Preface ........................................................ ix
Chapter 1 Introduction ......................................... 1
1.1 Microscopic-Macroscopic Transformation ..................... 3
1.2 Metamaterials .............................................. 4
1.3 Free-Space Measurements and Focusing ....................... 5
1.4 Waveguide Measurements ..................................... 6
1.5 Resonator Measurements ..................................... 7
1.6 Radio Frequency (RF) Measurements ......................... 10
1.7 Measurement Accuracy and Extraction Sensitivity ........... 16
References ..................................................... 17
Chapter 2 Fundamentals ........................................ 19
2.1 Spectral Transformations .................................. 19
2.1.1 Sturm-Liouville Eigenvalue Problems ................ 19
2.1.2 Sin-Series and Cos-Series Expansions ............... 20
2.1.3 Fourier Series and Fourier Transform ............... 21
2.1.4 Fourier-Bessel Series and Hankel Transform ......... 23
2.1.5 Multidimensional Fourier Transform ................. 24
2.2 Maxwell's Equations in Free Space ......................... 26
2.2.1 Time Domain ........................................ 26
2.2.2 Frequency Domain and Auxiliary Potentials .......... 27
2.2.3 Spectral Domain and Plane Waves .................... 30
2.3 Constitutive Relations .................................... 35
2.3.1 Time Domain and Transient and Steady-State
Constitutive Relations ............................. 35
2.3.2 Frequency Domain and Steady-State Constitutive
Relations .......................................... 41
References ..................................................... 45
Chapter 3 Propagation in Homogeneous Media .................... 47
3.1 Source-Free Electromagnetic Fields in Homogeneous Media ... 48
3.2 Plane Waves and Polarization .............................. 53
3.2.1 Plane Waves ........................................ 56
3.2.2 Polarization ....................................... 57
3.3 Electromagnetic Fields in Material Layers ................. 61
3.3.1 Infinitely Extended Material Slabs ................. 61
3.3.2 Cylindrical Shells ................................. 66
3.3.3 Spherical Shells ................................... 68
3.4 Antennas and Antenna Arrays ............................... 72
Electromagnetic Scattering and Material Characterization
3.4.1 Infinitesimally Short Current Element (Point
Electric Dipole) ................................... 72
3.4.2 Infinitesimal Current Loop (Point Magnetic
Dipole) ............................................ 77
3.4.3 Basic Antenna Characteristics ...................... 79
3.4.4 Antenna Arrays ..................................... 84
3.5 Dispersion ................................................ 87
3.6 The Concept of Focusing ................................... 90
3.7 Focusing Using a Linear Antenna Array ..................... 92
References ................................................ 97
Chapter 4 Guided Wave Propagation .............................. 99
4.1 Guided Waves in Homogeneously Filled Waveguides .......... 102
4.1.1 ТЕМ Modes ......................................... 103
4.1.2 ТЕ and TM Modes ................................... 106
4.2 Eigenmodes of Inhomogeneously Filled Waveguides .......... 115
4.2.1 Coupled Mode Formulation .......................... 116
4.2.2 Modal Orthogonality and Complex Modes ............. 123
4.3 Waveguides with Lossy Boundaries ......................... 125
4.4 Excitation of Waveguides ................................. 130
4.4.1 Coupled Mode Formulation .......................... 131
4.4.2 Excitation Sources with a Finite Axial Extent ..... 137
4.5 Waveguide Junctions ....................................... 140
4.5.1 Junction Between Two Empty Waveguides with
Different Cross Sections .......................... 141
4.5.2 Junction Between Empty and Inhomogeneously
Filled Waveguides Sharing the Same Cross Section .. 144
References .................................................... 146
Chapter 5 Electromagnetic Cavity Resonators .................. 147
5.1 Construction of Complete Sets of Three-Dimensional
Vector Functions ......................................... 149
5.1.1 Divergenceless Eigenmodes ......................... 149
5.1.2 Irrotational Eigenmodes ........................... 151
5.2 Resonance Modes in Homogeneously Filled Cavities ......... 154
5.3 Resonance Modes in Inhomogeneously Filled Cavities ....... 161
5.3.1 Coupled Mode Formulation .......................... 161
5.3.2 Modal Orthogonality and Stored Energies ........... 170
5.4 Cavity Resonators with Lossy Boundaries .................. 175
5.5 Excitation of Cavity Resonators .......................... 179
5.5.1 Coupled Mode Formulation .......................... 180
5.5.2 Source-Free Fields ................................ 185
5.6 Aperture Coupling of Cavity Resonators ................... 188
References .................................................... 193
Chapter 6 Free-Space Measurements—Planar Interfaces ........... 195
6.1 Incident, Scattered, and Total Fields .................... 195
6.2 Measurement Configuration ................................ 197
6.3 Plane-Wave Decomposition of the Far Field of
Illuminating Antennas .................................... 199
6.3.1 Spatially Dependent Field ......................... 199
6.3.2 βt -Dependent Field ............................... 201
6.3.3 Plane-Wave Interpretation ......................... 207
6.3.4 Short-and Open-Circuited Half Spaces .............. 208
6.4 Material Half Spaces (Reflection Measurements Only) ...... 210
6.4.1 Matching the βt -Dependent Fields ................. 210
6.4.2 The Spatially Dependent Free-Space Field .......... 214
6.4.3 Measurement Procedure ............................. 221
6.5 Transversally Directed Short Current Element as a
Radiating Antenna ........................................ 224
6.6 Short-Circuited Material Slabs (Reflection Measurements
Only) .................................................... 226
6.6.1 Matching the βt-Dependent Fields .................. 226
6.6.2 The Spatially Dependent Free-Space Field .......... 230
6.6.3 Measurement Procedure ............................. 231
6.7 Material Slabs (Both Reflection and Transmission
Measurements) ............................................ 235
6.7.1 Matching the βt-Dependent Fields .................. 235
6.7.2 The Spatially Dependent Free-Space Fields ......... 242
6.7.3 Measurement Procedure ............................. 243
References .................................................... 248
Chapter 7 Free-Space Measurements - Cylindrical and Spherical
Interfaces .................................................... 251
7.1 Measurement Configuration for Cylindrical Interfaces ..... 251
7.2 Cylindrical-Harmonics Expansion of the Far Field of
Illuminating Antennas .................................... 253
7.2.1 Spatially Dependent Field ......................... 253
7.2.2 Spectral (βt-Dependent) Field ..................... 254
7.3 Measurement of the Constitutive Parameters of Material
Cylinders ................................................ 258
7.3.1 The Spectral (βt-Dependent) Cylindrical
Harmonics ......................................... 259
7.3.2 The Spatial (z-Dependent) Cylindrical Harmonics ... 264
7.3.3 Measurement Procedure ............................. 270
7.4 Measurement Configuration for Spherical Interfaces ....... 275
7.5 Spherical-Surface-Harmonics Expansion of the Far Field
of Illuminating Antennas ................................. 277
7.5.1 Incident Field in Local Coordinates ............... 277
7.5.2 Radial Potentials of the Incident Field ........... 281
7.6 Measurement of the Constitutive Parameters of Material
Spheres .................................................. 283
7.6.1 Matching the Spherical Surface Harmonics .......... 283
7.6.2 Measurement Procedure ............................. 288
References .................................................... 293
About the Author .............................................. 295
Index ......................................................... 297
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