ELECTROMAGNETIC METAMATERIALS: TRANSMISSION LINE THEORY AND MICROWAVE APPLICATIONS The Engineering Approach CHRISTOPHE CALOZ Ecole Polytechnique de Montreal TATSUO ITOH University of California at Los Angeles (\I/) W,LEY ~ W/INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION
CONTENTS Preface Acknowledgments Acronyms xiii xv xvii 1 Introduction 1 1.1 Definition of Metamaterials (MTMs) and Left-Handed (LH) MTMs, 1 1.2 Theoretical Speculation by Viktor Veselago, 3 1.3 Experimental Demonstration of Left-Handedness, 4 1.4 Further Numerical and Experimental Connrmations, 9 1.5 "Conventional" Backward Waves and Novelty of LH MTMs, 10 1.6 Terminology, 12 1.7 Transmission Line (TL) Approach, 12 1.8 Composite Right/Left-Handed (CRLH) MTMs, 16 1.9 MTMs and Photonic Band-Gap (PBG) Structures, 17 1.10 Historical "Germs" of MTMs, 20 References, 22 2 Fundamentals of LH MTMs 27 2.1 Left-Handedness from Maxwell's Equations, 28 2.2 Entropy Conditions in Dispersive Media, 33 2.3 Boundary Conditions, 38 vii
Vlll CONTENTS 2.4 Reversal of Doppler Effect, 39 2.5 Reversal of Vavilov-Cerenkov Radiation, 41 2.6 Reversal of Snell's Law: Negative Refraction, 43 2.7 Focusing by a "Fiat LH Lens", 46 2.8 Fresnel Coefficients, 48 2.9 Reversal of Goos-Hänchen Effect, 50 2.10 Reversal of Convergence and Divergence in Convex and Concave Lenses, 51 2.11 Subwavelength Diffraction, 53 References, 57 3 TL Theory of MTMs 59 3.1 Ideal Homogeneous CRLH TLs, 59 3.1.1 Fundamental TL Characteristics, 60 3.1.2 Equivalent MTM Constitutive Parameters, 67 3.1.3 Balanced and Unbalanced Resonances, 70 3.1.4 Lossy Case, 74 3.2 LC Network Implementation, 79 3.2.1 Principle, 79 3.2.2 Difference with Conventional Filters, 83 3.2.3 Transmission Matrix Analysis, 85 3.2.4 Input Impedance, 100 3.2.5 Cutoff Frequencies, 103 3.2.6 Analytical Dispersion Relation, 106 3.2.7 Bloch Impedance, 113 3.2.8 Effect of Finite Size in the Presence of Imperfect Matching, 115 3.3 Real Distributed 1D CRLH Structures, 119 3.3.1 General Design Guidelines, 120 3.3.2 Microstrip Implementation, 122 3.3.3 Parameters Extraction, 124 3.4 Experimental Transmission Characteristics, 127 3.5 Conversion from Transmission Line to Constitutive Parameters, 131 References, 131 4 Two-Dimensional MTMs 133 4.1 Eigenvalue Problem, 134 4.1.1 General Matrix System, 134 4.1.2 CRLH Particularization, 138 4.1.3 Lattice Choice, Symmetry Points, Brillouin Zone, and 2D Dispersion Representations, 139 4.2 Driven Problem by the Transmission Matrix Method (TMM), 143 4.2.1 Principle of the TMM, 144 4.2.2 Scattering Parameters, 145
CONTENTS ix 4.2.3 Voltage and Current Distributions, 147 4.2.4 Interest and Limitations of the TMM, 154 4.3 Transmission Line Matrix (TLM) Modeling Method, 154 4.3.1 TLM Modeling of the Unloaded TL Host Network, 155 4.3.2 TLM Modeling of the Loaded TL Host Network (CRLH), 158 4.3.3 Relationship between Material Properties and the TLM Model Parameters, 159 4.3.4 Suitability of the TLM Approach for MTMs, 161 4.4 Negative Refractive Index (NRI) Effects, 162 4.4.1 Negative Phase Velocity, 162 4.4.2 Negative Refraction, 163 4.4.3 Negative Focusing, 165 4.4.4 RH-LH Interface Surface Plasmons, 167 4.4.5 Reflectors with Unusual Properties, 169 4.5 Distributed 2D Structures, 170 4.5.1 Description of Possible Structures, 171 4.5.2 Dispersion and Propagation Characteristics, 173 4.5.3 Parameter Extraction, 178 4.5.4 Distributed Implementation of the NRI Slab, 183 References, 190 5 Guided-Wave Applications 192 5.1 Dual-Band Components, 193 5.1.1 Dual-Band Property of CRLH TLs, 193 5.1.2 Quarter-Wavelength TL and Stubs, 197 5.1.3 Passive Component Examples: Quadrature Hybrid and Wilkinson Power Divider, 201 5.1.3.1 Quadrature Hybrid, 201 5.1.3.2 Wilkinson Power Divider, 202 5.1.4 Nonlinear Component Example: Quadrature Subharmonically Pumped Mixer, 205 5.2 Enhanced-Bandwidth Components, 210 5.2.1 Principle of Bandwidth Enhancement, 211 5.2.2 Rat-Race Coupler Example, 215 5.3 Super-compact Multilayer "Vertical" TL, 217 5.3.1 "Vertical" TL Architecture, 219 5.3.2 TL Performances, 221 5.3.3 Diplexer Example, 225 5.4 Tight Edge-Coupled Coupled-Line Couplers (CLCs), 227 5.4.1 Generalities on Coupled-Line Couplers, 228 5.4.1.1 TEM and Quasi-TEM Symmetrie Coupled-Line Structures with Small Interspacing: Impedance Coupling (IC), 228 5.4.1.2 Non-TEM Symmetrie Coupled-Line Structures with Relatively Large Spacing: Phase Coupling (PC), 232
5.4.1.3 Summary on Symmetrie Coupled-Line Structures, 233 5.4.1.4 Asymmetrie Coupled-Line Structures, 234 5.4.1.5 Advantages of MTM Couplers, 235 5.4.2 Symmetrie Impedance Coupler, 235 5.4.3 Asymmetrie Phase Coupler, 245 5.5 Negative and Zeroth-Order Resonator, 249 5.5.1 Principle, 249 5.5.2 LC Network Implementation, 251 5.5.3 Zeroth-Order Resonator Characteristics, 253 5.5.4 Circuit Theory Verification, 256 5.5.5 Microstrip Realization, 258 References, 259 Radiated-Wave Applications 261 6.1 Fundamental Aspects of Leaky-Wave Structures, 262 6.1.1 Principle of Leakage Radiation, 262 6.1.2 Uniform and Periodic Leaky-Wave Structures, 266 6.1.2.1 Uniform LW Structures, 266 6.1.2.2 Periodic LW Structures, 268 6.1.3 Metamaterial Leaky-Wave Structures, 269 6.2 Backfire-to-Endfire (BE) Leaky-Wave (LW) Antenna, 270 6.3 Electronically Scanned BE LW Antenna, 275 6.3.1 Electronic Scanning Principle, 276 6.3.2 Electronic Beamwidth Control Principle, 277 6.3.3 Analysis of the Structure and Results, 279 6.4 Reflecto-Directive Systems, 282 6.4.1 Passive Retro-Directive Reflector, 283 6.4.2 Arbitrary-Angle Frequency Tuned Reflector, 286 6.4.3 Arbitrary-Angle Electronically Tuned Reflector, 287 6.5 Two-Dimensional Structures, 290 6.5.1 Two-Dimensional LW Radiation, 290 6.5.2 Conical-Beam Antenna, 292 6.5.3 Full-Space Scanning Antenna, 296 6.6 Zeroth Order Resonating Antenna, 297 6.7 Dual-Band CRLH-TL Resonating Ring Antenna, 300 6.8 Focusing Radiative "Meta-Interfaces", 304 6.8.1 Heterodyne Phased Array, 305 6.8.2 Nonuniform Leaky-Wave Radiator, 310 References, 313 The Future of MTMs 31 6 7.1 "Real-Artificial" Materials: the Challenge of Homogenization, 316 7.2 Quasi-Optical NRI Lenses and Devices, 319 7.3 Three-Dimensional Isotropie LH MTMs, 323
CONTENTS xi 7.4 Optical MTMs, 328 7.5 "Magnetless" Magnetic MTMs, 329 7.6 Terahertz Magnetic MTMs, 330 7.7 Surface Plasmonic MTMs, 331 7.8 Antenna Radomes and Frequency Selective Surfaces, 338 7.9 Nonlinear MTMs, 339 7.10 Active MTMs, 341 7.11 Other Topics of Interest, 341 References, 342 Index 347