Wave Propagation and Radiation in Gyrotropic and Anisotropic Media

by Abdullah Eroglu

Overview

As technology matures, communication system operation regions shift from mic- wave and millimeter ranges to sub-millimeter ranges. However, device perf- mance at very high frequencies suffers drastically from the material deficiencies. As a result, engineers and scientists are relentlessly in search for the new types of materials, and composites which will meet the device performance requirements and not present any deficiencies due to material electrical and magnetic properties. Anisotropic and gyrotropic materials are the class of the materials which are very important in the development high performance microwave devices and new types composite layered structures. As a result, it is a need to understand the wave propagation and radiation characteristics of these materials to be able to realize them in practice. This book is intended to provide engineers and scientists the required skill set to design high frequency devices using anisotropic, and gyrotropic materials by providing them the theoretical background which is blended with the real world engineering application examples. It is the author’s hope that this book will help to fill the gap in the area of applied electromagnetics for the design of microwave and millimeter wave devices using new types of materials. Each chapter in the book is designed to give the theory first on the subject and solidify it with application examples given in the last chapter. The application examples for the radiation problems are given at the end of Chap. 5 and Chap. 6 for anisotropic and gyrotropic materials, respectively, after the theory section.

Product Details

ISBN-13:	9781441960238
Publisher:	Springer US
Publication date:	09/13/2010
Edition description:	2010
Pages:	222
Product dimensions:	6.40(w) x 9.30(h) x 0.80(d)

Table of Contents

1 Introduction 1

1.1 History of Novel Materials 1

1.2 Maxwell's Equations 2

1.3 Boundary Conditions 4

1.4 Tensors and Dyadic Analysis 7

1.5 Eigenvalue Problems 10

1.6 k-Domain Method 12

References 14

2 Wave Propagation and Dispersion Characteristics in Anisotropic Medium 15

2.1 Dispersion Relations and Wave Matrices 15

2.2 General Form of Dispersion Relations and Wave Matrices 16

2.2.1 Dispersion Relation and Wave Matrix for Uniaxially Anisotropic Medium 18

2.2.2 Dispersion Relation and Wave Matrix for Biaxially Anisotropic Medium 24

2.3 Plane Waves in Anisotropic Medium 26

3 Wave Propagation and Dispersion characteristics in Gyrotropic Medium 29

3.1 Introduction 29

3.2 Constitutive Relations 29

3.3 Dispersion Relations and Wave Matrices 32

3.3.1 Dispersion Relations for Gyrotropic Medium 35

3.4 Plane Waves in Gyrotropic Medium 40

3.4.1 Longitudinal Propagation, θ = 0° 42

3.4.2 Transverse Propagation, θ = 90° 44

3.5 Cut-off and Resonance Conditions 45

3.6 Dispersion Curves and Propagation Characteristics 46

3.6.1 Isotropic Case, No Magnetic Field, Y = 0 47

3.6.2 The Longitudinal Propagation, θ = 0° 48

3.6.3 The Transverse Propagation, θ = 90° 49

3.7 CMA (Clemmow-Mullaly-Allis) Diagram 55

References 55

4 Method of Dyadic Green's Functions 57

4.1 Introduction 57

4.2 Dyadic Green's Functions 57

4.3 Theory of Dyadic Differential Functions 57

4.4 Duality Principle for Dyadic Green's Functions 63

4.5 Formulation of Dyadic Green's Functions 64

4.6 Dyadic Green's Functions for Uniaxially Anisotropic Medium 67

4.6.1 Dyadic Green's Functions for Unbounded Uniaxially Anisotropic Medium 68

4.6.2 Dyadic Green's Functions for Layered Uniaxially Anisotropic Medium 72

4.7 Dyadic Green's Functions for Gyrotropic Medium 73

4.7.1 Electric Type DGF G_ee (r, r′) for a Gyroelectric Medium 73

4.7.2 Magnetic Type DGF G_mm (r, r′) for a Gyroelectric Medium 79

4.8 Application of Duality Principle 82

4.8.1 Electric Type DGF G_ee (r, r′) for a Gyroelectric Medium 83

4.8.2 Magnetic Type DGF G_mm (r, r′) for a Gyroelectric Medium 84

References 85

5 Radiation in Anisotropic Medium 87

5.1 Formulation of the Problem 87

5.2 Far Field Radiation: Dipole Is Over Layered Uniaxially Anisotropic Media 89

5.3 Far Field Radiation: Dipole Is Embedded Inside Two-Layered Anisotropic Media 92

5.4 Physical Interpretation of Dyadic Green's Functions for Radiation Fields 96

5.4.1 G₀₀ (r, r′): Dipole Is Placed Over the Anisotropic Layer 96

5.4.2 G₀₁ (r, r′): Dipole Is Embedded Inside the Anisotropic Layer 97

5.5 Numerical Results 98

5.5.1 Special Cases 98

5.5.2 Effect of Anisotropy 101

5.5.3 Effect of Layer Thickness 104

5.5.4 Effect of Dipole Location 107

Appendix 108

References 114

6 Radiation in Gyrotropic Medium 115

6.1 Formulation of the Problem 115

6.2 Analytical Solution of Far Fields 117

6.3 Numerical Results 134

6.3.1 Numerical Verification 134

6.3.2 Radiation Patterns 136

References 141

7 Wave Theory of Composite Layered Structure 143

7.1 Wave Propagation in Multilayered Isotropic Media 143

7.1.1 Single-Layered Isotropic Media 144

7.1.2 Multilayered Isotropic Media 147

7.2 Wave Propagation in Multilayered Anisotropic Media 150

7.2.1 Single-Layered Anisotropic Media: Vertically Uniaxial Case 150

7.2.2 Single-Layered Anisotropic Media: Optic Axis Titled in One Direction 154

7.2.3 Two-Layered Anisotropic Media: Vertically Uniaxial Case 158

7.2.4 Two-Layered Anisotropic Media: Optic Axis Titled in One Direction 164

7.2.5 Multilayered Anisotropic Media 166

References 168

8 Microwave Devices Using Anisotropic and Gyrotropic Media 169

8.1 Waveguide Design 169

8.1.1 Waveguide Design with Isotropic Media 171

8.1.2 Waveguide Design with Gyrotropic Media 174

8.1.3 Waveguide Design with Anisotropic Media 182

8.1.4 Design Examples 186

8.2 Microstrip Directional Coupler Design 188

8.2.1 Microstrip Directional Coupler Design using Isotropic Medium 188

8.2.2 Microstrip Directional Coupler Design using Anisotropic Medium 192

8.2.3 Microstrip Directional Coupler Design using Gyrotropic Medium 193

8.2.4 Design Examples 197

8.3 Spiral Inductor Design 200

8.4 Microstrip Filter Design 206

8.5 Nonreciprocal Phase Shifter Design 212

References 214

Index 217