Physics and Applications of Negative Refractive Index Materials

七月流火

Physics and Applications of Negative Refractive Index Materials

1 Introduction 1
1.1 General historical perspective . . . . . . . . . . . . . . . . . . 2
1.2 The concept of metamaterials . . . . . . . . . . . . . . . . . . 8
1.3 Modeling the material response . . . . . . . . . . . . . . . . . 14
1.3.1 Basic equations . . . . . . . . . . . . . . . . . . . . . . 14
1.3.2 Dispersive model for the dielectric permittivity . . . . 18
1.4 Phase velocity and group velocity . . . . . . . . . . . . . . . . 22
1.5 Metamaterials and homogenization procedure . . . . . . . . . 24
1.5.1 General concepts . . . . . . . . . . . . . . . . . . . . . 24
1.5.2 Negative effective medium parameters . . . . . . . . . 25
1.5.2.1 Terminology . . . . . . . . . . . . . . . . . . 26
2 Metamaterials and homogenization of composites 29
2.1 The homogenization hypothesis . . . . . . . . . . . . . . . . . 30
2.2 Limitations and consistency conditions . . . . . . . . . . . . . 33
2.3 Forward problem . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.3.1 Relation between R and T and the electromagnetic
fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.3.2 Determining the electromagnetic fields . . . . . . . . . 35
2.4 Inverse problems: retrieval and constitutive parameters . . . . 42
2.4.1 Standard media . . . . . . . . . . . . . . . . . . . . . . 42
2.4.2 Left-handed media . . . . . . . . . . . . . . . . . . . . 45
2.5 Homogenization from averaging the internal fields . . . . . . . 49
2.5.1 Maxwell-Garnett effective medium theory . . . . . . . 50
2.5.2 Layered media as anisotropic effective media . . . . . 52
2.5.3 Averaging the internal fields in periodic media . . . . 54
2.6 Generalization to anisotropic and bianisotropic media . . . . 57
2.6.1 Forward model . . . . . . . . . . . . . . . . . . . . . . 58
2.6.2 Inversion algorithm . . . . . . . . . . . . . . . . . . . . 65
3 Designing metamaterials with negative material parameters 77
3.1 Negative dielectric materials . . . . . . . . . . . . . . . . . . . 79
3.1.1 Metals and plasmons at optical frequencies . . . . . . 79
3.1.2 Wire mesh structures as low frequency plasmas . . . . 83
3.1.2.1 Other photonic metallic wire materials . . . . 91
3.2 Metamaterials with negative magnetic permeability . . . . . . 92
3.2.1 Diamagnetism in a stack of metallic cylinders . . . . . 93
3.2.2 Split-ring resonator media . . . . . . . . . . . . . . . . 95
3.2.2.1 Pendry’s split rings . . . . . . . . . . . . . . . 98
3.2.3 The Swiss Roll media for radio frequencies . . . . . . . 100
3.2.4 Scaling to high frequencies . . . . . . . . . . . . . . . . 104
3.2.5 Magnetism from dielectric scatterers . . . . . . . . . . 108
3.2.6 Arrangements of resonant plasmonic particles . . . . . 112
3.2.7 Isotropic magnetic metamaterials . . . . . . . . . . . . 116
3.3 Metamaterials with negative refractive index . . . . . . . . . 119
3.3.1 Combining the “electric” and “magnetic” atoms . . . 120
3.3.2 Negative refractive index at optical frequencies . . . . 123
3.4 Chiral metamaterials . . . . . . . . . . . . . . . . . . . . . . . 131
3.5 Bianisotropic metamaterials . . . . . . . . . . . . . . . . . . . 134
3.6 Active and non-linear metamaterials . . . . . . . . . . . . . . 137
3.6.1 Nonlinear split-ring resonators . . . . . . . . . . . . . 139
3.6.2 Actively controllable metamaterials . . . . . . . . . . . 143
4 Negative refraction and photonic bandgap materials 145
4.1 Photonic crystals and bandgap materials . . . . . . . . . . . . 146
4.1.1 One-dimensional photonic crystals: transmission lines
approach . . . . . . . . . . . . . . . . . . . . . . . . . 146
4.1.2 Two-dimensional photonic crystals: definitions and
solution . . . . . . . . . . . . . . . . . . . . . . . . . . 148
4.1.2.1 Direct lattice . . . . . . . . . . . . . . . . . . 149
4.1.2.2 Reciprocal lattice . . . . . . . . . . . . . . . . 149
4.1.2.3 Brillouin zone and irreducible Brillouin
zone . . . . . . . . . . . . . . . . . . . . . . . 151
4.1.3 Bloch theorem and Bloch modes . . . . . . . . . . . . 152
4.1.4 Electromagnetic waves in periodic media . . . . . . . . 152
4.2 Band diagrams and iso-frequency contours . . . . . . . . . . . 156
4.2.1 Free-space and standard photonic crystal . . . . . . . 156
4.2.2 Iso-frequency contours . . . . . . . . . . . . . . . . . . 160
4.3 Negative refraction and flat lenses with photonic crystals . . . 164
4.3.1 Achieving negative refraction . . . . . . . . . . . . . . 164
4.3.2 Image quality and stability . . . . . . . . . . . . . . . 168
4.4 Negative refraction vs. collimation or streaming . . . . . . . . 171
5 Media with ε < 0 and μ < 0: theory and properties 175
5.1 Origins of negative refraction . . . . . . . . . . . . . . . . . . 176
5.1.1 Dispersion relation . . . . . . . . . . . . . . . . . . . . 177
5.1.2 Anisotropic media with positive constitutive
parameters . . . . . . . . . . . . . . . . . . . . . . . . 180
5.1.3 Photonic crystals . . . . . . . . . . . . . . . . . . . . . 182
5.1.4 Left-handed media . . . . . . . . . . . . . . . . . . . . 183
5.1.5 Moving media . . . . . . . . . . . . . . . . . . . . . . . 183
5.2 Choice of the wave-vector and its consequences . . . . . . . . 185
5.2.1 Modified Snell’s law of refraction . . . . . . . . . . . . 188
5.2.2 Reversed Doppler shift . . . . . . . . . . . . . . . . . . 190
5.2.3 Reversed Goos-H¨anchen shift . . . . . . . . . . . . . . 192
5.2.4 Reversed ˇCerenkov radiation . . . . . . . . . . . . . . 193
5.2.5 Modified Mie scattering . . . . . . . . . . . . . . . . . 198
5.3 Anisotropic and chiral media . . . . . . . . . . . . . . . . . . 201
5.3.1 Indefinite media . . . . . . . . . . . . . . . . . . . . . 202
5.3.2 Amphoteric refraction . . . . . . . . . . . . . . . . . . 204
5.3.3 Reversal of critical angle and Brewster angle . . . . . 208
5.3.4 Negative refraction due to bianisotropic effects . . . . 210
5.3.5 Flat lenses with anisotropic negative media . . . . . . 213
6 Energy and momentum in negative refractive index
materials 219
6.1 Causality and energy density in frequency dispersive
media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
6.1.1 Causality in left-handed media . . . . . . . . . . . . . 220
6.1.2 Causality and phase propagation . . . . . . . . . . . . 221
6.1.3 Energy in dispersive media . . . . . . . . . . . . . . . 227
6.2 Electromagnetic energy in left-handed media . . . . . . . . . 230
6.2.1 Erroneous concept of negative energy in lossy
dispersivemedia . . . . . . . . . . . . . . . . . . . . . 230
6.2.2 Lossy Lorentz media . . . . . . . . . . . . . . . . . . . 231
6.3 Momentum transfer in media with negative material
parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
6.4 Limit of plane wave and small losses . . . . . . . . . . . . . . 236
6.4.1 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
6.4.2 Momentum . . . . . . . . . . . . . . . . . . . . . . . . 237
6.5 Traversal of pulses in materials with negative material
parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
6.5.1 Wigner delay time for pulses in NRM . . . . . . . . . 240
6.5.2 Traversal times based on the flow of radiative
energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
6.5.2.1 Traversal times through negative refractive
index media . . . . . . . . . . . . . . . . . . . 246
6.5.2.2 Traversal times for evanescent waves . . . . . 247
7 Plasmonics of media with negative material parameters 253
7.1 Surface electromagnetic modes in negative refractive
materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
7.1.1 Surface plasmon modes on a plane interface . . . . . . 255
7.1.2 Surface plasmon polariton modes of a slab . . . . . . . 260
7.2 Waveguides made of negative index materials . . . . . . . . . 265
7.3 Negative refraction of surface plasmons . . . . . . . . . . . . . 267
7.4 Plasmonic properties of structured metallic surfaces . . . . . 273
7.5 Surface waves at the interfaces of nonlinear media . . . . . . . 276
8 Veselago’s lens is a perfect lens 281
8.1 Near-field information and diffraction limit . . . . . . . . . . 283
8.2 Mathematical demonstration of the perfect lens . . . . . . . . 286
8.2.1 Role of surface plasmons . . . . . . . . . . . . . . . . . 290
8.2.2 Quasi-static limit and silver lens . . . . . . . . . . . . 292
8.2.3 “Near-perfect” lens with an asymmetric slab . . . . . 294
8.3 Limitations due to real materials and imperfect NRMs . . . . 297
8.3.1 Analysis of the lens transfer function for mismatched
material parameters . . . . . . . . . . . . . . . . . . . 301
8.3.2 Focussing properties of a finite slab of NRM . . . . . . 305
8.4 Issues with numerical simulations and time evolution . . . . . 311
8.4.1 Temporal evolution of the focus . . . . . . . . . . . . . 315
8.5 Negative stream of energy in the perfect lens geometry . . . . 316
8.6 Effects of spatial dispersion . . . . . . . . . . . . . . . . . . . 319
9 Designing super-lenses 323
9.1 Overcoming the limitations of real materials . . . . . . . . . . 324
9.1.1 Layering the lens . . . . . . . . . . . . . . . . . . . . . 325
9.1.2 A layered stack to direct radiation . . . . . . . . . . . 327
9.1.3 Use of amplifying media to reduce dissipation . . . . . 331
9.2 Generalized perfect lens theorem . . . . . . . . . . . . . . . . 333
9.2.1 Proof based on the symmetries of the Maxwell
equations . . . . . . . . . . . . . . . . . . . . . . . . . 338
9.2.2 Contradictions between the ray picture and the full
wave solutions . . . . . . . . . . . . . . . . . . . . . . . 339
9.3 The perfect lens in other geometries . . . . . . . . . . . . . . 341
9.3.1 A transformation technique . . . . . . . . . . . . . . . 343
9.3.2 Perfect lenses in curved geometries: cylindrical and
spherical lenses . . . . . . . . . . . . . . . . . . . . . . 344
9.3.3 Hyperlens: a layered curved lens . . . . . . . . . . . . 352
9.3.4 Perfect two-dimensional corner lens . . . . . . . . . . . 354
9.3.5 Checkerboards and a three-dimensional corner lens . . 356
10 Brief report on electromagnetic invisibility 361
10.1 Concept of electromagnetic invisibility . . . . . . . . . . . . . 361
10.2 Excluding electromagnetic fields . . . . . . . . . . . . . . . . . 364
10.2.1 Principle . . . . . . . . . . . . . . . . . . . . . . . . . . 364
10.2.2 Design procedure . . . . . . . . . . . . . . . . . . . . . 367
10.3 Cloaking with localized resonances . . . . . . . . . . . . . . . 368
A The Fresnel coefficients for reflection and refraction 373
B The dispersion and Fresnel coefficients for a bianisotropic
medium 375
C The reflection and refraction of light across a material slab 379
References 381
&copy; 2009
【文件名】:1162@52RD_Physics and Applications of Negative Refractive Index.part1.rar
【格　式】:rar
【大　小】:3788K
【简　介】:
【目　录】:


[br]<p align=right><font color=red>+5 RD币</font></p>