Introduction to Nanophotonics

Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 9
Preface......Page 15
Notations and acronyms......Page 17
1.1 Light and matter on a nanometer scale......Page 21
1.2 What is nanophotonics?......Page 22
1.3 Where are the photons in nanophotonics and in this book?......Page 23
References......Page 24
PART I ELECTRONS AND ELECTROMAGNETIC WAVES IN NANOSTRUCTURES......Page 27
2.1 Wavelengths and dispersion laws......Page 29
2.2 Density of states......Page 33
2.3 Maxwell and Helmholtz equations......Page 36
2.4 Phase space, density of states and uncertainty relation......Page 38
2.5 Wave function and the Schrodinger equation......Page 40
A rectangular well with inflnite walls......Page 42
A rectangular well with flnite barriers......Page 44
Quantum harmonic oscillator......Page 45
Particle in a spherically symmetric potential......Page 47
Electron in Coulomb potential......Page 50
Problems......Page 52
References......Page 54
3.1 Isomorphism of the Schrodinger and Helmholtz equations......Page 55
Potential and refraction steps......Page 57
Rectangular barriers and wells......Page 61
Potential and refraction barriers/steps compared......Page 70
3.3 Dielectric function of free electron gas and optical properties of metals......Page 71
3.4 Propagation through a potential barrier: evanescent waves and tunneling......Page 74
Finite barriers: tunneling......Page 78
3.5 Resonant tunneling in quantum mechanics and in optics......Page 85
3.6 Multiple wells and barriers: spectral splitting......Page 90
3.7 Historical comments......Page 93
Problems......Page 96
References......Page 97
4.1 Bloch waves......Page 99
4.2 Reciprocal space and Brillouin zones......Page 104
4.3 Electron band structure in solids......Page 106
4.4 Quasiparticles: holes, excitons, polaritons......Page 109
4.5 Defect states and Anderson localization......Page 113
4.6 Quantum confinement effects in solids......Page 117
4.7 Density of states for different dimensionalities......Page 119
4.8 Quantum wells, quantum wires and quantum dots......Page 120
Quantum wells and quantum well superlattices......Page 121
Quantum wires and nanorods......Page 125
Quantum dots......Page 126
References......Page 127
5.1 From atom to crystal......Page 130
Weak confinement regime......Page 132
Strong confinement limit......Page 134
5.3 Quantum chemical theory......Page 138
Diffusion-controlled growth in glass matrices......Page 140
Colloidal nanocrystals in solutions and polymers......Page 142
Quantum dot heterostructures......Page 144
5.5 Absorption spectra, electron–hole pair states and many-body effects......Page 145
5.6 Luminescence......Page 150
5.8 Quantum dot matter......Page 153
5.9 Applications: nonlinear optics......Page 159
5.10 Applications: quantum dot lasers......Page 162
Nanocrystals in glasses and polymers......Page 164
Injection lasers based on self-organized quantum dot heterostructures......Page 166
Spectral converters......Page 168
White light sources......Page 169
Fluorescent labels......Page 173
Electroluminescent structures......Page 174
Electroabsorption......Page 175
External electric field effect on luminescence......Page 176
Problems......Page 177
References......Page 178
6.1 Optical response of metals......Page 186
6.2 Plasmons......Page 194
6.3 Optical properties of metal nanoparticles......Page 199
Surface plasmons in a nanoparticle......Page 200
A metal nanoparticle viewed as a “plasmonic atom”......Page 206
6.4 Size-dependent absorption and scattering......Page 207
6.5 Coupled nanoparticles......Page 211
6.6 Metal–dielectric core–shell nanoparticles......Page 212
Problems......Page 215
References......Page 216
7.1 The photonic crystal concept......Page 219
7.2 Bloch waves and band structure in one-dimensionally periodic structures......Page 220
7.3 Multilayer slabs in three dimensions: band structure and omnidirectional reflection......Page 227
7.4 Band gaps and band structures in two-dimensional lattices......Page 230
7.5 Band gaps and band structure in three-dimensional lattices......Page 233
7.6 Multiple scattering theory of periodic structures......Page 235
7.7 Translation to other electromagnetic waves......Page 236
7.8 Periodic structures in Nature......Page 237
Synthesis of mesoporous materials with 2-dimensional periodicity......Page 238
Synthesis of materials with 3-dimensional periodicity......Page 241
One-dimensional periodicity......Page 245
Two-dimensional periodicity: transmission bands......Page 247
Two-dimensional periodicity: antireflection effect......Page 248
Two-dimensional periodicity: form-anisotropy and birefringence......Page 249
Three-dimensional photonic crystal slabs......Page 251
7.11 The speed of light in photonic crystals......Page 252
7.12 Nonlinear optics of photonic crystals......Page 256
Problems......Page 259
References......Page 260
8.1 The 1/L transmission law: an optical analog to Ohm’s law......Page 266
8.2 Coherent backscattering......Page 271
8.3 Towards the Anderson localization of light......Page 273
Optical fractal filters......Page 278
Spectral scalability resulting from geometrical self-similarity......Page 282
Splitting of transmission bands in symmetrical fractal filters......Page 288
One-dimensional quasiperiodicity: Fibonacci potentials and Fibonacci filters......Page 290
Laser pulse shaping with Fibonacci filters......Page 295
Two-dimensional quasiperiodicity: Penrose quasicrystals......Page 297
8.6 Surface states in optics: analog to quantum Tamm states......Page 298
8.7 General constraints on wave propagation in multilayer structures: transmission bands, phase time, density of modes and energy localization......Page 300
Transmission spectra and phase shifts......Page 301
The conservation law......Page 303
Phase time and traversal velocity......Page 305
Density of modes conservation......Page 306
Summary and conclusion......Page 308
8.8 Applications of turbid structures: Christiansen’s filters and Letokhov’s lasers......Page 309
Problems......Page 310
References......Page 311
9.1 Microcavities and microlasers......Page 315
9.2 Guiding light through photonic crystals......Page 318
9.3 Holey fibers......Page 323
9.4 Whispering gallery modes: photonic dots, photonic molecules and chains......Page 325
9.5 Propagation of waves and number coding/recognition......Page 329
9.6 Outlook: current and future trends......Page 331
Problems......Page 332
References......Page 333
10.1 Tunneling of light: getting through the looking glass......Page 337
10.2 Light at the end of a tunnel: problem of superluminal propagation......Page 340
The Hartman paradox in quantum mechanics......Page 341
Electromagnetic analog of the Hartman paradox......Page 343
Phase time in frustrated total reflection......Page 344
Superluminal propagation and energy flow in a photonic crystal slab......Page 346
Conclusions and outlook......Page 349
10.3 Scanning near-field optical microscopy......Page 350
References......Page 354
11.1 Local electromagnetic fields near metal nanoparticles......Page 356
Local fields near a single metal particle......Page 357
Spatially arranged particles......Page 358
Local field enhancement in terms of the energy conservation law......Page 360
11.2 Optical response of a metal–dielectric composite beyond Maxwell-Garnett theory......Page 361
11.3 Extraordinary transparency of perforated metal films......Page 364
11.4 Metal–dielectric photonic crystals......Page 366
11.5 Nonlinear optics with surface plasmons......Page 368
11.6 Metal nanoparticles in a medium with optical gain......Page 370
11.7 Metamaterials with negative refractive index......Page 373
Optics with µ = 1......Page 374
Optics with “left-handed” materials......Page 376
11.8 Plasmonic sensors......Page 381
Problems......Page 383
References......Page 384
12.1 Transfer of concepts and ideas from quantum theory of solids to nanophotonics......Page 388
12.3 Optical lessons of quantum intuition......Page 390
Problems......Page 392
References......Page 393
PART II LIGHT–MATTER INTERACTION IN NANOSTRUCTURES......Page 395
Basic statements......Page 397
Brief historical notes......Page 399
13.2 Wave–particle duality in optics......Page 401
13.3 Electromagnetic vacuum......Page 402
13.4 The Casimir effect......Page 404
13.5 Probability of emission of photons by a quantum system......Page 405
13.6 Does “Fermi’s golden rule” help to understand spontaneous emission?......Page 409
13.7 Spontaneous scattering of photons......Page 410
References......Page 412
14 Density of states effects on optical processes in mesoscopic structures......Page 415
14.1 The Purcell effect......Page 416
14.2 An emitter near a planar mirror......Page 420
14.3 Spontaneous emission in a photonic crystal......Page 421
14.4 Thin layers, interfaces and strati.ed dielectrics......Page 424
14.5 Possible subnatural atomic linewidths in plasma......Page 427
14.6 Barnett–Loudon sum rule......Page 428
14.7 Local density of states: operational de.nition and conservation law......Page 430
14.8 A few hints towards understanding local density of states......Page 431
14.9 Thermal radiation in mesoscopic structures......Page 433
14.10 Density of states effects on the Raman scattering of light......Page 435
14.11 Directional emission and scattering of light defined by partial density of states......Page 436
References......Page 439
15.1 Cavity quantum electrodynamics in the strong coupling regime......Page 444
15.2 Single-atom maser and laser......Page 448
15.3 Light–matter states in a photonic band gap medium......Page 449
15.4 Single photon sources......Page 451
References......Page 453
16.1 Classification of secondary radiation......Page 456
16.2 How emission and scattering of light can be enhanced......Page 457
16.3 Local density of states in plasmonic nanostructures......Page 459
16.4 “Hot spots” in plasmonic nanostructures......Page 461
16.5 Raman scattering enhancement in metal–dielectric nanostructures......Page 464
16.6 Luminescence enhancement in metal–dielectric nanostructures......Page 467
References......Page 472
Author index......Page 475
Subject index......Page 478