NEGATIVE-REFRACTION METAMATERIALS Fundamental Principles and Applications Edited by G. V Eleftheriades K. G. Balmain *IEEE IEEE PRESS WILEY INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION Contents Contributors xi Preface xiii Negative-Refractive-Index Transmission-Line Metamaterials 1 Ashwin K. Iyer and George U. Eleftheriades 1 .1 Introduction 1 1.1.1 Veselago and the Left-Handed Medium (LHM) 1 1.1.2 Negative Refraction at a Planar Interface 2 1.1 .3 Flat Lenses and Focusing 3 1.2 Background 4 1 .2.1 Artificial Dielectrics 4 1 .2.2 Negative Permittivity 5 1 .2.3 Negative Permeability 7 1.2.4 The First LHM 8 1.2.5 Terminology 11 1 .3 Transmission-Line Theory of Negative-Refractive-Index Media 12 1 .3.1 Application of the Transmission-Line Theory of Dielectrics to the Synthesis of LHM 18 1 .4 Periodically Loaded NRI-TL Metamaterials 21 1 .4.1 Dispersion Characteristics 22 1.4.2 Effective Medium Limit 28 1 .4.3 Closure of the Stopband: The Impedance-Matched Condi- tion 30 1 .4.4 Equivalent NRI-TL Unit Cell in the Effective Medium Limit 33 1 .5 Microwave Circuit Simulations 36 1.5.1 Negative Refraction 38 1.5.2 Focusing 39 1.6 Experimental Verification ofFocusing 41 v vi CONTENTS 1.7 Conclusion 46 References 48 2 Microwave Devices and Antennas UsingNegative-Refractive-Index Trans- mission-Line Metamaterials 53 George V. Eleftheriades 2.1 Introduction 53 2.2 Fundamental Properties 54 2.3 Effective Medium Theory 55 2.4 A Super-Resolving Negative-Refractive-Index Transmission-Line Lens 57 2.5 Compact and Broadband Phase-Shifting Lines 62 2.6 Series-Fed Antenna Arrays with Reduced Beam Squinting 65 2.7 A Broadband Metamaterial Balun in Microstrip 69 2.8 Broadband Power Combiners Using Zero-Degree Phase-Shifting Lines 72 2.9 Electrically Small Ring Antenna with Vertical Polarization 73 2.10 A Leaky-Wave Backward Antenna Radiating its Fundamental Spa- tial Harmonic 75 2.11 A High-Directivity Backward NRI/Microstrip Coupler 77 2.12 Phase-Agile Branch-Line Microstrip Couplers 82 2.13 Conclusion 83 Appendix 85 References 88 3 Super-Resolving Negative-Refractive-Index Transmission-Line Lenses 93 Anthony Grbic and George V Eleftheriades 3.1 The Distributed Dual Transmission Line 94 3.2 The Periodic Dual Transmission Line 95 3.3 Interpreting Negative Permittivity and Permeability 98 3.3.1 Negative Permittivity 98 3.3.2 Negative Permeability 102 3.3.3 Combining Negative e and Negative p, 105 3.4 The 2-D Dual Transmission Line 106 3.4.1 The Generalized 2-D Periodic Electrical Network 108 3.4.2 Periodic Analysis of the 2-D Dual Transmission Line 111 3.4.3 The 2-D Dual TL as an Effective Medium 115 3.5 The Negative-Refractive-Index (NRI) TL Lens 119 CONTENTS vii 3.5.1 The Transmission-Line Implementation of Veselago's NRI Lens 120 3.5.2 Propagation Characteristics of the TL Mesh 121 3.5 .3 Conditions for "Perfect" Imaging in the NRI-TL Lens 124 3.6 Reflection and Transmission Through the Lossless NRI-TL Lens 126 3.6.1 Phase Compensation ofPropagating Waves 130 3.6.2 Growth and Restoration ofEvanescent Waves 130 3.7 The Super-Resolving NRI Transmission-Line Lens 133 3.7.1 The Effect ofPeriodicity onImageResolution and the Growth of Evanescent Waves 140 3.7.2 The Optical Transfer Function of the NRI-TL Lens 141 3.7.3 The Resolving Capability of a Lossy NRI-TL Lens 144 3.8 An Experimental NRI-TL Lens 150 3.9 Characterization of an Experimental NM-TL Lens 153 3.10 An Isotropic 3-D TL Metamaterial with a NRI 157 References 164 4 Gaussian Beam Interactions with Double-Negative (DNG) Metamaterials 171 Richard W. Ziolkowski 4.1 Introduction 171 4.2 2-D FDTD Simulator 174 4.3 Normal Incidence Results 178 4.3.1 Flat DNG Lenses 179 4.3.2 Phase CompensatorBeam Translator 186 4.4 Oblique Incidence Results 188 4.5 Goos-Hänchen Effect 192 4.6 Subwavelength Focusing with a Concave DNG Lens 198 4.7 Conclusions 208 References 209 5 Negative Index Lenses 213 David Schurig and David R. Smith 5.1 Introduction 213 5 .2 Geometric Optics 215 5.2.1 Path Variation Example 221 5.3 Gaussian Optics 223 5.3.1 Single Surface 223 5.3 .2 Multiple Surfaces 231 viii CONTENTS 5.3.3 Thin Lenses 232 5.4 Aberrations 233 5.4.1 System Optic Elements 236 5.4.2 Aperture Stop and Exit Pupil 236 5 .4.3 Focal Points 237 5.4.4 General and Reference Ray 237 5.4.5 Optical Path-Length Difference 238 5.4.6 Expand the Difference 240 5.4.7 Example: Thin Lenses 241 References 247 6 Planar Anisotropic Resonance-Cone Metamaterials 249 Keith G. Balmain andAndrea A. E. Lattgen 6.1 Introduction 249 6.2 Homogeneous Anisotropic-Medium Analysis 250 6.3 Free-Standing Anisotropic-Grid Metamaterial 254 6.4 Anisotropic Grid Over Infinite Ground 254 6.5 Anisotropic Grid with Vertical Inductors, Over Infinite Ground 257 6.6 Conclusions 265 References 265 7 Negative Refraction and Subwavelength Imaging in Photonic Crystals 269 Chiyan Luo and John D. Joannopoulos 7.1 Introduction 269 7.1 .1 Introduction to Photonic Crystals 270 7.2 Negative Refraction in Photonic Crystals 272 7.2.1 Analysis of Refraction in Uniform Materials 272 7.2.2 Analysis ofRefraction in Photonic Crystals 273 7.2.3 Dispersion Contours of 2-D Photonic Crystals 276 7.2.4 All-Angle Negative Refraction 278 7.2.5 Negative Refraction in Three-Dimensionally Periodic Sys- tems 283 7.2.6 Case of Metallic Photonic Crystals 284 7.2.7 Summary 285 7.3 Subwavelength Imaging with Photonic Crystals 286 7.3.1 Veselago-Pendry Left-Handed Lens 286 7.3.2 Origin of Near-Field Amplification 290 7.3.3 Photonic-Crystal Superlenses 295 7.3.4 Numerical Results 300 CONTENTS ix 7 .3.4.1 Surface Band Structure 300 7.3.4.2 Transmission Spectrum 301 7.3.5 Image Patterns of a Superlens 302 7 .3.6 Discussion 306 7.4 Conclusions 309 References 311 8 Plasmonic Nanowire Metamaterials 313 Andrey K. Sarychev and Vladimir M. Shalaev 8.1 Introduction 313 8 .2 Electrodynamics of a Single Metal Nanowire 314 8.3 Conducting Stick Composites: Effective Medium Approach 321 8.4 Conducting Stick Composites: Giant Enhancement of Local Fields 324 8.5 Magnetic Response of Conducting Stick Composites 328 8.6 Planar Nanowire Composites 330 8.7 Conclusions 334 References 335 9 An Overview of _Salient Properties of Planar Guided-Wave Structures with Double-Negative (DNG) and Single-Negative (SNG) Layers 339 Andrea AM and NaderEngheta 9.1 Introduction 340 9.2 Parallel-Plate Waveguides with DNG and SNG Metamaterials 341 9.2.1 Large-Aperture Monomodal Waveguides with ENG-MNG Pairs 343 9.2.2 Waveguiding in Ultra-thin Structures withLateral Dimension Below Diffraction Limits 346 9.2.3 Power Propagation in DPS-DNG Waveguides 348 9.3 Open Slab Waveguides with DNG Metamaterials 357 9.4 The Contradirectional (Backward) Couplers 365 References 375 10 Dispersion Engineering: The Use of Abnormal Velocities and Negative Index of Refraction to Control Dispersive Effects 381 Mohamniad Mojahedi and George U. Elefiheriades 10.1 Introduction 381 10.2 Abnormal Group Velocity 385 10.3 Wave Propagation in a Slab with Negative Index ofRefraction 387 10.4 PLTL with an Effective NIR and Negative Group Index 392 x CONTENTS 10.4.1 General Theory of PLTL Exhibiting Negative Phase Delay 392 10.4.2 Frequency Domain Simulations 393 10.4.3 Frequency Domain Measurements 397 10.4.4 Time Domain Simulations 400 10.4.4.1 Negative Group Delay 400 10.4.4.2 Luminal Front Velocity 400 10.4.4.3 Physical Mechanism Underlying Negative Group Delay 402 10.4.5 Time-Domain Measurements 404 10.5 Conclusions 407 References 408 INDEX 413.