Inhaltsverzeichnis

Vorwort

Preface

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, reflectionless interfaces, flat 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 flow or Poynting vector opposite to that of the propagation vector. This attribute enables the localized wave behavior on a subwavelength scale, not only inside lenses and in the near field outside of them, but also in principle in the far field of them, to have field 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 field behavior they are seeking. 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. These regimes take one from the wavelength size on the order of the separation between inclusions to that where many inclusions are sampled by a wavelength of the electromagnetic field. Generally in photonic crystals and metamaterials, a Brillouin zone in reciprocal space exists due to the regular repetitive pattern of unit cells of inclusions, where each unit cell contains an arrangement of inclusions, in analogy to that seen in natural materials made up of atoms. Only here, the arrangements consist of artificial "atoms" constituting an artificial lattice.

The first two chapters of this book (Chaps. 1 and 2) address the use of uniform media to generate the negative refraction, and examine what happens to optical waves in crystals, electron waves in heterostructures, and guided waves in bicrystals. The first chapter also contrasts the underlying physics in various approaches adopted or proposed for achieving negative refraction and examines the effects of anisotropy, as does the second chapter for negative index materials (left-handed materials). Obtaining left-handed material behavior by utilizing a permeability tensor modification employing magnetic material inclusions is investigated in Chap. 3. Effects of spatial dispersion in the permittivity tensor can be important to understanding excitonicelectromagnetic interactions (exciton-polaritons) and their ability to generate negative indices and negative refraction. This and other polariton issues are discussed in Chap. 4.

The next group of chapters, Chaps. 5 and 6, in the book looks at negative refraction in photonic crystals. This includes studying the effects in the microwave frequency regime on such lattices constructed as flat lenses or prisms, in two dimensional arrangements of inclusions, which may be of dielectric or metallic nature, immersed in a dielectric host medium, which could be air or vacuum. Even slight perturbations or crystalline disorder effects can be studied, as is done in Chap. 7 on quasi-crystals. Analogs to photonic fields do exist in mechanical systems, and Chap. 8 examines this area for acoustic fields which in the macroscopic sense are phonon fields on the large scale.

Finally, the last group of chapters investigates split ring resonator and wire unit cells to make metamaterials for creation of negative index materials. Chapter 9 does this as well as treating some of the range between metamaterials and photonic crystals by modeling and measuring split ring resonators and metallic disks. Chapter 10 looks at the effects of the split ring resonator and wire unit cells on left-handed guided wave propagation, finding very low loss frequency bands. Designing and fabricating split ring resonator and wire unit cells for lens applications is the topic of Chap. 11. This chapter has extensive modeling studies of various configurations of the elements and arrangements of their rectangular symmetry system lattice. The last chapter in this group and of the book, Chap. 12, delves into the area of nonlinear effects, expected with enhanced field densities in specific areas of the inclusions. For example, field densities may be orders of magnitude higher in the vicinity of the gaps in the split rings, than elsewhere, and it is here that a material could be pushed into its nonlinear regime.

The chapters here all report on recent research within the last few years, and it is expected that the many interesting fundamental scientific discoveries that have occurred and the applications which have resulted from them on negative index of refraction and negative index materials, will have a profound effect on the technology of the future. The contributors to this book prepared their chapters coming from very diversified backgrounds, and as such, provide the reader with unique perspectives toward the subject matter. Although the chapters are presented in the context of negative refraction and related phenomena, the contributions should be found relevant to broad areas in fundamental physics and material science beyond the original context of the research. We expect this area to continue to yield new discoveries, applications, and insertion into devices and components as time progresses. Evidence of this is already available in recent developments for repetitive metal patterns on surfaces of thin films and plasmonic based metallic-dielectric hybrid structures showing focusing (some with magnification) or even negative refraction and negative refractive index into the infrared and optical regimes. These polariton based phenomena do not necessarily require double negativity, which represents another alternative to achieve sub-wavelength imaging in addition to photonic crystals and metamaterial split ring resonator type configurations.

Washington and Golden, June 2007

Clifford M. Krowne

Yong Zhang

Klappentext

Springer Series in Materials Science 98

Clifford M. Krowne

Yong Zhang

Editors

Physics of Negative Refraction and Negative Index Materials

Optical and Electronic Aspects and Diversified Approaches

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 photoniccrystal lenses, subwavelength focusing of LHM/NR photonic crystals, focusing of sound with NR and NIMs, and LHM quasi-crystal materials for focusing.

ISBN 978-3-540-72131-4

springer.com

Register

Index

E, D, B and E, D, B, H approaches, 105
E, D, B approach, 103
e(w)-m(w) description, 104
YV0₄ bicrystal, 12

(GRIN) lens, 305

(PIM) lenses, 295
Cerenkov effect, 262

A

aberration, 7, 317
absorber, 136, 141
absorption, 230
acoustic waves, 183, 184
additional boundary conditions, 113
additional exciton-polariton waves, 11
All-angle-negative-refraction, 135
alumina, 158
amphoteric refraction, 13
angular, 153
anisotropic, 83
anisotropic index of refraction, 218
anisotropic medium, 274
anisotropy, 19, 20, 157
anisotropy scheme, 5
anomalous, 86
antenna, 157
antiresonance, 217
arithmetic mean, 90
arrow distributions, 43
artificial resonances, 184

B

backward wave, 2, 134
ballistic electron beam, 14
band structure, 231
bandgap, 139, 143
bandwidth limitations, 264
basis current functions, 20
basis function, 39
basis function limits, 42
basis sets, 38
beam, 154
Bessel function, 306
biaxial, 25
biaxial crystal, 42
bicrystal heterostructure, 67
boundary condition, 89
Bragg diffraction, 136, 139, 144, 145
Bragg wave, 142, 144, 145
Brillouin, 155
Brillouin zone, 141
broken spatial inversion, 110

C

calculated transmission spectrum, 231
Chebyshev polynomials, 288
Cherenkov, 100
Cherenkov cone, 101
Cherenkov radiation, 100
Chinese remainder theorem, 284
chiral, 110
Chiral (gyrotropic) systems, 114
chiral route to negative refraction, 116
chirality parameter, 118
chromatic aberration, 222
circular, 161
circular dichroism, 114
composite, 76
conductivity, 269
constitutive parameters, 21
continuous rods, 253
Courant-Friederichs-Lewy condition, 220
Cu-Ge, 93
Cylindrical NIM Lenses, 299

D

damping, 77
deaf band, 201
dielectric functions, 105
dielectric tensor, 96, 102
dipolar resonance, 199
dipole approximation, 193, 194
disk array, 218
dispersion, 134, 135, 146, 149
dispersion behavior, 19
dispersion diagrams, 251
dispersion law, 129
dispersion relations, 103
dispersion surface, 206, 207
dispersive metamaterials, 252
displacement of the focus, 236
displacement of the source, 235
dissipation, 118
distance of focus method, 247
distributions, 19
domain twin interface, 14
Doppler, 100
Doppler shift, 262
double negativity, 183, 184
double-negativity scheme, 4
double-split-ring, 219
double-split-ring resonator, 217

E

E-polarized, 81
effective index of refraction, 218, 247
effective magnetic resonance frequency, 254
effective medium, 122, 264, 265, 272
effective medium approximation, 78
Effective permittivity, 252
effective plasma, 252
effective refractive index, 136, 137, 200
effective-medium formulae, 195
EFS, 137-139, 143
eigenvalues, 38
eigenvectors, 38
eikonal equation, 277, 295
eikonal surface f, 317
electric crossover frequency, 256
electric magnitude distribution, 43
electric permittivity, 183
electric resonance, 252
electric-dipole allowed transitions, 108
electric-dipole forbidden transitions, 109
electric-quadrupole transitions, 109
electromagnetic field, 19
EM, 162
energy current density, 83
energy flux, 346-349, 366
energy-momentum relationship of
excitons, 112
equal-frequency, 151
equations, 21
evanescent propagation, 257
evanescent waves, 209
even mode, 37
exciton effective mass, 113
excitonic transitions, 114
excitons, 107
excitons with negative effective mass, 111
extraordinary, 9

F

fabrication, 163
FDTD, 156, 244
FDTD simulations, 220, 337
ferroelectric, 66
ferromagnetic resonance, 77
field asymmetry, 19
field distributions, 20
field patterns, 251
finite difference time domain, 218, 226
flat lens, 149, 150
FMR, 80
focus, 167, 172, 174, 177, 180, 241
focus distances, 230
focus width, 230, 233, 242
focusing, 162, 168, 174, 222, 231, 232
focusing by planar slabs, 218
Frenkel excitons, 113
frequencies, 252
frequency dispersion, 264
frequency-dependent effective mass, 187
frequency-dependent index, 219
Fresnel modulation, 240
fundamental mode, 257, 258

G

Galerkin technique, 41
gap, 254
Gaussian, 152
generation of harmonics, 127
geometry of the split-ring resonator, 227
geometry of this disk array, 231
governing equations, 20
Green's function, 19, 29, 206
Green's function method, 251
GRIN Lens, 311
group longitudinal velocities, 257
group velocity, 2, 135, 137, 138, 144, 159, 265, 275
guided propagating waves, 251
guided wave device, 42
guided wave structures, 19
guiding structure, 255
gyrotropic, 110

H

H-polarized, 81
harmonic mean, 90
Helmholtz-Kirchhoff
theorem, 278, 280
heterostructure bicrystal, 19
hexagonal annulus arrays, 218
hexagonal array, 239
hexagonal arrays of 1 cm copper disks, 240
hexagonal disk array measurements refraction, 242
hexagonal disk arrays, 218, 226
higher order modes, 259
Homogeneous Effective Medium, 282
horn, 155
hysteresis, 332, 333, 337, 340

I

Ideal Negative Index Medium, 220
idealized NIM, 219
image, 162, 168, 172-174, 176, 179, 180, 221
image resolution, 168
immersion lens, 7
indefinite index medium, 275
Indefinite Media, 272
index, 152-156
index of refraction, 233, 237, 262
index of refraction from the displacement of the focus, 242
integral equation of the homogeneous Fredholm type of the second kind, 30
interplay of two resonances, 110
inverse tensor, 103
isotropic, 21
isotropic index medium, 275
isotropic systems, 105
isotropy, 49, 154

L

L. I. Mandelstam, 96, 97
lattice, 159
leftand right-hand polarized waves, 117
left-handed, 133, 137, 150
left-handed electromagnetism (LHE), 133, 137, 143, 144, 146
left-handed material (LHM), 133, 136, 144, 262
left-handed medium (LHM), 2 line width, 253
locally resonant sonic materials, 190
longitudinal, 105, 157
longitudinal frequency, 116
Lorentzian, 220
loss tangent, 258, 266
loss widths, 252
Losses, 265, 289

M

macroscopic Maxwell equations, 102
magnetic crossover frequency, 256
magnetic line width, 255
magnetic magnitude distribution, 45
magnetic permeability, 96, 121, 183
magnetic resonance, 252
magnetic-dipole transitions, 109
magnitude field distributions, 43
Maxwell's, 21
Maxwell's equations, 262
measurements, 224
metallic, 157
metallic conductivity, 255
Metallodielectric, 149
metamaterial, 121, 149, 252
microstrip, 19
microstrip guided wave structure, 251
microstrip left-handed material, 251
microwave, 133-137, 139, 141, 145, 146
Mie resonances, 192
millimeter wavelength, 251
molecular transitions, 108
monopolar resonance, 199
monopole, 157
monopole source, 233
movement of focus, 236
multilayer, 88
multiple scattering theory, 190

N

negative dielectric permittivity, 96
negative effective density, 184
negative effective mass, 188, 189
negative effective modulus, 184
negative group velocity, 95
negative index material (NIM), 133-135, 142
negative index of refraction, 133, 263
negative index passband, 233
negative phase velocity, 20, 290
negative refraction (NR), 1, 10, 95, 133-136, 138-141, 143-146, 148-152, 154, 167, 168, 171, 172, 174, 175, 178-180, 244
NIM Lens, 295, 308
NIM Optics, 295
nonlinear
- dielectric permittivity, 336
- effects, 330-337
- magnetic response, 333, 334, 340, 342
- metamaterial, 332, 333
- resonance, 333-335
- response, 333-334
- response, Kerr-type, 334, 343, 345, 352, 355
nonlinear lens, 367-368
nonlinear material with negative refraction, 127
nonlinear optical effects, 6 nonlinearity, 333
nonlocal dielectric response, 96
normal waves, 129

O

odd mode, 37
omnidirectional, 156
Onsager principle of symmetry of
- kinetic coefficients, 103
Onsager relation, 108
optical activity, 25, 114
optical activity tensors, 21
optical branches, 98
optical frequencies, 121
optical nonlinear susceptibilities, 127
ordinary wave, 9
orientational superlattice, 15
oscillator strengths, 109

P

parallel plate waveguide (PPW), 133-135, 140
Parseval theorem, 40
partial waves, 193
perfect lens, 1
perfectly matched layer, 220
Periodic Effective Medium, 287
permeability, 133, 252
permittivity, 133, 134, 158
permittivity tensor, 8, 21, 49
phase longitudinal velocities, 257
phase velocity, 272
photonic crystal, 148-151, 167, 226
- metallic, 135
photonic crystal (PC), 134, 135, 141, 218
photonic crystal scheme, 6 photonic crystal simulations, 231
photonic crystal slab, 234
physical meaning, 121
PIM lens, 301, 307
PIM, NIM, and GRIN Lenses, 314
planar slab focusing, 217
plasma frequency, 109, 217, 219
point sources, 213
polariton, 4, 95
polaritons with negative group velocity, 111
Polarization Coupling, 270
polystyrene, 152
positive index, 226, 233
Poynting vector, 2, 10, 91, 96, 133, 134, 257
principal axis system, 28
prism, photonic crystal, 136, 137, 144
propagation, 149-152
propagation constant, 42, 69
pulse, 222

Q

quadratic nonlinearity, 357
quasicrystal, 168-170, 172, 176, 177, 179, 180

R

randomly oriented, 92
reflection, 7, 155
refraction, 85, 86, 151
refraction of our hexagonal disk, 236
refraction through the disk medium, 236
refractive index, 133, 136, 138, 139, 141, 142, 144
refractive index, negative, 133
resolution, 211
resonance frequency, 219
retrieval, 281, 286
right-handed, 133, 137
right-handed electromagnetism (RHE), 134, 137, 138
right-handed materials, 263
right-handed medium (RHM), 2

S

S-parameter, 247
sculptured thin film, 15
second harmonics generation, SHG, 355-357
- enhanced, 363
- pulses, 363
Siedel aberrations, 295
slab, 221
Snell, 156
Snell's law, 133, 136, 139, 142, 222, 230, 234, 236, 262, 276, 277
soliton
- bright, 342, 350
- dark, 342
spatial, 340-342
- temporal, 339
sonic bandgaps, 190
spatial, 152
spatial dispersion, 3, 96, 102, 205
spatial dispersion approach, 102
spatial dispersion framework, 129
spatial dispersion of dielectric effects, 126
spatial electric field components, 33
spatial inversion, 105
spatial-dispersion scheme, 3 spectral, 150
spectral domain, 29, 33
spectral summations, 39
spherical harmonics, 195
Spherical NIM Lenses, 305
split ring, 254
split ring-rod, 252
split-ring resonators, 223
square double ring geometry, 224
SRR resonance, 230
stability of the focus, 222
stripline, 67
structure loss, 266
subwavelength, 148-150
sum rule, 108
superfocusing, 222, 234
superprism, 150
surface currents, 37
surface impedance, 206
surface polaritons, 118
surface transition layer, 118
surface wave, 56
- linear, 343, 344
- nonlinear, 343, 345-349
symmetric approach, 103
symmetry breaking, 354, 355

T

TE, 163
tensor, 80
thermodynamic equilibrium, 96
time-dependent dielectric polarization, 123
TM, 163
total eigenvector field solution, 41
total induced current, 123
total induced magnetic moment, 122
total vector surface current, 41
totally reflected, 86
transmission, 239, 240
transmission and focusing, 240
transmission displays, 229
transmission spectra, 224
transverse, 105
transverse (w)-longitudinal (w||) splitting gap, 97
transverse electric (TE), 135, 141, 143, 145
transverse magnetic (TM), 135, 138, 140-143
transverse polaritons, 96
triangular lattice, 135-139, 141
triangular PC, 143

U

ultra-short pulses, 128
uniaxial symmetry, 8

uniform media, 2, 8

V

vector potential, 107
velocity of energy propagation, 96
volumetric fields, 65

W

wave, 9
wavelength, 151
wire array, 217, 223
wire radius r_e , 253
with negative group velocity, 129

Z

Zernike polynomials, 319
zero reflection, 10, 14

Autoren

The editors are well known senior research scientists at two nationally recognized research laboratories in the US, and the contributing authors, from internationally located universities, national labs, and industry, are all major contributors to the curently important and active field of negative refractive and negative index materials.