Frontiers in Electromagnetics

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ISBN: 9780780347014 | 0780347013
Cover: Hardcover
Copyright: 12/10/1999

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"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 a comprehensive analysis and ample references on innovative subjects that range from combining electromagnetic theory with mathematical concepts to the most recent 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 unmatched in the field, FRONTIERS IN ELECTROMAGNETICS provides readers with a solid foundation to understand this rapidly changing area of technology. Topics covering fast-developing applications in electromagnetics include:Fractal electrodynamics, fractal antennas and arrays, and scattering from fractally rough surfacesKnot electrodynamicsThe role of group theory and symmetryFractional calculusLommel and multiple expansions. Professors: To request an examination copy simply e-mail collegeadoption@ieee.org." Sponsored by: IEEE Microwave Theory and Techniques Society, IEEE Antennas and Propagation Society.

Preface

xxi

List of Contributors

xxiii

PART I GEOMETRY, TOPOLOGY, AND GROUPS

Fractal Electrodynamics: Surfaces and Superlattices

(47)

Dwight L. Jaggard

Aaron D. Jaggard

Panayiotis V. Frangos

Introduction

(2)

Background

(1)

Overview

(1)

Introduction to Fractals

(12)

What are Fractals?

(1)

Fractal Characteristics

(2)

Bandlimited Fractals and Prefractals

(1)

Bandlimited Weierstrass Function

(1)

Triadic Cantor Set

(1)

Fractal Dimension

(1)

Motivation

(1)

Definition

(1)

Extensions

(1)

Fractals and Their Construction

(1)

Bandlimited Weierstrass Function

(1)

Sierpinski Gasket

(1)

Polyadic Cantor Bars---Minimal Lacunarity

(1)

Lacunarity

(1)

Concept

(1)

Examples---Polyadic Cantor Bars with Variable Lacunarity

(1)

Definition

(1)

Fractals and Waves

(1)

Scattering from Fractal Surfaces

(14)

Problem Geometry

(1)

Approximate Scattering Solution

(1)

Formulation of Approximate Surface Scattering Solution

(2)

Scattering Cross Sections for the Approximate Case

(3)

Observations on the Approximate Case

(1)

Exact Scattering Solution

(1)

Formulation of Exact Surface Scattering Solution

(1)

Scattering Cross Sections for the Exact Case

(5)

Observations on the Exact Case

(1)

Reflection from Cantor Superlattices

(13)

Problem Geometry

(1)

Doubly Recursive Solution

(2)

Results

(1)

Twist Plots

(1)

Nulls and Their Structure

(2)

Polarization

(2)

Fractal Descriptors: Imprinting and Extraction

(1)

Frequency-Domain Approach

(2)

Time-Scale Approach

(2)

Observations on Superlattice Scattering

(1)

Conclusion

(6)

References

(6)

Fractal-Shaped Antennas

(46)

Carles Puente

Jordi Romeu

Angel Cardama

Introduction

(2)

Fractals, Antennas, and Fractal Antennas

(9)

Main Fractal Properties

(1)

Fractal Self-Similarity

(3)

The Fractal Dimension

(1)

Why Fractal-Shaped Antennas?

(1)

Multifrequency Fractal Antennas

(2)

Small Fractal Antennas

(2)

Multifrequency Fractal-Shaped Antennas

(22)

The Equilateral Sierpinski Antenna

(1)

The Sierpinski Gasket

(1)

Input Impedance and Return-Loss

(3)

Radiation Patterns

(1)

Current Density Distribution

(2)

Iterative Transmission Line Network Model

(3)

Variations on the Sierpinski Antenna

(1)

Variations on the Flare Angle

(7)

Shifting the Operating Bands

(3)

Fractal Tree-Like Antennas

(3)

Small Fractal Antennas

(13)

Some Theoretical Considerations

(1)

About the Koch Curve

(1)

Theoretical Hypothesis

(1)

The Small but Long Koch Monopole

(1)

Antenna Description

(1)

Input Parameters

(2)

The Quality Factor

(3)

Current Distributions

(1)

Conclusion

(1)

References

(3)

The Theory and Design of Fractal Antenna Arrays

(110)

Douglas H. Werner

Pingjuan L. Werner

Dwight L. Jaggard

Aaron D. Jaggard

Carles Puente

Randy L. Haupt

Introduction

(2)

The Fractal Random Array

(4)

Background and Motivation

(2)

Sample Design of a Fractal Random Array and Discussion

(2)

Aperture Arrays or Diffractals

100

(22)

Calculation of Radiation Patterns

101

(1)

Symmetry Relations

102

(1)

Cartesian Diffractals

103

(1)

Cantor Square Diffraction

104

(1)

Purina Square Diffraction

105

(1)

Sierpinski Square Diffraction

105

(1)

Discussion

105

(8)

Cantor Ring Diffractals

113

(1)

Triadic Cantor Ring Diffractal

114

(2)

Polyadic Cantor Diffractal

116

(4)

Discussion

120

(2)

Fractal Radiation Pattern Synthesis Techniques

122

(20)

Background

122

(1)

Weierstrass Linear Arrays

123

(7)

Fourier-Weierstrass Line Sources

130

(7)

Fourier-Weierstrass Linear Arrays

137

(3)

Weierstrass Concentric-Ring Planar Arrays

140

(2)

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

142

(21)

Background

142

(2)

Weierstrass Fractal Array Factors

144

(9)

Koch Fractal Array Factors

153

(3)

Reducing the Number of Elements: Array Truncation

156

(1)

Koch-Pattern Construction Algorithm

157

(4)

The Backman-Koch Array Factor

161

(2)

Deterministic Fractal Arrays

163

(18)

Cantor Linear Arrays

164

(6)

Sierpinski Carpet Arrays

170

(6)

Cantor Ring Arrays

176

(1)

Formulation

176

(1)

Results and Discussion

177

(4)

The Concentric Circular Ring Sub-Array Generator

181

(19)

Theory

181

(3)

Examples

184

(1)

Linear Arrays

184

(2)

Planar Square Arrays

186

(3)

Planar Triangular Arrays

189

(4)

Hexagonal Arrays

193

(7)

Conclusion

200

(4)

References

200

(4)

Target Symmetry and the Scattering Dyadic

204

(33)

Carl E. Baum

Introduction

204

(4)

Reciprocity

208

(1)

Symmetry Groups for Target

208

(2)

Target Symmetry

210

(1)

Symmetry in General Bistatic Scattering

211

(1)

Symmetry in Backscattering

212

(4)

Symmetry in Forward-Scattering

216

(6)

Symmetry in Low-Frequency Scattering

222

(4)

Preliminaries for Self-Dual Targets

226

(1)

Duality

227

(1)

Scattering by Self-Dual Target

228

(1)

Backscattering by Self-Dual Target

229

(2)

Forward-Scattering by Self-Dual Target

231

(2)

Low-Frequency Scattering by Self-Dual Target

233

(1)

Conclusion

234

(3)

References

235

(2)

Complementary Structures in Two Dimensions

237

(21)

Carl E. Baum

Introduction

237

(1)

Quasi-Static Boundary Value Problems in Two Dimensions

238

(2)

Two-Dimensional Complementary Structures

240

(1)

Lowest-Order Self-Complementary Rotation Group: C2c Symmetry

241

(2)

N-Fold Rotation Axis: CN Symmetry

243

(4)

Self-Complementary Rotation Group: CNc Symmetry

247

(3)

Reciprocation of Two-Dimensional Structures

250

(4)

Reflection Self-Complementarity

254

(1)

Conclusion

255

(3)

References

256

(2)

Topology in Electromagnetics

258

(31)

Gerald E. Marsh

Introduction

258

(4)

Magnetic Field Helicity

262

(1)

Solar Prominence Helicity

263

(2)

Twist, Kink, and Link Helicity

265

(5)

Helicity and the Asymptotic Hopf Invariant

270

(6)

Magnetic Energy in Multiply Connected Domains

276

(6)

Gauge Invariance

282

(1)

Conclusion

282

(7)

Appendix: The Classical Hopf Invariant

284

(2)

References

286

(3)

The Electrodynamics of Torus Knots

289

(40)

Douglas H. Werner

Introduction

289

(2)

Theoretical Development

291

(11)

Background

291

(3)

Electromagnetic Fields of a Torus Knot

294

(5)

The Torus Knot EFIE

299

(3)

Special Cases

302

(2)

Small Knot Approximation

302

(2)

The Canonical Unknot

304

(1)

Elliptical Torus Knots

304

(4)

Background

304

(3)

Electromagnetic Fields

307

(1)

Additional Special Cases

308

(12)

Circular Torus Knots

308

(1)

Small-Knot Approximation

309

(1)

General Case

309

(1)

Special Case when p = q

310

(1)

Special Case when p = 2q

310

(1)

Small-Knot Approximations for Circular Torus Knots

311

(1)

Special Case when p = q and γ = α

311

(1)

Special Case when p = 2q and γ = α

311

(1)

Small-Knot Approximation

312

(1)

General Case

312

(1)

Special Case when p/q = 2n

313

(2)

Special Case when p/q = 2n - 1

315

(2)

Special Case when p/q = (2n - 1)/2

317

(2)

Circular Loop and Linear Dipole

319

(1)

Results

320

(5)

Conclusion

325

(4)

Appendix

326

(1)

References

327

(2)

PART II Optimization and Estimation

Biological Beamforming

329

(42)

Randy L. Haupt

Hugh L. Southall

Teresa H. O'Donnell

Biological Beamforming

329

(1)

Genetic Algorithm Beamforming

330

(2)

Low Sidelobe Phase Tapers

332

(3)

Phase-Only Adaptive Nulling

335

(2)

Adaptive Algorithm

337

(2)

Adaptive Nulling Results

339

(5)

Neural Network Beamforming

344

(1)

Neural Networks

345

(1)

Direction Finding

346

(12)

Analogy Between the Neural Network and the Butler Matrix

346

(6)

Single-Source DF: Comparison to Monopulse

352

(1)

Network Architecture for Single-Source DF

352

(1)

Network Training

353

(1)

Rapid Convergence

354

(1)

Monopulse Direction Finding

355

(1)

Experimental DF Results

355

(2)

Multiple-Source Direction Finding

357

(1)

Neural Network Beamsteering

358

(13)

Network Architecture for Beamsteering

358

(2)

The Experimental Phased-Array Antenna

360

(1)

Experimental Beamsteering Results in a Clean Environment

360

(4)

Neural Beamsteering in the Presence of a Near-Field Scatterer

364

(1)

Neural Network Beamsteering

365

(1)

Theoretical Predictions

365

(2)

Description of the Scattering Experiment

367

(1)

Experimental Beamsteering Results with a Near-Field Scatterer

368

(1)

References

368

(3)

Model-Order Reduction in Electromagnetics Using Model-Based Parameter Estimation

371

(66)

Edmund K. Miller

Tapan K. Sarkar

Background and Motivation

371

(2)

Waveform-Domain and Spectral-Domain Modeling

373

(4)

Selecting a Fitting Model

376

(1)

Sampling First-Principle Models and Observables in the Waveform Domain

377

(7)

Waveform-Domain Function Sampling

377

(3)

Waveform-Domain Derivative Sampling

380

(1)

Combining Waveform-Domain Function Sampling and Derivative Sampling

381

(3)

Sampling First-Principle Models and Observables in the Spectral Domain

384

(7)

Spectral-Domain Function Sampling

384

(2)

Spectral-Domain Derivative Sampling

386

(1)

Adapting and Optimizing Sampling of the GM

387

(1)

Possible Adaptive Sampling Strategies

388

(1)

Estimating FM Error or Uncertainty as an Adaptation Strategy

389

(2)

Initializing and Updating the Fitting Models

391

(1)

Application of MBPE to Spectral-Domain Observables

391

(11)

Non-Adaptive Modeling

392

(3)

Adaptive Modeling

395

(4)

Filtering Noisy Spectral Data

399

(1)

Estimating Data Accuracy

399

(3)

Waveform-Domain MBPE

402

(5)

Radiation-Pattern Analysis and Synthesis

403

(1)

Adaptive Sampling of Far-Field Patterns

404

(3)

Inverse Scattering

407

(1)

Other EM Fitting Models

407

(3)

Antenna Source Modeling Using MBPE

408

(1)

MBPE Applied to STEM

409

(1)

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

410

(17)

The Two Application Domains in Integral-Equation Modeling

413

(1)

Formulation-Domain Modeling

414

(1)

Waveform-Based MBPE in the Formulation Domain

414

(1)

Modeling Frequency Variations: Antenna Applications

415

(2)

Modeling Frequency Variations: Elastodynamic Scattering

417

(1)

Modeling Spatial Variations: The Sommerfeld Problem

417

(3)

Modeling Spatial Variations: Waveguide Fields

420

(1)

Modeling Spatial Variations: Moment-Method Impedance Matrices

421

(3)

Using Spectral MBPE in the Solution Domain

424

(1)

Modeling the Admittance Matrix

424

(1)

Sampling Admittance-Matrices Derivatives

425

(2)

Observations and Concluding Comments

427

(10)

Appendix 9.1: Estimating Data Rank

429

(2)

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

431

(2)

References

433

(4)

Adaptive Decomposition in Electromagnetics

437

(37)

Joseph W. Burns

Nikola S. Subotic

Introduction

437

(1)

Adaptive Decomposition

438

(2)

Overdetermined Dictionaries

440

(3)

Physics-Based Dictionaries

441

(2)

Data-Based Dictionaries

443

(1)

Solution Algorithms

443

(10)

Method of Frames

444

(1)

Best Orthogonal Basis

444

(1)

Basis Pursuit

445

(1)

Basis Pursuit Decomposition Example

446

(2)

Matching Pursuit

448

(1)

Matching Pursuit Decomposition Example

449

(1)

Reweighted Minimum Norm

450

(1)

Reweighted Minimum Norm Decomposition Example

451

(2)

Applications

453

(17)

Scattering Decomposition for Inverse Problems

454

(1)

Identification of Scattering Centers in Range Profiles

454

(3)

Identification of Scattering Centers in SAR Imagery

457

(3)

Decompositions for Data Filtering

460

(1)

Measurement Contamination Mitigation

461

(7)

Current Decomposition for Forward Problems

468

(1)

Basis Transformation

468

(1)

Adaptive Construction of Basis Functions

469

(1)

Conclusion

470

(4)

References

470

(4)

PART III ANALYTICAL METHODS

Lommel Expansions in Electromagnetics

474

(49)

Douglas H. Werner

Introduction

474

(2)

The Cylindrical Wire Dipole Antenna

476

(10)

The Cylindrical Wire Kernel

478

(3)

The Uniform Current Vector Potential and Electromagnetic Fields

481

(5)

The Thin Circular Loop Antenna

486

(23)

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

489

(1)

Examples

490

(1)

Fourier Cosine Series Representation of the Loop Current

490

(5)

The Uniform Current Loop Antenna

495

(3)

The Cosinusoidal Current Loop Antenna

498

(3)

General Far-Field Approximations

501

(1)

The Traveling-Wave Current Loop Antenna

501

(8)

A Generalized Series Expansion

509

(5)

Applications

514

(5)

Conclusion

519

(4)

References

520

(3)

Fractional Paradigm in Electromagnetic Theory

523

(30)

Nader Engheta

Introduction

523

(1)

What is Meant by Fractional Paradigm in Electromagnetic Theory?

524

(5)

A Recipe for Fractionalization of a Linear Operator L

528

(1)

Fractional Paradigm and Electromagnetic Multipoles

529

(7)

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

536

(4)

Fractional Paradigm in Wave Propagation

540

(3)

Fractionalization of the Duality Principle in Electromagnetism

543

(4)

Summary

547

(6)

Appendix

547

(1)

References

548

(5)

Spherical-Multipole Analysis in Electromagnetics

553

(56)

Siegfried Blume

Ludger Klinkenbusch

Introduction

553

(3)

Sphero-Conal Coordinates

556

(2)

Spherical-Multipole Analysis of Scalar Fields

558

(10)

Scalar Spherical-Multipole Expansion in Sphero-Conal Coordinates

558

(7)

Scalar Orthogonality Relations

565

(1)

Orthogonality of Lame Products

565

(1)

Orthogonality of Scalar Multipole Functions

566

(1)

Scalar Green's Functions in Sphero-Conal Coordinates

567

(1)

Spherical-Multipole Analysis of Electromagnetic Fields

568

(16)

Vector Spherical-Multipole Expansion of Solenoidal Electromagnetic Fields

568

(3)

Vector Orthogonality Relations

571

(1)

Orthogonality of the Transverse Vector Functions

571

(2)

Orthogonality of the Vector Spherical-Multipole Functions

573

(3)

Dyadic Green's Functions in Sphero-Conal Coordinates

576

(5)

Plane Electromagnetic Waves in Sphero-Conal Coordinates

581

(3)

Applications in Electrical Engineering

584

(25)

Electromagnetic Scattering by a PEC Semi-Infinite Elliptic Cone

584

(3)

Electromagnetic Scattering by a PEC Finite Elliptic Cone

587

(7)

Shielding Properties of a Loaded Spherical Shell with an Elliptic Aperture

594

(5)

Appendix 13.1 Solutions of the Vector Helmholtz Equation

599

(3)

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

602

(2)

Appendix 13.3 The Euler Summation Technique

604

(2)

References

606

(3)

PART IV NUMERICAL METHODS

A Systematic Study of Perfectly Matched Absorbers

609

(35)

Mustafa Kuzuoglu

Raj Mittra

Introduction

609

(3)

Systematic Derivation of the Equations Governing Perfectly Matched Absorbers

612

(12)

Different PML Realizations for a TM Model Problem

613

(1)

The Split-Field Realization

614

(1)

The Anisotropic Realization

615

(1)

The Bianisotropic Realization

616

(1)

Cartesian Mesh Truncations and Corner Regions

617

(2)

Example of FEM Implementation of the Cartesian PML

619

(1)

Interpretation of the Cartesian PML in Terms of Complex Coordinate Stretching

620

(2)

PMLs in Curvilinear Coordinates

622

(1)

Split-Field (Non-Maxwellian) Realization

623

(1)

Anisotropic Realization

623

(1)

Bianisotropic Realization

624

(1)

Causality and Static PMLs

624

(8)

Constitutive Relations of a Causal PML

625

(2)

Non-Causal PML Media

627

(2)

Static PMLs

629

(3)

Reciprocity in Perfectly Matched Absorbers

632

(6)

Verification of Reciprocity in the Anisotropic and Bianisotropic Realizations

632

(4)

Example of a Non-Reciprocal PML

636

(2)

Conclusion

638

(6)

References

639

(5)

Fast Calculation of Interconnect Capacitances Using the Finite Difference Model Applied in Conjunction with the Perfectly Matched Layer (PML) Approach for Mesh Truncation

644

(22)

Vladimir Veremey

Raj Mittra

Introduction

644

(2)

Finite Difference Mesh Truncation by Means of Anisotropic Dielectric Layers

646

(3)

Perfectly Matched Layers for Mesh Truncation in Electrostatics

647

(2)

α-Technique for FD Mesh Truncation

649

(3)

Wraparound Technique for Mesh Truncation

652

(1)

Two-Step Calculation Method

653

(1)

Numerical Results

654

(8)

Microstrip Line Over a Conducting Plane

654

(1)

Coupled Microstrip Bends Over a Conducting Plane

655

(1)

Crossover

655

(4)

Combinations of Bends and Crossovers Above a Conducting Plane

659

(3)

Two-Comb Structure Over a Ground Plane

662

(1)

Efficient Computation of Interconnect Capacitances Using the Domain Decomposition Approach

662

(3)

Conclusion

665

(1)

References

665

(1)

Finite-Difference Time-Domain Methodologies for Electromagnetic Wave Propagation in Complex Media

666

(42)

Jeffrey L. Young

Introduction

666

(1)

Maxwell's Equations and Complex Media

667

(2)

FDTD Method

669

(2)

Non-Dispersive, Anisotropic Media

671

(3)

Cold Plasma

674

(8)

Direct Integration Method One: CP-DIM1

675

(1)

Direct Integration Method Two: CP-DIM2

676

(1)

Direct Integration Method Three: CP-DIM3

676

(1)

Direct Integration Method Four: CP-DIM4

677

(1)

Direct Integration Method Five: CP-DIM5

677

(1)

Recursive Convolution Method One: CP-RCM1

677

(2)

Recursive Convolution Method Two: CP-RCM2

679

(1)

Comparative Analysis

680

(2)

Magnetoionic Media

682

(1)

Isotropic, Collisionless Warm Plasma

683

(3)

Debye Dielectric

686

(7)

Direct Integration Method One: D-DIM1

687

(1)

Direct Integration Method Two: D-DIM2

688

(1)

Direct Integration Method Three: D-DIM3

689

(1)

Recursive Convolution Method One: D-RCM1

689

(1)

Recursive Convolution Method Two: D-RCM2

690

(1)

Comparative Analysis

690

(2)

Parameter Selection

692

(1)

Lorentz Dielectric

693

(6)

Direct Integration Method One: L-DIM1

694

(1)

Direct Integration Method Two: L-DIM2

695

(1)

Direct Integration Method Three: L-DIM3

695

(1)

Recursive Convolution Method One: L-RCM1

696

(1)

Recursive Convolution Method Two: L-RCM2

696

(1)

Comparative Analysis

697

(1)

Numerical Results

698

(1)

Magnetic Ferrites

699

(3)

Nonlinear Dispersive Media

702

(2)

Summary

704

(4)

References

705

(3)

A New Computational Electromagnetics Method Based on Discrete Mathematics

708

(24)

Rodolfo E. Diaz

Franco Deflaviis

Massimo Noro

Nicolaos G. Alexopoulos

Introduction

708

(2)

The Fitzgerald Mechanical Model

710

(3)

Extension to Debye Materials

713

(8)

The Simulation of General Ponderable Media

721

(8)

Non-Linear Dielectrics

721

(2)

How Should Moving Ponderable Media be Modeled?

723

(3)

Collisions Between Pulses and Objects

726

(3)

Conclusion

729

(3)

References

730

(1)

Glossary

731

(1)

Artifical Bianisotropic Composites

732

(39)

Frederic Mariotte

Bruno Sauviac

Sergei A. Tretyakov

Introduction

732

(2)

Chiral Media and Omega Media

734

(9)

Classification of Bianisotropic Composites

734

(1)

Constitutive Equations and Electromagnetic Properties of Chiral Media

735

(1)

The Three General Formulations

736

(2)

Energy Considerations for Material Parameters

738

(1)

Wave Propagation in Chiral Materials

738

(3)

Field Equations for Uniaxial Omega Regions

741

(1)

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

741

(2)

Electromagnetic Scattering by Chiral Objects and Medium Modeling

743

(13)

Baseline to Model Bianisotropic Composites

743

(1)

Analytical Integral Equation Method for a Standard Helix

743

(1)

Numerical Integral Equation Method Using the Thin-Wire Approximation

744

(4)

Dipole Representation and Equivalent Polarizabilities for Chiral Scatterers

748

(1)

Calculation of Dipole Moments

748

(1)

Polarizabilities Calculation

749

(1)

Analytical Antenna Model for Canonical Chiral Objects and Omega Scatterers

750

(1)

Antenna Representation for the Chiral Scatterer---Polarizability Dyadic

751

(2)

Antenna Representation for the Omega Scatterer

753

(1)

Composite Modeling: Effective Medium Parameters

754

(1)

Isotropic Chiral Composites

754

(1)

Bianisotropic Composites

755

(1)

A Relation Between the Polarizabilities

756

(1)

Reflection and Transmission in Chiral and Omega Slabs: Applications

756

(11)

Continuity Problems with a Chiral Medium

756

(4)

Properties of a Single Slab

760

(4)

Properties of a Chiral Dallenbach Screen

764

(1)

Reflection and Transmission in Uniaxial Omega Slabs

765

(1)

Zero-Reflection Condition. Omega Slabs on Metal Surface

766

(1)

Future Developments and Applications

767

(4)

References

769

(2)

Index

771

(14)

About the Editors

785

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Frontiers in Electromagnetics

Summary

Author Biography

Table of Contents

Supplemental Materials