6 Complex-Valued Numerical Wavenumbers 120
4.6.1 Case 1: Numerical Wave Propagation Along the Principal Lattice Axes 121
4.6.2 Case 2: Numerical Wave Propagation Along a Grid Diagonal 123
4.6.3 Example of Calculation of Numerical Phase Velocity and Attenuation 126
4.6.4 Example ofCalculation ofWave Propagation 126
4.7 Numerical Stability 128
4.7.1 Complex-Frequency Analysis 130
4.7.2 Example of a Numerically Unstable Two-Dimensional FDTD Model 135
4.7.3 Linear Growth Mode When the Normalized Courant Factor Equals 1 137
4.8 Generalized Stability Problem 137
4.8.1 Absorbing and Impedance Boundary Conditions 137
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Contents VI1
"
4.8.2 Variable and Unstructured Meshing 137
4.8.3 Lossy, Dispersive, Nonlinear, and Gain Materials 138
4.9 Modified Yee-Based Algorithms for Mitigating Numerical Dispersion 138
4.9.1 Strategy 1: Center a Specific Numerical Phase-Velocity Curve About c 138
4.9.2 Strategy 2: Use Fourth-Order-Accurate Explicit Spatial Differences 139
4.9.3 Strategy 3: Use a Hexagonal Grid, If Possible 146
4.9.4 Strategy 4: Use Discrete Fourier Transforms to Calculate lhe Spatial Derivatives 150
4.10 Alternating-Direction-lmplicit Time-Stepping Algorithm for Operation
Beyond the Courant Limit 154
4.10.1 Numerical Formulation of the Zheng/Chen /Zhang Algorilhm 155
4.10.2 Sources 161
4.10.3 Numerical Stability 161
4.10.4 Numerical Dispersion 163
4.10.5 Additional Accuracy Limitations and Their lmplications 164
4.11 Summary 164
References 165
Problems 166
Projects 167
5 Incident Wave Source Conditions
Allen Taflove, Geoff Waldschmidt, Chr川opher Wagneκ John Schneider, and Susan Hagness 169
5.1 Introduction
5.2 Pointwise E and H Hard Sources in One Dimension
5.3 Pointwise E and H Hard Sources in Two Dimensions
5.3.1 Green Function for the Scalar Wave Equation in Two Dimensions
5.3.2 Obtaining Comparative FDTD Data
5.3.3 Results for Effective Action Radius of a Hard-Sourced Field Component
5.4 J and M Current Sources in Three Dimensions
5.4 .1 Sources and Charging
5.4.2 Sinusoidal Sources
5.4.3 Transient (Pulse) Sources
5.4.4 Intrinsic Lattice Capacitance
5.4.5 Intrinsic Lattice lnductance
5.4.6 lmpact upon FDTD Simulations of Lumped-Element Capacitors and lnductors
5.5 The Plane-Wave Source Condition
5.6 The Total-Field / Scattered-Field Technique: ldeas and One-Dimensional Formulation
5.6.1 ldeas
5.6.2 One-Dimensional Fo口nulation
5.7 Two-Dimensional Formulation of the TF/SF Technique
5.7.1 Consistency Conditions
5.7.2 Calculation of the Incident Field
5.7.3 Illustrative Example
5.8 Three-Dimensional Formulation of the TF / SF Technique
5.8.1 Consistency Conditions
5.8.2 Calculation of the lncident Field
5.9 Advanced Dispersion Compensation in the TF/SFTechnique
5.9.1 Matched Numerical Dispersion Technique
5.9.2 Analytical Field Propagation
5.10 Scattered-Field Fo口nulation
5.10.1 Application to PEC Structures
5.10.2 Application to Lossy Dielectric Structures
5.10.3 Choice oflncident Plane-Wave Formulation
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VI1 I
6
Computational Electrodynamics: The Finite-Difference Time-Domain Method
5.11 Waveguide Source Conditions
5.1 1.1 Pulsed Electric Field Modal Hard Source
5 门2 Total-Field / Reflected-Field Modal Formulation
5.1 1.3 Resistive Source and Load Conditions
5.12 Summary
References
Problems
Projects
Analytical Absorbing Boundary Conditions
6.1 Introduction
6.2 Bayliss-Turkel Radiation Operators
6.2.1 Sphe口cal Coordinates
6.2.2 Cylindrical Coordinates
6.3 Engquist-Majda One-Way Wave Equations
6.3.1 One-Term and Two-Term Taylor Series Approximations
6.3.2 Mur Fini比-Differcnce Scheme
6.3.3 Trefethen-Halpern Generalized and Higher-Order ABCs
6.3 .4 Theoretical Reflection Coefficient Analysis
6.3.5 Numerical Experiments
6.4 Higdon Radiation Operators
6.4.1 Fo口nuJation
6.4.2 First Two Higdon Operators
6.4.3 Discussion
6.5 Liao Extrapolation in Space and Time
6.5.1 Formulation
6.5.2 Discussion
6.6 Ramahi Complementary Operators
6.6.1 Basic Idea
6.6.2 Complementary Operators
6.6.3 Effect of Multiple Wave Reflections
6.ι4 Basis of the Concurrent Complementary Operator Method
6.6.5 IIlustrative FDTD Modeling Results Obtained Using the C-COM
6.7 Summary
References
Problems
7 Perfectly 岛1atched Layer Absorbing Boundary Conditions
Stephen Gedney
7.1 Introduction
7.2 Plane Wave Incident upon a Lossy Half-Space
7.3 Plane Wave Incident upon Berel咆町's PML Medium
7.3.1 Two-Dimensional TE, Case
7.3.2 Two-Dimensional TM Case z
7.3.3 Three-Dimensional Case
7.4 Stretched-Coordinate Fo口nulation of Bereng町's PML
7.5 An Anisotropic PML Abso由ing Medium
7.5.1 Perfectly Matched Uniaxial Medium
7.5 .2 Relationship to Bereng町's Split-Field PML
7.5.3 A Generalized Three-Dimensional Formulation
7.5.4 Inhomogeneous Media
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7.6 Theoretical Perfonnance of the PML
7.6.1 The Continuous Space
7.6.2 The Discrete Space
7.7 Complex Frequency-Shifted Tensor
7.7.1 Introduction
7.7.2 Strategy to Reduce Late-Time (Low-Frequency) Reflections
7.8 Efficient Implementation of UPML in FDTD
7.8. 1 Derivation of the Finite-Difference Expressions
7.8.2 Computer Implementation of the UPML
7.9 Efficient Implementation of CPML in FDTD
7.9.1 Derivation of the Finite-Difference Expressions
7.9.2 Computer Implementation of the CPML
7.10 Application of CPML in FDTD to General Media
7.10.1 Introduction
7.10.2 Example: Application of CPML to the Debye Medium
7.11 Numerical Experiments with PML
7.1 1.1 Cuπent Source Radiating in an Unbounded Two-Dimensional Region
7.1 1.2 Highly Elongated Domains and Edge Singularities
7.1 1.3肿licrostrip Patch Antenna Array
7.1 1.4 Dispersive Media
7.12 Summary and Conc\usions
References
Projects
8 Near-to-Far-Field Transformation
Allen Tq斤。时, Xu Li, and Susan Hagness
8.1 lntroduction
8.2 Two-Dimer>sional Transfo口口ation . Phasor Domain
8.2.1 Application of Green's Theorem
8.2.2 Far-Field Limit
8.2.3 Reduction to Standard Fonn
8.3 Obtaining Phasor Quantities Via Discrete Fourier Transfonnation
8.4 Surface Equivalence Theorem
8.5 Extension to Three Dimensions, Phasor Domain
8.6 Time-Domain Near-to-Far-Field Transfonnation
8.7 Modified NTFF Procedure to More Accurately Calculate Backscattering from
Strongly Forward-Scattering Objects
8.8 Summary
References
Project
9 Dispersive, Nonlinear, and Gain Materials
Al/en Tafloνe, Susan Hagness, Wojciech Gwarek, Masafumi Fujii, and Shih-Hui Ch"
9.1 Introduction
9.2 Generic Isotropic Material Dispersions
9.2.1 Debye Media
9.2.2 Lorentz ι1edia
9.2.3 Drude Media
9.3 Piecewise-Linear Recursive-Convolution Method, Linear Material Case
9.3.1 General Fonnulation
9.3.2 Application to Debye Media
WL& , FZfs IX
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x Computational Electrodynamics: The Finite-Difference Time-Domain Method
9.3.3 Application to Lorentz Media
9.3.4 Numerical Results
9.4 Auxiliary Differential Equation Method, Linear Material Case
9.4.1 Fo口nulation for Multiple Debye Poles
9.4.2 Fonnulation for Multiple Lorentz Pole Pairs
9.4.3 Foπnulation for Multiple Drude Poles
9.4.4 lIIustrative Numerical Resulls
9.5 Modeling of Linear Magnetized Ferrites
9.5 .1 Equivalent RLC Model
9.5.2 Time-Stepping AIgorithm
9.5.3 EXlension to the Thre坦-Dimensional Case, Including Loss
9.5.4 lIIustralive Numerical Resulls
9.5.5 Comparison of Computer Resources
9.6 Auxiliary Differential Equation Method, Nonlinear Dispersi ve Material Case
9.6.1 Strategy
9.6.2 Contribution of the Linear Debye Polarization
9.6.3 Contribution of the Linear Lorentz Polarization
9.6.4 COnlributions of the Third-Order Nonlinear Polarization
9.6.5 Electric Field Update
9.6.6 lIIuslralive Numerical Results for Temporal Solitons
9.6.7 lIIustrative Numerical Results for Spatial Solitons
9.7 Auxiliary Differential 向uation Method, Macroscopic Modeling of Saturable,
Dispersive Optical Gain Materials
9.7.1 Theory
9.7.2 Validation Studies
9.8 Auxiliary Differential Equation Method, Modeling of Lasing Action in a
Four-Level Two-Eleclron Alomic Syslem
9.8. 1 Quanlum Physics Basis
9.8.2 Coupling lo Maxwell's Equations
9.8.3 Time-Slepping AIgorilhm
9.8.4 Illuslrative Results
9.9 Summary and Conclusions
References
Problems
10 Local Subcell Models of Fine Geometrical Features
A/lell Tafloνe, Malgorzata Celuch-Marcysiak, and Susan Hagness
10.1 Inlroduction
10.2 Basis of Contour-Palh FDTD Modeling
10.3 The Simplest Contour-Palh Subcell Models
10.3.1 Diagonal Splil-Cell Model for PEC Surfaces
10.3.2 A verage Properties Model for Malerial Surfaces
10.4 The COnlour-Palh Model of the Narrow SIOl
10.5 The Contour-Palh Model of lhe Thin Wire
10.6 Locally Confonnal Models of Cu凹ed Surfaces
10.6.1 Yu-Mittra Technique for PEC Slruclures
10.6.2 Illuslrative Results for PEC Structures
10.6.3 Yu-Mittra Technique for Material Structures
10.7 Maloney-Smitl> Technique for Thin Material Sheets
10.7. 1 Basis
10.7.2 llIustrative Results
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10.8 Surface Impedance
10.8.1 The Monochromatic SIBC
10.8.2 Convolution-Based Models of the Frequency-Dependent SIBC
10.8.3 Equivalent-Circuit Model of the Frequency-Dependent SIBC
10.8.4 Sources of Error
10.8.5 Discussion
10.9 Thin Coatings on a PEC Surface
10.9.1 Method of Lee et al
10.9.2 Method of Kärkkäinen
10.10 Relativistic Motion of PEC Boundaries
10.10.1 Basis
10.10.2 Illustrative Results
10.11 Summary and Discussion
References
Selected Bibliography
Projects
11 Nonuniform Grids, Nonorthogonal Grids,
Unstructured Grids, and Subgrids
Stephen Gedney, Faiza Lansing, and Nico/as Chavannes
11.1 Introduction
11.2 Nonuniforrn Orthogonal Grids
11.3 Locally Conforrnal Grids, Globally Orthogonal
11 .4 Global Curvilinear Coordinates
11 .4.1 Nonorthogonal Curvilinear FDTD AIgorithm
11 .4.2 Stability Criterion
11.5 Irregular Nonorthogonal Structured Grids
门6 Iπ'egular Nonorthogonal Unstructured Grids
11.6.1 Generalized Yee AIgorithm
11.6.2 Inhomogeneous Media
11.6.3 Practicallmplementation of the Generalized Yee AIgorithm
11.7 A Planar Generalized Yee AIgorithm
11.7.1 Time-Stepping Expressions
11.7.2 Projection Operators
11. 7.3 Efficient Time-Stepping Implementation
11.7.4 Modeling Example: 32-GHz Wilkinson Power Divider
11.8 Cartesian Subgrids
门8. I Geometry
11.8.2 Time-Stepping Scheme
11.8.3 Spatial Interpolation
11.8.4 Nume口cal Stability Considerations
11.8.5 Reflection from the Interface of the Primary Grid and Subgrid
1 Iι.6 lllustrative Results: Helical Antenna on Generic Cellphone at 900 MHz
11.8.7 Computational Efficiency
11.9 Summary and Conclusions
References
Problems
Projects
COnlencs XI
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12 Bodies of Revolution
Thomas Jurgens, Jeffrey Blaschak, and Gregory Saewert
12.1 lntroduction
12.2 Field Expansion
12.3 Difference Equations for Off-Axis Cells
l23l Ampere's Law Contour Path Integral to Calcuiatc eF
12.3.2 Ampere's Law Contour Path Integral to Calculate e.
12.3.3 Ampe的LawContourpath Integral tocalculate ei
12.3.4 Difference Equations
12.3.5 Surface-Conforming Contour Path Integrals
12.4 Difference Equations for On-Axis Cells
l24l Ampere-s Law Contourpath Intedral to Calculate ez on the z-AXIS
12.4.2 Ampere's Law Contour Path Integral to Calculate e. on the z-Axis
12.4 .3 Faraday's Law Calculation of h, on the z-Axis
12.5 Numerical Stability
12.6 PML Absorbing Boundary Condition
12.6.1 BOR-FDTD Background
12.6.2 Extension of PML to the General BOR Case
12.6.3 Examples
12.7 Application to Particle Accelerator Physics
12.7. 1 Definitions and Concepts
12.7.2 Examples
12.8 Summary
References
Problems
Projects
13 Periodic Structures •
James Maloney and Morris Kesler
13.1 Introduction
13.2 Review of Scattering from Periodic Structures
13.3 Direct Field Methods
13.3.1 Nom>al Incidence Case
13.3.2 Multiple Unit Cells for Oblique Incidence
13.3.3 Sine-Cosine Method
13.3.4 Angled-Update Method
13.4 Introduction to the Field-Tran sformati on Technique
13.5 Multiple-Grid Approach
13.5.1 Forτnulation
13.5.2 Numerical Stability Analysis
13.5 .3 Numerical Dispersion Analysis
13.5.4 Lossy Materials
13.5.5 Lossy Screen Example
13.6 Split-Field Method, Two Dimensions
13.6.1 Formulation
13.6.2 Numerical Stability Analysis
13.6.3 Numerical Dispersion Analysis
13.6.4 Lossy Materials
13.6.5 Lossy Screen Example
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COnlenlS XIII
13.7 Split-Field Method, Three Dimensions
13.7.1 Formulation
13.7.2 Numerical Stability Analysis
13.7.3 UPML Absorbing Boundary Condition
13.8 Application of the Periodic FDTD Method
13.8.1 Electromagnetic Bandgap Structures
13.8.2 Frequency-Selective Surfaces
13.8.3 Antenna Arrays
13.9 Summary and Conc1usions
Acknowledgments
References
Projects
14 Antennas
James Maloney, Glenn Smith, Eric Thiele, Om Gandhi, Nicolas Chavannes, and Susan Hagness 607
14.1 Introduction 607
14.2 Formulation of the Antenna Problem 607
14.2. 1 Transmitting Antenna 607
14.2.2 Receiving Antenna 609
14.2.3 Symmetry 610
14.2.4 Excitation 611
14.3 Antenna Feed Models 612
14.3.1 Detailed Modeling of the Feed 613
14.3.2 Simple Gap Feed Model for a Monopole Antenna 614
14.3.3 Improved Simple Feed Model 617
14.4 Near-to-Far-Field Transformations 621
14.4.1 Use of Symmetry 621
14.4.2 Time-Domain Near-to-Far-Field Transfo口nation 622
14.4.3 Frequency-Domain Near-to-Far-Field Transformation 624
14.5 Plane-Wave Sour,∞ 625
14.5.1 Effect of an Incremental Displacement of the Surface Currents 625
14.5.2 Effect of an Incremental Time Shift 627
14.5.3 Relation to Total-Field I Scattered-Field Lattice Zoning 628
14.6 Casc Study 1: The Standard-Gain Hom 628
14.7 Case Study ll: The Vivaldi SlotIine Array 634
14.7.1 Background 634
14.7.2 The Planar Element 635
14.7.3 The Vivaldi Pair 637
14.7.4 The Vivaldi Quad 639
14.7.5 The Linear Phased Aπay 640
14.7.6 Phased-Array Radiation Characteristics Indicated by the FDTD Modeling 641
14.7.7 Active Impedance ofthe Phased Array 644
14.8 Near-Field Simulations 647
14.8.1 Generic 900-MHz CeIlphone Handset in Free Space 647
14.8.2 900-MHz Dipole Antenna Near a Layered Bone-Brain Half-Space 649
14.8 .3 840-MHz Dipole Antenna Near a Rectangular Brain Phantom 650
14.8.4 900-MHz Infinitesimal Dipole Antenna Near a Spherical Brain Phantom 650
14.8.5 1.9-GHz Half-Wavelength Dipole Near a Spherical Brain Phantom 652
14.9 Case Study 1lI: The Motorola T250 Tri-Band Phone 653
14.9.1 FDTD Phone Model 654
14.9.2 Measurement Procedures 656
14.9.3 Free-Space Near-Field Investigations and Assessment ofDesign Capabilities 656
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xiv Computational Electrodynamics: The Finite-Diffcrence Time-Domain Method
14.9.4 Performance in Loaded Conditions (SAM and MRI-Based Human Head Model) 657
14.9.5 Radiation Perfo口nance in Free Space and Adjaccnt to the SAM Head 659
14.9.6 Computational Requirements 661
14.9.7 Overall Assessment 661
14.10 Selected Additional Applications 661
14.10.1 Use of Electromagnetic Bandgap Materials 662
14.10.2 Ground-Penetrating Radar 663
14.10.3 Antenna-RadomeInteraction 667
14.10.4 Biomedical Applications of Antennas
14.11 Summary and Conclusions
References

15 High-Speed Electronic Circuits with Active and Nonlinear Components
Melinda Piket-May, Wojciech Gwarek, Tzong-Lin Wu, Bijan Houshmand, Tatsuo ltoh,
and Jamesina Simpson 677
15.1 Introduction
15.2 Basic Circuit Parameters forTEM Striplines and Microstrips
15.2.1 Transmission Line Parameters
15.2.2 Impedance
15.2.3 S-Parameters
15.2.4 Differential Capacitance
15.2.5 Differentiallnductance
15.3 Lumped Inductance Due to a Discontinuity
15.3.1 Flux I Curτent De白mtlQn
15.3.2 Fitting Z(ω) or S(ω) to an Equivalent Circuit
15.3.3 Discussion: Choice of Methods
15.4 Inductance of Complex Power-Distribution Systems
15.4 .1 Method Description
15.4.2 Example: Multiplane Meshed Printed-Circuit Board
15.4.3 Discussion
15.5 Parallel Coplanar Microstrips
15.6 Multilayered Interconnect Modeling
15.7 S-Parameter Extraction for General Waveguides
15.8 Digita\ Signal Processing and Spectrum Estimation
15.8.1 Pro町's Method
15.8.2 Autoregressive Models
15.8.3 Padé Approximation
15.9 Modeling of Lumped Circuit Elements
15.9.1 FDTD Formulation Extended to Circuit Elements
15.9.2 The Resistor
15.9.3 The Resistive Voltage Source
15.9.4 The Capacitor
15.9.5 The Inductor
15.9.6 The Arbitrary Two-Terminal Linear Lumped Network
15.9.7 The Diode
15.9.8 The Bipolar Junction Transistor
15.10 Direct Linking ofFDTD and SPICE
15.10.1 BasicIdea
15.10.2 Norton Equivalent Circuit "Looking Into" the FDTD Space Lattice
15.10.3 Thevenin Equivalent Circuit "Looking Into" the FDTD Space Lattice
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Contents xv
15.11 Case Study: A 6-GHz MESFET Amplifier Model 723
15.1 1.1 Large-Signal Nonlinear Model 723
15.1 1.2 Amplifier Configuration 725
15.11.3 Analysis of the Circuit without the Packaging Structure 726
15.1 1.4 Analysis of the Circuit with the Packaging Structure 728
15.12 Emerging Topic: Wireless High-Speed Digital Interconnects Using Defect-Mode
Electromagnetic Bandgap Waveguides 731
15.12.1 Stopband of the Defect-Free Two-Dimensional EBG Structure 732
15.12.2 Passband of the Two-Dimensional EBG Structure with Waveguiding Defect 732
15.12.3 Laboratory Experiments and Supponing FDTD Modeling . 734
15.13 Summary and Conclusions 736
Acknowledgments 737
References 737
Selected Bibliography 740
Projects 741
16 Photonics
Geoffrey Burr, Susan Hagness, and Allen Tajloνe
16.1 Introduction
16.2 Introduction to Index-Contrast Guided-Wave Structures
16.3 FDTD Modeling Issues
16.3.1 Optical Waveguides
16.3.2 Material Dispersion and Nonlinearities
16.4 Laterally Coupled Microcavity Ring Resonators
16.4.1 Modeling Considerations: Two-Dimensional FDTD Simulations
16.4.2 Coupling to Straight Waveguides
16.4.3 Coupling to Curved Waveguides
16.4.4 Elongated Ring Designs C"Racetracks")
16.4.5 Resonances of the Circular Ring
16.5 Laterally Coupled Microcavity Disk Resonators
16.5.1 Resonances
16.5.2 Suppression of Higher-Order Radial Whispering-Galiery Modes
16.6 Venically Coupled Racetrack
16.7 Introduction to Distributed Bragg Reflector Devices
16.8 Application to Venical-Cavity Surface-Emitting Lasers
16.8.1 Passive Studies
16.8.2 Active Studies: Application of the Classical Gain Model
16.8.3 Application of a New Semiclassical Gain Model
16.9 Quasi-One-Dimensional DBR Structures
16.10 Introduction to Photonic Crystals
16.11 Ca1culation of Band Structure
16.1 1.1 The "Order-N" Method
16.11.2 Frequency Resolution
16.1 1.3 Filter Diagonalization Method
16.11 .4 The Triangular Photonic Crystal Lattice
16. 门5 Sources of Erτor and Their Mitigation
16.12 Ca1culation of Mode Pattems
16.13 Variational Approach
16.14 Modeling of Defect-Mode Photonic Crystal Waveguides
16.14.1 Band Diagram of a Photonic Crystal Slab
16.14.2 Band Diagram of a Photonic Crystal Waveguide
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xvi CompUlalional Eleclrodynamics: The Finile-Difference Time-Domain Melhod
16.14.3 Inlrinsic Loss in Pholonic Cryslal Waveguides 798
16.14.4 Transmission in Pholonic CrySlal Waveguides 803
16.14.5 Aperiodic Photonic-Crystal Waveguides 806
16.14.6 Photonic Crystal Waveguide Extrinsic Scattering Loss from the Green Function 806
16.15 Modeling of Photonic Crystal Resonators 807
16.16 Modeling Examples of Photonic Crystal Resonators 810
16.16. 1 Electrically Driven Microcavity Laser 810
16.16.2 Photonic Crystal Cross-Waveguide Switch 812
16.17 Introduction to Frequency Conversion in Second-Order Nonlinear Optical
Materials 813
16.18 PSTD-4 Algorithm 813
16.19 Extension to Second-Order Nonlinear Media 814
16.20 Application to a Nonlinear Waveguide with a QPM Grating 814
16.21 Application to Nonlinear Photonic Crystals 817
16.22 Introduction to Nanoplasmonic Devices 820
16.23 FDTD Modeling Considerations 820
16.24 FDTD Modeling Applications 821
16.25 Introduction to Biophotonics 822
16.26 FDTD Modeling Applications 822
16.26.1 Vertebrate Retinal Rod 822
16.26.2 Precancerous Cervical Cells 824
16.26.3 Sensitivity of Backscattering Signatures to r、Janometer-Scale Cellular Changes 827
16.27 PSTD Modeling Application to Tissue Optics 828
16.28 Summary 830
Acknowledgments 830
References 830
17 Advances in PSTD Techniques
Qing Liu and Gang Zhao
17.1 Introduction
847
847
17.2 Approximation of Derivatives 847
17.2.1 Derivative Matrix for the Second-Order Finite-Difference Method 848
17.2.2 Derivative Matrices for Fourth-Order and N'th-Order Finite-Difference Methods 849
17.2.3 Trigonometric Interpolation and FFI' Method 850
17.2.4 Nonperiodic Functions and Chebyshev Method 851
17 .3 Single-Domain Fourier PSTD Method 854
17.3 .1 Approximation of Spatial Derivatives 855
17.3.2 Numerical Stability and Dispersion 856
17.4 Single-Domain Chebyshev PSTD Method 857
17.4.1 Spatial and TemporaI Grids 857
17.4.2 Maxwell's Equations in Curvilinear Coordinates 858
17.4.3 Spatial Derivatives 860
17.4.4 Time-Integration Scheme 861
17.5 Multidomain Chebyshev PSTD Method 861
17.5.1 Subdomain Spatial Derivatives and Time Integration 862
17.5.2 Subdomain Patching by Characteristics 863
17.5.3 Subdomain Patching by Physical Conditions 864
17.5.4 Filter Design for Comer Singularities 864
17.5.5 Multidomain PSTD Results for 2.5-Dimensional Problems 866
17.5.6 Multidomain PSTD Results for Three-Dimensional Problems 868
17.6 Penalty Method for Multidomain PSTD Algorithm 868
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17.7 Discontinuous Galerkin Method for PSTD Boundary Patching
17.7.1 Weak Forrn of Maxwell's Equations
17.7.2 Space Discretization and Domain Transforrnation
17.7.3 Mass Matrix and Stiffness Matrix
17.7.4 Flux on the Boundary
17.7.5 Numerical Results for DG-PSTD Method
17.8 Summary and Conclusions
Appendix 17 A: Coefficients for the Five-Stage, Fourth-Order Runge-Kutta Method
References
18 Advances in Unconditionally Stable Techniques
Hans De Raedt
18.1 Introduction
18.2 General Framework
18.3 Matrix-Exponential Concepts
18.4 Product-Fo口ηula Approach
18.4 .1 The Classic Yee AIgorithm as a Particular Realization
18.4.2 The ADI Method as a Second Realization
18.4.3 Unconditionally Stable AIgorithms: Real-Space Approach
18.4.4 Unconditionally Stable AIgorithms: Fourier-Space Approach
18.5 Chebyshev Polynomial AIgorithm
18.6 Extension 10 Linear Dispersive Media
18.7 Extension to Perfectly Matched Layer Absorbing Boundary Conditions
18.8 Summary
Appendix 18A: Some Technical Details
Appendix 18B: Stability Analysis of Equation (1 8.17)
Appendix 18C: Stability Analysis ofEquation (18.19)
References
Projects
19 Advances in Hybrid FDTD-FE Techniques
Thomas RyLander, Fredrik EdeLv址, Anders Bondeson, and DougLas Riley
19.1 Introduction
19.2 Time-Domain Finite Elements
19.2.1 Coupled Curl Equations
19.2.2 Wave Equation
19.2.3 Equivalcnces Between Finite Elements and FDTD
ContelZls
19.3 Tetrahedral, Hexahedral (Brick), and Pyr田nidal Zcroth-Order Edge and Facet Elements
19.3.1 Tetrahedral Finite Elements
19.3.2 Hexahedral (Brick) Finite Elements
19.3.3 Pyramidal Finite Elements
19.4 Stable Hybrid FDTD-FE Interface
19.4.1 Spatial Discretization
19.4.2 Time-Stepping on a Hybrid Space Lattice
19.4.3 Generalized Newmark Scheme
19.4.4 Proof of Stability
19.4.5 Alternative Time-Stepping Schemes
19.4.6 Extensions of the Hybrid FDTD-FE Concept
19.4.7 Ref1ection at the Interface of FDTD and FE Regions of a Hybrid Space Lattice
19.4.8 Scattering from the PEC Sphere
19.5 Mesh-Generation Approaches
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