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Overview of Microcavities 1
Properties of microcavities 2
Q-factor and finesse 2
Intracavity field enhancement and field distribution 3
Tuneability and mode separation 3
Angular mode pattern 4
Low-threshold lasing 4
Purcell factor and lifetimes 5
Strong vs. weak coupling 5
Microcavity realizations 5
Planar microcavities 6
Metal microcavities 8
Dielectric Bragg mirrors 9
Spherical mirror microcavities 10
Pillar microcavities 12
Whispering-gallery modes 15
Two-dimensional whispering galleries 16
Three-dimensional whispering-galleries 18
Photonic-crystal cavities 19
Random lasers 20
Plasmonic cavities 20
Microcavity lasers 21
Conclusion 21
Classical description of light 23
Free space 24
Light-field dynamics in free space 24
Propagation in crystals 27
Plane waves in bulk crystals 27
Absorption of light 31
Kramers-Kronig relations 32
Coherence 32
Statistical properties of light 32
Spatial and temporal coherence 33
Wiener-Khinchin theorem 38
Hanbury Brown-Twiss effect 41
Polarization-dependent optical effects 43
Birefringence 43
Magneto-optical effects 44
Propagation of light in multilayer planar structures 45
Photonic eigenmodes of planar systems 49
Photonic bands of 1D periodic structures 52
Planar microcavities 59
Stripes, pillars, and spheres: photonic wires and dots 64
Cylinders and pillar cavities 66
Spheres 69
Further reading 73
Quantum description of light 75
Pictures of quantum mechanics 76
Historical background 76
Schrodinger picture 76
Antisymmetry of the wavefunction 85
Symmetry of the wavefunction 86
Heisenberg picture 88
Dirac (interaction) picture 93
Other formulations 95
Density matrix 95
Second quantization 97
Quantization of the light field 99
Quantum states 100
Fock states 100
Coherent states 101
Glauber-Sudarshan representation 102
Thermal states 103
Mixture states 105
Quantum correlations of quantum fields 106
Statistics of the field 110
Polarization 113
Outlook on quantum mechanics for microcavities 115
Further reading 116
Semiclassical description of light-matter coupling 117
Light-matter interaction 118
Classical limit 118
Einstein coefficients 120
Optical transitions in semiconductors 123
Excitons in semiconductors 127
Frenkel and Wannier-Mott excitons 127
Excitons in confined systems 131
Quantum wells 132
Quantum wires and dots 135
Exciton-photon coupling 137
Surface polaritons 140
Exciton-photon coupling in quantum wells 142
Exciton-photon coupling in quantum wires and dots 147
Dispersion of polaritons in planar microcavities 150
Motional narrowing of cavity polaritons 160
Microcavities with quantum wires or dots 164
Quantum description of light-matter coupling in semiconductors 169
Historical background 170
Rabi dynamics 170
Bloch equations 173
Full quantum picture 176
Dressed bosons 179
Lindblad dissipation 187
Jaynes-Cummings model 192
Dicke model 198
Excitons in semiconductors 199
Quantization of the exciton field 200
Excitons as bosons 202
Excitons in quantum dots 202
Exciton-photon coupling 208
Dispersion of polaritons 210
The polariton Hamiltonian 211
Coupling in quantum dots 213
Weak-coupling microcavities 215
Purcell effect 216
The physics of weak coupling 216
Spontaneous emission 217
The case of QDs, 2D excitons and 2D electron-hole pairs 219
Fermi's golden rule 220
Dynamics of the Purcell effect 223
Case of QDs and QWs 225
Experimental realizations 226
Lasers 228
The physics of lasers 229
Semiconductors in laser physics 233
Vertical-cavity surface-emitting lasers 236
Resonant-cavity LEDs 240
Quantum theory of the laser 241
Nonlinear optical properties of weak-coupling microcavities 246
Bistability 247
Phase matching 249
Conclusion 249
Strong coupling: resonant effects 251
Optical properties background 252
Quantum well microcavities 252
Variations on a theme 254
Motional narrowing 256
Polariton emission 256
Near-resonant-pumped optical nonlinearities 258
Pulsed stimulated scattering 258
Quasimode theory of parametric amplification 263
Microcavity parametric oscillators 265
Resonant excitation case and parametric amplification 268
Semiclassical description 268
Stationary solution and threshold 269
Theoretical approach: quantum model 270
Three-level model 271
Threshold 274
Two-beam experiment 274
One-beam experiment and spontaneous symmetry breaking 274
Dressing of the dispersion induced by polariton condensates 276
Bistable behaviour 277
Strong coupling: polariton Bose condensation 279
Introduction 280
Basic ideas about Bose-Einstein condensation 280
Einstein proposal 280
Experimental realization 282
Modern definition of Bose-Einstein condensation 283
Specificities of excitons and polaritons 284
Thermodynamic properties of cavity polaritons 285
Interacting bosons and Bogoliubov model 286
Polariton superfluidity 289
Quasicondensation and local effects 292
High-power microcavity emission 294
Thresholdless polariton lasing 297
Kinetics of formation of polariton condensates: semiclassical picture 302
Qualitative features 302
The semiclassical Boltzmann equation 305
Numerical solution of Boltzmann equations, practical aspects 307
Effective scattering rates 307
Numerical simulations 308
Kinetics of formation of polariton condensates: quantum picture in the Born-Markov approximation 310
Density matrix dynamics of the ground-state 312
Discussion 316
Coherence dynamics 317
Kinetics of formation of polariton condensates: quantum picture beyond the Born-Markov approximation 319
Two-oscillator toy theory 319
Coherence of polariton-laser emission 329
Numerical simulations 335
Order parameter and phase diffusion coefficient 336
Semiconductor luminescence equations 338
Claims of exciton and polariton Bose-Einstein condensation 341
Further reading 342
Spin and polarization 345
Spin relaxation of electrons, holes and excitons in semiconductors 346
Microcavities in the presence of a magnetic field 351
Resonant Faraday rotation 352
Spin relaxation of exciton-polaritons in microcavities: experiment 355
Spin relaxation of exciton-polaritons in microcavities: theory 360
Optical spin Hall effect 364
Optical induced Faraday rotation 366
Interplay between spin and energy relaxation of exciton-polaritons 368
Polarization of Bose condensates and polariton superfluidity 372
Magnetic-field effect and superfluidity 374
Finite-temperature case 378
Spin dynamics in parametric oscillators 381
Classical nonlinear optics consideration 381
Polarized OPO: quantum model 383
Conclusions 385
Further reading 386
Glossary 387
Linear algebra 395
Scattering rates of polariton relaxation 399
Polariton-phonon interaction 399
Interaction with longitudinal optical phonons 400
Interaction with acoustic phonons 401
Polariton-electron interaction 402
Polariton-polariton interaction 404
Polariton decay 404
Polariton-structural-disorder interaction 405
Derivation of the Landau criterion of superfluidity and Landau formula 407
Landau quantization and renormalization of Rabi splitting 409
References 413

Rapid development of microfabrication and assembly of nanostructures has opened up many opportunities to miniaturize structures that confine light, producing unusual and extremely interesting optical properties. Microcavities addresses the large variety of optical phenomena taking place in confined solid state structures: microcavities. Realisations include planar and pillar microcavities, whispering gallery modes, and photonic crystals. The microcavities represent a unique laboratory for quantum optics and photonics. They exhibit a number of beautiful effects including lasing, superfluidity, superradiance, entanglement etc.

Written by four practitioners strongly involved in experiments and theories of microcavities, it is addressed to any interested reader having a general physical background, but in particular to undergraduate and graduate students at physics faculties.