Physics of Negative Refraction and Negative Index Materials: Optical and Electronic Aspects and Diversified Approaches (Springer Series in Materials Science (98))

This book deals with the subject of optical and electronic negative refraction (NR) and negative index materials NIM). Diverse approaches for achieving NR and NIM are covered, such as using photonic crystals, phononic crystals, split-ring resonators (SRRs) and continuous media, focusing of waves, guided-wave behavior, and nonlinear effects. Specific topics treated are polariton theory for LHMs (left handed materials), focusing of waves, guided-wave behavior, nonlinear optical effects, magnetic LHM composites, SRR-rod realizations, low-loss guided-wave bands using SRR-rods unit cells as LHMs, NR of electromagnetic and electronic waves in uniform media, field distributions in LHM guided-wave structures, dielectric and ferroelectric NR bicrystal heterostructures, LH metamaterial photonic-crystal lenses, subwavelength focusing of LHM/NR photonic crystals, focusing of sound with NR and NIMs, and LHM quasi-crystal materials for focusing. Contents......Page 9 1.1.1 Negative Refraction......Page 18 1.1.2 Negative Refraction with Spatial Dispersion......Page 20 1.1.3 Negative Refraction with Double Negativity......Page 21 1.1.4 Negative Refraction Without Left-Handed Behavior......Page 22 1.1.6 From Negative Refraction to Perfect Lens......Page 23 1.2 Conditions for Realizing Negative Refraction and Zero Reflection......Page 25 1.3 Conclusion......Page 32 References......Page 33 2.1.1 Introduction......Page 36 2.1.2 Anisotropic Green’s Function Based Upon LHM or DNM Properties......Page 38 2.1.3 Determination of the Eigenvalues and Eigenvectors for LHM or DNM......Page 49 2.1.4 Numerical Calculations of the Electromagnetic Field for LHM or DNM......Page 59 2.1.5 Conclusion......Page 82 2.2.1 Introduction......Page 83 2.2.4 Beam Steering and Control Component Action......Page 84 2.2.5 Electromagnetic Fields......Page 86 2.2.6 Surface Current Distributions......Page 87 References......Page 89 3.1 Introduction......Page 91 3.2 Description of "Left-Handed" Electromagnetic Waves: The Effect of the Imaginary Wave Vector......Page 92 3.3 Electromagnetic Wave Propagations in Homogeneous Magnetic Materials......Page 94 3.4.1 "Left-Handed" Characteristic of Electromagnetic Wave Propagation in Uniaxial Anisotropic "Left-Handed" Media......Page 96 3.4.2 Characteristics of Refraction of Electromagnetic Waves at the Interfaces of Isotropic Regular Media and Anisotropic "Left-Handed" Media......Page 101 3.5 Multilayer Structures Left-Handed Material: An Exact Example......Page 104 References......Page 109 4.1 Introduction......Page 111 4.2.1 Mandelstam and Negative Refraction......Page 113 4.2.2 Cherenkov Radiation......Page 116 4.3.1 Dielectric Tensor......Page 118 4.3.2 Isotropic Systems with Spatial Inversion......Page 121 4.3.3 Connection to Microscopics......Page 122 4.3.4 Isotropic Systems Without Spatial Inversion......Page 126 4.4.1 Excitons with Negative Effective Mass in Nonchiral Media......Page 127 4.4.2 Chiral Systems in the Vicinity of Excitonic Transitions......Page 130 4.4.3 Chiral Systems in the Vicinity of the Longitudinal Frequency......Page 132 4.4.4 Surface Polaritons......Page 134 4.5 Magnetic Permeability at Optical Frequencies......Page 137 4.5.1 Magnetic Moment of a Macroscopic Body......Page 138 4.6.1 Generation of Harmonics from a Nonlinear Material with Negative Refraction......Page 143 4.6.2 Ultra-Short Pulse Propagation in Negative Refraction Materials......Page 144 4.7 Concluding Remarks......Page 145 References......Page 146 5.1 Introduction......Page 149 5.2 Materials with Negative Refraction......Page 150 5.3.1 Metallic PC in Parallel-Plate Waveguide......Page 151 5.3.2 Numerical Simulation of TM Wave Scattering......Page 156 5.3.3 Metallic PC in Free Space......Page 157 5.3.4 High-Order Bragg Waves at the Surface of Metallic Photonic Crystals......Page 160 5.4 Conclusion and Perspective......Page 161 References......Page 162 6.1 Introduction......Page 164 6.2 Negative Refraction and Subwavelength Imaging of TM Polarized Electromagnetic Waves......Page 165 6.3 Negative Refraction and Point Focusing of TE Polarized Electromagnetic Waves......Page 169 6.4 Negative Refraction and Focusing Analysis for a Metallodielectric Photonic Crystal......Page 172 6.5 Conclusion......Page 177 References......Page 178 7.1 Introduction......Page 181 7.2 Negative Refraction by High-Symmetric Quasicrystal......Page 182 7.3 Focus and Image by High-Symmetric Quasicrystal Slab......Page 186 7.4 Negative Refraction and Focusing of Acoustic Wave by High-Symmetric Quasiperiodic Phononic Crystal......Page 193 7.5 Summary......Page 194 References......Page 195 8.1 Introduction......Page 197 8.2 A Simple Model......Page 200 8.3 An Example of Negative Mass......Page 204 8.4 Acoustic Double-Negative Material......Page 207 8.4.1 Construction of Double-Negative Material by Mie Resonances......Page 211 8.6 Focusing by Uniaxial Effective Medium Slab......Page 219 References......Page 229 9.1 Introduction......Page 230 9.2 Theory......Page 232 9.3 FDTD Simulations in an Ideal Negative Index Medium......Page 233 9.4 Simulations and Experiments with Split-Ring Resonators and Wire Arrays......Page 236 9.5 Split-Ring Resonator Arrays as a 2D Photonic Crystal......Page 239 9.6 Hexagonal Disk Array 2D Photonic Crystal Simulations: Focusing......Page 244 9.7 Modeling Refraction Through the Disk Medium......Page 249 9.8 Hexagonal Disk Array Measurements – Transmission and Focusing......Page 253 9.9 Hexagonal Disk Array Measurements – Refraction......Page 255 References......Page 261 10.1 Introduction......Page 264 10.2 Metamaterial Representation......Page 265 10.3 Guiding Structure......Page 268 10.4 Numerical Results......Page 270 10.5 Conclusions......Page 271 References......Page 272 11.1 Electromagnetic Negative Index Materials......Page 273 11.1.1 The Physics of NIMs......Page 274 11.1.2 Design of the NIM Unit Cell......Page 276 11.1.3 Origin of Losses in Left-Handed Materials......Page 278 11.1.4 Reduction in Transmission Due to Polarization Coupling......Page 282 11.1.6 NIM Indefinite Media and Negative Refraction......Page 284 11.2 Demonstration of the NIM Existence Using Snell's Law......Page 289 11.3 Retrieval of ε[sub(eff)] and μ[sub(eff)] from the Scattering Parameters......Page 293 11.3.1 Homogeneous Effective Medium......Page 294 11.3.2 Lifting the Ambiguities......Page 295 11.3.3 Inversion for Lossless Materials......Page 298 11.3.4 Periodic Effective Medium......Page 299 11.3.5 Continuum Formulation......Page 300 11.4.1 Measurement of NIM Losses......Page 301 11.4.2 Experimental Confirmation of Negative Phase Shift in NIM Slabs......Page 302 11.5.1 NIM Lenses and Their Properties......Page 307 11.5.2 Aberration Analysis of Negative Index Lenses......Page 308 11.6 Design and Characterization of Cylindrical NIM Lenses......Page 311 11.6.1 Cylindrical NIM Lens in a Waveguide......Page 312 11.7.1 Characterization of the Empty Aperture......Page 317 11.7.2 Design and Characterization of the PIM lens......Page 319 11.7.3 Design and Characterization of the NIM Lens......Page 320 11.7.4 Design and Characterization of the GRIN Lens......Page 323 11.7.5 Comparison of Experimental Data for Empty Aperture, PIM, NIM, and GRIN Lenses......Page 326 11.7.6 Comparison of Simulated and Experimental Aberrations for the PIM, NIM, and GRIN Lenses......Page 329 11.8 Conclusion......Page 339 References......Page 340 12.1 Introduction......Page 342 12.2 Nonlinear Response of Metamaterials......Page 344 12.2.1 Nonlinear Magnetic Permeability......Page 345 12.2.2 Nonlinear Dielectric Permittivity......Page 347 12.2.3 FDTD Simulations of Nonlinear Metamaterial......Page 348 12.2.4 Electromagnetic Spatial Solitons......Page 351 12.3.1 Nonlinear Surface Waves......Page 354 12.3.2 Nonlinear Pulse Propagation and Surface-Wave Solitons......Page 360 12.3.3 Nonlinear Guided Waves in Left-Handed Slab Waveguide......Page 362 12.4.1 Second-Harmonics Generation......Page 366 12.4.2 Enhanced SHG in Double-Resonant Metamaterials......Page 374 12.4.3 Nonlinear Quadratic Flat Lens......Page 378 12.5 Conclusions......Page 380 References......Page 381 C......Page 383 F......Page 384 M......Page 385 Q......Page 386 T......Page 387 Z......Page 388 There are many potentially interesting phenomena that can be obtained with wave refraction in the “wrong” direction, what is commonly now referred to as negative refraction. All sorts of physically new operations and devices come to mind, such as new beam controlling components, re?ectionless interfaces,?at lenses, higher quality lens or “super lenses,” reversal of lenses action, new imaging components, redistribution of energy density in guided wave components, to name only a few of the possibilities. Negative index materials are generally, but not always associated with negative refracting materials, and have the added property of having the projection of the power?ow or Poynting vector opposite to that of the propagation vector. This attribute enables the localized wave behavior on a subwavelength scale, not only inside lensesandinthenear?eldoutsideofthem,butalsoinprincipleinthefar?eld of them, to have?eld reconstruction and localized enhancement, something not readily found in ordinary matter, referred to as positive index materials. Often investigators have had to create, even when using positive index materials, interfaces based upon macroscopic or microscopic layers, or even heterostructure layers of materials, to obtain the?eld behavior they are se- ing. For obtaining negative indices of refraction, microscopic inclusions in a host matrix material have been used anywhere from the photonic crystal regime all the way into the metamaterial regime.