Frontiers in electromagnetics / edited by Douglas H. Werner, Raj Mittra.

Format:

Book

Contributor:

Werner, Douglas H., 1960-

Mittra, Raj.

IEEE Antennas and Propagation Society.

IEEE Microwave Theory and Techniques Society.

Series:

IEEE Press series on RF and microwave technology

IEEE Press series on microwave technology and RF

Language:

English

Subjects (All):

Electromagnetism.

Physical Description:

xxv, 787 pages, 8 pages of plates : illustrations (some color) ; 26 cm.

Place of Publication:

New York : IEEE Press, [2000]

Summary:

"Frontiers in Electromagnetics" is the first all-in-one resource to bring in-depth original papers on today's major advances in long-standing electromagnetics problems. Highly regarded editors Douglas H. Werner and Raj Mittra have meticulously selected new contributed papers from preeminent researchers in the field to provide state-of-the-art discussions on emerging areas of electromagnetics. Antenna and microwave engineers and students will find key insights into current trends and techniques of electromagnetics likely to shape future directions of this increasingly important topic.

Each chapter includes comprehensive analysis and ample references on innovative subjects that range from combining electromagnetic theory with mathematical concepts to the very latest techniques in electromagnetic optimization and estimation. The contributors also present the latest developments in analytical and numerical methods for solving electromagnetics problems. With a level of expertise simply unmatched in the field, "Frontiers in Electromagnetics" provides readers with a solid foundation to understand this rapidly changing area of technology.

Topics covered on fast-developing applications in electromagnetics include: -- Fractal electrodynamics, fractal antennas and arrays, and scattering from fractally rough surfaces-- Knot electrodynamics-- The role of group theory and symmetry-- Fractional calculus-- Lommel expansions

Contents:

Part I Geometry, Topology, and Groups

Chapter 1 Fractal Electrodynamics: Surfaces and Superlattices / Dwight L. Jaggard, Aaron D. Jaggard, Panayiotis V. Frangos 1

1.2 Introduction to Fractals 3

1.2.1 What are Fractals? 3

1.2.2 Fractal Dimension 7

1.2.3 Fractals and Their Construction 9

1.2.4 Lacunarity 12

1.2.5 Fractals and Waves 15

1.3 Scattering from Fractal Surfaces 15

1.3.1 Problem Geometry 16

1.3.2 Approximate Scattering Solution 17

1.3.3 Exact Scattering Solution 22

1.4 Reflection from Cantor Superlattices 29

1.4.1 Problem Geometry 30

1.4.2 Doubly Recursive Solution 30

1.4.3 Results 32

1.4.4 Fractal Descriptors: Imprinting and Extraction 37

1.4.5 Observations on Superlattice Scattering 41

Chapter 2 Fractal-Shaped Antennas / Carles Puente, Jordi Romeu, Angel Cardama 48

2.2 Fractals, Antennas, and Fractal Antennas 50

2.2.1 Main Fractal Properties 50

2.2.2 Why Fractal-Shaped Antennas? 54

2.3 Multifrequency Fractal-Shaped Antennas 59

2.3.1 The Equilateral Sierpinski Antenna 59

2.3.2 Variations on the Sierpinski Antenna 67

2.3.3 Fractal Tree-Like Antennas 78

2.4 Small Fractal Antennas 81

2.4.1 Some Theoretical Considerations 81

2.4.2 The Small but Long Koch Monopole 83

Chapter 3 The Theory and Design of Fractal Antenna Arrays / Douglas H. Werner, Pingjuan L. Werner, Dwight L. Jaggard, Aaron D. Jaggard, Carles Puente, Randy L. Haupt 94

3.2 The Fractal Random Array 96

3.2.2 Sample Design of a Fractal Random Array and Discussion 98

3.3 Aperture Arrays or Diffractals 100

3.3.1 Calculation of Radiation Patterns 101

3.3.2 Symmetry Relations 102

3.3.3 Cartesian Diffractals 103

3.3.4 Cantor Ring Diffractals 113

3.4 Fractal Radiation Pattern Synthesis Techniques 122

3.4.2 Weierstrass Linear Arrays 123

3.4.3 Fourier-Weierstrass Line Sources 130

3.4.4 Fourier-Weierstrass Linear Arrays 137

3.4.5 Weierstrass Concentric-Ring Planar Arrays 140

3.5 Fractal Array Factors and Their Role in the Design of Multiband Arrays 142

3.5.2 Weierstrass Fractal Array Factors 144

3.5.3 Koch Fractal Array Factors 153

3.6 Deterministic Fractal Arrays 163

3.6.1 Cantor Linear Arrays 164

3.6.2 Sierpinski Carpet Arrays 170

3.6.3 Cantor Ring Arrays 176

3.7 The Concentric Circular Ring Sub-Array Generator 181

3.7.1 Theory 181

Chapter 4 Target Symmetry and the Scattering Dyadic / Carl E. Baum 204

4.2 Reciprocity 208

4.3 Symmetry Groups for Target 208

4.4 Target Symmetry 210

4.5 Symmetry in General Bistatic Scattering 211

4.6 Symmetry in Backscattering 212

4.7 Symmetry in Forward-Scattering 216

4.8 Symmetry in Low-Frequency Scattering 222

4.9 Preliminaries for Self-Dual Targets 226

4.10 Duality 227

4.11 Scattering by Self-Dual Target 228

4.12 Backscattering by Self-Dual Target 229

4.13 Forward-Scattering by Self-Dual Target 231

4.14 Low-Frequency Scattering by Self-Dual Target 233

Chapter 5 Complementary Structures in Two Dimensions / Carl E. Baum 237

5.2 Quasi-Static Boundary Value Problems in Two Dimensions 238

5.3 Two-Dimensional Complementary Structures 240

5.4 Lowest-Order Self-Complementary Rotation Group: C[subscript 2c] Symmetry 241

5.5 N-Fold Rotation Axis: C[subscript N] Symmetry 243

5.6 Self-Complementary Rotation Group: C[subscript Nc] Symmetry 247

5.7 Reciprocation of Two-Dimensional Structures 250

5.8 Reflection Self-Complementarity 254

Chapter 6 Topology in Electromagnetics / Gerald E. Marsh 258

6.2 Magnetic Field Helicity 262

6.3 Solar Prominence Helicity 263

6.4 Twist, Kink, and Link Helicity 265

6.5 Helicity and the Asymptotic Hopf Invariant 270

6.6 Magnetic Energy in Multiply Connected Domains 276

6.6.1 Gauge Invariance 282

Appendix The Classical Hopf Invariant 284

Chapter 7 The Electrodynamics of Torus Knots / Douglas H. Werner 289

7.2 Theoretical Development 291

7.2.2 Electromagnetic Fields of a Torus Knot 294

7.2.3 The Torus Knot EFIE 299

7.3 Special Cases 302

7.3.1 Small Knot Approximation 302

7.3.2 The Canonical Unknot 304

7.4 Elliptical Torus Knots 304

7.4.2 Electromagnetic Fields 307

7.5 Additional Special Cases 308

7.5.1 Circular Torus Knots 308

7.5.2 Small-Knot Approximation 309

7.5.3 Small-Knot Approximations for Circular Torus Knots 311

7.5.4 Small-Knot Approximation 312

7.5.5 Circular Loop and Linear Dipole 319

7.6 Results 320

Part II Optimization and Estimation

Chapter 8 Biological Beamforming / Randy L. Haupt, Hugh L. Southall, Teresa H. O'Donnell 329

8.1 Biological Beamforming 329

8.2 Genetic Algorithm Beamforming 330

8.3 Low Sidelobe Phase Tapers 332

8.4 Phase-Only Adaptive Nulling 335

8.5 Adaptive Algorithm 337

8.6 Adaptive Nulling Results 339

8.7 Neural Network Beamforming 344

8.8 Neural Networks 345

8.9 Direction Finding 346

8.9.1 Analogy Between the Neural Network and the Butler Matrix 346

8.9.2 Single-Source DF: Comparison to Monopulse 352

8.9.3 Multiple-Source Direction Finding 357

8.10 Neural Network Beamsteering 358

8.10.1 Network Architecture for Beamsteering 358

8.10.2 The Experimental Phased-Array Antenna 360

8.10.3 Experimental Beamsteering Results in a Clean Environment 360

8.10.4 Neural Beamsteering in the Presence of a Near-Field Scatterer 364

Chapter 9 Model-Order Reduction in Electromagnetics Using Model-Based Parameter Estimation / Edmund K. Miller, Tapan K. Sarkar 371

9.2 Waveform-Domain and Spectral-Domain Modeling 373

9.2.1 Selecting a Fitting Model 376

9.3 Sampling First-Principle Models and Observables in the Waveform Domain 377

9.3.1 Waveform-Domain Function Sampling 377

9.3.2 Waveform-Domain Derivative Sampling 380

9.3.3 Combining Waveform-Domain Function Sampling and Derivative Sampling 381

9.4 Sampling First-Principle Models and Observables in the Spectral Domain 384

9.4.1 Spectral-Domain Function Sampling 384

9.4.2 Spectral-Domain Derivative Sampling 386

9.4.3 Adapting and Optimizing Sampling of the GM 387

9.4.4 Initializing and Updating the Fitting Models 391

9.5 Application of MBPE to Spectral-Domain Observables 391

9.5.1 Non-Adaptive Modeling 392

9.5.2 Adaptive Modeling 395

9.5.3 Filtering Noisy Spectral Data 399

9.5.4 Estimating Data Accuracy 399

9.6 Waveform-Domain MBPE 402

9.6.1 Radiation-Pattern Analysis and Synthesis 403

9.6.2 Adaptive Sampling of Far-Field Patterns 404

9.6.3 Inverse Scattering 407

9.7 Other EM Fitting Models 407

9.7.1 Antenna Source Modeling Using MBPE 408

9.7.2 MBPE Applied to STEM 409

9.8 MBPE Application to a Frequency-Domain Integral Equation, First-Principles Models 410

9.8.1 The Two Application Domains in Integral-Equation Modeling 413

9.8.2 Formulation-Domain Modeling 414

9.8.3 Using Spectral MBPE in the Solution Domain 424

9.9 Observations and Concluding Comments 427

Appendix 9.1 Estimating Data Rank 429

Appendix 9.2 Using the Matrix Pencil to Estimate Waveform-Domain Parameters 431

Chapter 10 Adaptive Decomposition in Electromagnetics / Joseph W. Burns, Nikola S. Subotic 437

10.2 Adaptive Decomposition 438

10.3 Overdetermined Dictionaries 440

10.3.1 Physics-Based Dictionaries 441

10.3.2 Data-Based Dictionaries 443

10.4 Solution Algorithms 443

10.4.1 Method of Frames 444

10.4.2 Best Orthogonal Basis 444

10.4.3 Basis Pursuit 445

10.4.4 Matching Pursuit 448

10.4.5 Reweighted Minimum Norm 450

10.5 Applications 453

10.5.1 Scattering Decomposition for Inverse Problems 454

10.5.2 Decompositions for Data Filtering 460

10.5.3 Current Decomposition for Forward Problems 468

Part III Analytical Methods

Chapter 11 Lommel Expansions in Electromagnetics / Douglas H.

Werner 474

11.2 The Cylindrical Wire Dipole Antenna 476

11.2.1 The Cylindrical Wire Kernel 478

11.2.2 The Uniform Current Vector Potential and Electromagnetic Fields 481

11.3 The Thin Circular Loop Antenna 486

11.3.1 An Exact Integration Procedure for Near-Zone Vector Potentials of Thin Circular Loops 489

11.4 A Generalized Series Expansion 509

11.5 Applications 514

Chapter 12 Fractional Paradigm in Electromagnetic Theory / Nader Engheta 523

12.2 What is Meant by Fractional Paradigm in Electromagnetic Theory? 524

12.2.1 A Recipe for Fractionalization of a Linear Operator L 528

12.3 Fractional Paradigm and Electromagnetic Multipoles 529

12.4 Fractional Paradigm and Electrostatic Image Methods for Perfectly Conducting Wedges and Cones 536

12.5 Fractional Paradigm in Wave Propagation 540

12.6 Fractionalization of the Duality Principle in Electromagnetism 543

Chapter 13 Spherical-Multipole Analysis in Electromagnetics / Siegfried Blume, Ludger Klinkenbusch 553

13.2 Sphero-Conal Coordinates 556

13.3 Spherical-Multipole Analysis of Scalar Fields 558

13.3.1 Scalar Spherical-Multipole Expansion in Sphero-Conal Coordinates 558

13.3.2 Scalar Orthogonality Relations 565

13.3.3 Scalar Green's Functions in Sphero-Conal Coordinates 567

13.4 Spherical-Multipole Analysis of Electromagnetic Fields 568

13.4.1 Vector Spherical-Multipole Expansion of Solenoidal Electromagnetic Fields 568

13.4.2 Vector Orthogonality Relations 571

13.4.3 Dyadic Green's Functions in Sphero-Conal Coordinates 576

13.4.4 Plane Electromagnetic Waves in Sphero-Conal Coordinates 581

13.5 Applications in Electrical Engineering 584

13.5.1 Electromagnetic Scattering by a PEC Semi-Infinite Elliptic Cone 584

13.5.2 Electromagnetic Scattering by a PEC Finite Elliptic Cone 587

13.5.3 Shielding Properties of a Loaded Spherical Shell with an Elliptic Aperture 594

Appendix 13.1 Solutions of the Vector Helmholtz Equation 599

Appendix 13.2 Paths of Integration for the Eigenfunction Expansion of the Dyadic Green's Function 602

Appendix 13.3 The Euler Summation Technique 604

Part IV Numerical Methods

Chapter 14 A Systematic Study of Perfectly Matched Absorbers / Mustafa Kuzuoglu, Raj Mittra 609

14.2 Systematic Derivation of the Equations Governing Perfectly Matched Absorbers 612

14.2.1 Different PML Realizations for a TM Model Problem 613

14.2.2 Cartesian Mesh Truncations and Corner Regions 617

14.2.3 Example of FEM Implementation of the Cartesian PML 619

14.2.4 Interpretation of the Cartesian PML in Terms of Complex Coordinate Stretching 620

14.2.5 PMLs in Curvilinear Coordinates 622

14.3 Causality and Static PMLs 624

14.3.1 Constitutive Relations of a Causal PML 625

14.3.2 Non-Causal PML Media 627

14.3.3 Static PMLs 629

14.4 Reciprocity in Perfectly Matched Absorbers 632

14.4.1 Verification of Reciprocity in the Anisotropic and Bianisotropic Realizations 632

14.4.2 Example of a Non-Reciprocal PML 636

Chapter 15 Fast Calculation of Interconnect Capacitances Using the Finite Difference Model Applied In Conjunction with the Perfectly Matched Layer (PML) Approach for Mesh Truncation / Vladimir Veremey, Raj Mittra 644

15.2 Finite Difference Mesh Truncation by Means of Anisotropic Dielectric Layers 646

15.2.1 Perfectly Matched Layers for Mesh Truncation in Electrostatics 647

15.3 [alpha]-Technique for FD Mesh Truncation 649

15.4 Wraparound Technique for Mesh Truncation 652

15.5 Two-Step Calculation Method 653

15.6 Numerical Results 654

15.6.1 Microstrip Line Over a Conducting Plane 654

15.6.2 Coupled Microstrip Bends Over a Conducting Plane 655

15.6.3 Crossover 655

15.6.4 Combinations of Bends and Crossovers Above a Conducting Plane 659

15.6.5 Two-Comb Structure Over a Ground Plane 662

15.7 Efficient Computation of Interconnect Capacitances Using the Domain Decomposition Approach 662

Chapter 16 Finite-Difference Time-Domain Methodologies for Electromagnetic Wave Propagation in Complex Media / Jeffrey L. Young 666

16.2 Maxwell's Equations and Complex Media 667

16.3 FDTD Method 669

16.4 Non-Dispersive, Anisotropic Media 671

16.5 Cold Plasma 674

16.5.1 Direct Integration Method One: CP-DIM1 675

16.5.2 Direct Integration Method Two: CP-DIM2 676

16.5.3 Direct Integration Method Three: CP-DIM3 676

16.5.4 Direct Integration Method Four: CP-DIM4 677

16.5.5 Direct Integration Method Five: CP-DIM5 677

16.5.6 Recursive Convolution Method One: CP-RCM1 677

16.5.7 Recursive Convolution Method Two: CP-RCM2 679

16.5.8 Comparative Analysis 680

16.6 Magnetoionic Media 682

16.7 Isotropic, Collisionless Warm Plasma 683

16.8 Debye Dielectric 686

16.8.1 Direct Integration Method One: D-DIM1 687

16.8.2 Direct Integration Method Two: D-DIM2 688

16.8.3 Direct Integration Method Three: D-DIM3 689

16.8.4 Recursive Convolution Method One: D-RCM1 689

16.8.5 Recursive Convolution Method Two: D-RCM2 690

16.8.6 Comparative Analysis 690

16.8.7 Parameter Selection 692

16.9 Lorentz Dielectric 693

16.9.1 Direct Integration Method One: L-DIM1 694

16.9.2 Direct Integration Method Two: L-DIM2 695

16.9.3 Direct Integration Method Three: L-DIM3 695

16.9.4 Recursive Convolution Method One: L-RCM1 696

16.9.5 Recursive Convolution Method Two: L-RCM2 696

16.9.6 Comparative Analysis 697

16.9.7 Numerical Results 698

16.10 Magnetic Ferrites 699

16.11 Nonlinear Dispersive Media 702

Chapter 17 A New Computational Electromagnetics Method Based on Discrete Mathematics / Rodolfo E. Diaz, Franco Deflaviis, Massimo Noro, Nicolaos G. Alexopoulos 708

17.2 The Fitzgerald Mechanical Model 710

17.3 Extension to Debye Materials 713

17.4 The Simulation of General Ponderable Media 721

17.4.1 Non-Linear Dielectrics 721

17.4.2 How Should Moving Ponderable Media be Modeled? 723

17.4.3 Collisions Between Pulses and Objects 726

Chapter 18 Artificial Bianisotropic Composites / Frederic Mariotte, Bruno Sauviac, Sergei A. Tretyakov 732

18.2 Chiral Media and Omega Media 734

18.2.1 Classification of Bianisotropic Composites 734

18.2.2 Constitutive Equations and Electromagnetic Properties of Chiral Media 735

18.2.3 Wave Propagation in Chiral Materials 738

18.2.4 Field Equations for Uniaxial Omega Regions 741

18.2.5 Plane Eigenwaves, Propagation Factors, and Wave Impedances of Omega Media 741

18.3 Electromagnetic Scattering by Chiral Objects and Medium Modeling 743

18.3.1 Baseline to Model Bianisotropic Composites 743

18.3.2 Analytical Integral Equation Method for a Standard Helix 743

18.3.3 Numerical Integral Equation Method Using the Thin-Wire Approximation 744

18.3.4 Dipole Representation and Equivalent Polarizabilities for Chiral Scatterers 748

18.3.5 Analytical Antenna Model for Canonical Chiral Objects and Omega Scatterers 750

18.3.6 Composite Modeling: Effective Medium Parameters 754

18.4 Reflection and Transmission in Chiral and Omega Slabs: Applications 756

18.4.1 Continuity Problems with a Chiral Medium 756

18.4.2 Properties of a Single Slab 760

18.4.3 Properties of a Chiral Dallenbach Screen 764

18.4.4 Reflection and Transmission in Uniaxial Omega Slabs 765

18.4.5 Zero-Reflection Condition. Omega Slabs on Metal Surface 766

18.5 Future Developments and Applications 767.

Notes:

Includes bibliographical references and index.

"IEEE Antennas & Propagation Society, sponsor, IEEE MTTS, Microwave Theory and Techniques Society, sponsor."

"IEEE order no. PC5754"--T.p. verso.

ISBN:

0780347013

OCLC:

41465633