Wave Propagation and Radiation in Gyrotropic and Anisotropic Media (eBook)

Wave Propagation and Radiation in Gyrotropic and Anisotropic Media 3
Preface 7
Acknowledgements 9
Contents 11
Chapter 1: Introduction 15
1.1 History of Novel Materials 15
1.2 Maxwell´s Equations 16
1.3 Boundary Conditions 18
1.4 Tensors and Dyadic Analysis 21
1.5 Eigenvalue Problems 24
1.6 k-Domain Method 26
References 28
Chapter 2: Wave Propagation and Dispersion Characteristics in Anisotropic Medium 29
2.1 Dispersion Relations and Wave Matrices 29
2.2 General Form of Dispersion Relations and Wave Matrices 30
2.2.1 Disperison Relation and Wave Matrix for Uniaxially Anisotropic Medium 32
2.2.2 Disperison Relation and Wave Matrix for Biaxially Anisotropic Medium 38
2.3 Plane Waves in Anisotropic Medium 40
Chapter 3: Wave Propagation and Dispersion Characteristics in Gyrotropic Medium 43
3.1 Introduction 43
3.2 Constitutive Relations 43
3.3 Dispersion Relations and Wave Matrices 46
3.3.1 Dispersion Relations for Gyrotropic Medium 49
3.3.1.1 Method I: Dispersion Relation in Terms of k 51
3.3.1.2 Method II: Dispersion Relation in Terms of kz 
53 
3.4 Plane Waves in Gyrotropic Medium 54
3.4.1 Longitudinal Propagation, . = 0º 
56 
3.4.2 Transverse Propagation . = 90º 
58 
3.5 Cut-off and Resonance Conditions 59
3.6 Dispersion Curves and Propagation Characteristics 60
3.6.1 Isotropic Case, No Magnetic Field Y = 0 
61 
3.6.2 The Longitudinal Propagation, . = 0º 
62 
3.6.2.1 The Cut-off and Resonance Conditions for Type I Wave 62
3.6.2.2 The Cut-off and Resonance Conditions for Type II Wave 63
3.6.3 The Transverse Propagation, . = 90º 
63 
3.6.3.1 The Cut-off and Resonance Conditions for Type I Wave 65
3.6.3.2 The Cut-off and Resonance Conditions for Type II Wave 65
3.7 CMA (Clemmow-Mullaly-Allis) Diagram 69
References 69
Chapter 4: Method of Dyadic Green´s Functions 70
4.1 Introduction 70
4.2 Dyadic Green´s Functions 70
4.3 Theory of Dyadic Differential Functions 70
4.4 Duality Principle for Dyadic Green´s Functions 76
4.5 Formulation of Dyadic Green´s Functions 77
4.6 Dyadic Green´s Functions for Uniaxially Anisotropic Medium 80
4.6.1 Dyadic Green´s Functions for Unbounded Uniaxially Anisotropic Medium 81
4.6.2 Dyadic Green´s Functions for Layered Uniaxially Anisotropic Medium 85
4.7 Dyadic Green´s Functions for Gyrotropic Medium 86
4.7.1 Electric Type DGF Gee(r,r') for a Gyroelectric Medium 
86 
4.7.2 Magnetic Type DGF Gmm(r,r') for a Gyroelectric Medium 
92 
4.8 Application of Duality Principle 95
4.8.1 Electric Type DGF Gee(r,r') for a Gyromagnetic Medium 
96 
4.8.2 Magnetic Type DGF Gmmm 
97 
References 98
Chapter 5: Radiation in Anisotropic Medium 99
5.1 Formulation of the Problem 99
5.2 Far Field Radiation: Dipole Is Over Layered Uniaxially Anisotropic Media 101
5.3 Far Field Radiation: Dipole Is Embedded Inside Two-Layered Anisotropic Medium 104
5.4 Physical Interpretation of Dyadic Green´s Functions for Radiation Fields 108
5.4.1 G00 (r,r'): Dipole Is Placed Over the Anisotropic Layer 
108 
5.4.2 G01(r,r'): Dipole Is Embedded Inside the Anisotropic Layer 
109 
5.5 Numerical Results 110
5.5.1 Special Cases 110
5.5.1.1 Case I 110
5.5.1.2 Case II 112
5.5.1.3 Case III 112
5.5.2 Effect of Anisotropy 113
5.5.2.1 Dipole Is Placed Over 113
5.5.2.2 Dipole Is Embedded Inside 115
5.5.3 Effect of Layer Thickness 116
5.5.3.1 Dipole Is Over 116
5.5.3.2 Dipole Is Embedded Inside 118
5.5.4 Effect of Dipole Location 119
Appendix 120
References 126
Chapter 6: Radiation in Gyrotropic Medium 127
6.1 Formulation of the Problem 127
6.2 Analytical Solution of Far Fields 129
6.3 Numerical Results 146
6.3.1 Numerical Verification 146
6.3.2 Radiation Patterns 148
6.3.2.1 Radiation in Region 1 149
6.3.2.2 Radiation in Region 2 150
6.3.2.3 Radiation in Region 4 151
References 153
Chapter 7: Wave Theory of Composite Layered Structures 154
7.1 Wave Propagation in Multilayered Isotropic Media 154
7.1.1 Single-Layered Isotropic Media 155
7.1.1.1 TE Wave 155
7.1.1.2 TM Wave 157
7.1.2 Multilayered Isotropic Media 158
7.1.2.1 TE Wave 158
7.1.2.2 TM Wave 161
7.2 Wave Propagation in Multilayered Anisotropic Media 161
7.2.1 Single-Layered Anisotropic Media: Vertically Uniaxial Case 161
7.2.1.1 TE Wave 163
7.2.1.2 TM Wave 164
7.2.1.3 Numerical Example 164
7.2.2 Single-Layered Anisotropic Media: Optic Axis Tilted in One Direction 165
7.2.2.1 TE Wave 166
7.2.2.2 TM Wave 168
7.2.2.3 Numerical Example 169
7.2.3 Two-Layered Anisotropic Media: Vertically Uniaxial Case 169
7.2.3.1 TE Wave 170
7.2.3.2 TM Wave 172
7.2.3.3 Application Example: Microstrip with Anisotropic Medium 173
7.2.4 Two-Layered Anisotropic Media: Optic Axis Tilted in One Direction 175
7.2.4.1 TE Wave 176
7.2.5 Multilayered Anisotropic Media 177
7.2.5.1 TE Wave 177
References 179
Chapter 8: Microwave Devices Using Anisotropic and Gyrotropic Media 180
8.1 Waveguide Design 180
8.1.1 Waveguide Design with Isotropic Media 182
8.1.1.1 TEmn Modes 183
8.1.2 Waveguide Design with Gyrotropic Media 185
8.1.2.1 TEm0 Modes 190
8.1.3 Waveguide Design with Anisotropic Media 193
8.1.4 Design Examples 197
8.1.4.1 Isotropic Case 197
8.1.4.2 Gyrotropic Case 197
8.1.4.3 Anisotropic Case 198
8.2 Microstrip Directional Coupler Design 199
8.2.1 Microstrip Directional Coupler Design Using Isotropic Medium 199
8.2.2 Microstrip Directional Coupler Design Using Anisotropic Medium 203
8.2.3 Microstrip Directional Coupler Design Using Gyrotropic Medium 204
8.2.4 Design Examples 208
8.3 Spiral Inductor Design 211
8.4 Microstrip Filter Design 217
8.5 Nonreciprocal Phase Shifter Design 223
References 225
Index 227