Microcavities

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Overview

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. This book addresses the large variety of optical phenomena taking place in confined solid state structures: microcavities. Realizations 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.

About the Author:
Alexey Kavokin is Chair of Nanophysics and Photonics at the University of Southampton and Chair of Excellence at the University of Rome "Tor Vergata"

About the Author:
Jeremy Baumberg is Head of the Quantum Light and Matter group at the Physics and Astronomy School of the University of Southampton

About the Author:
Guillaume Malpuech is CNRS researcher, and head of group at the University Blaise Pascal, Clermont-Ferrand, France

About the Author:
Fabrice Laussy is research associate at Departamento de Fisica Teorica de la Materia Condensada, Universidad Autonoma de Madrid

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Product Details

Meet the Author

Professor Alexey Kavokin:

Chair of Nanophysics and Photonics at the University of Southampton and Chair of Excellence at the University of Rome "Tor Vergata"
Professor Jeremy Baumberg

Head of the Quantum Light and Matter group at the Physics and Astronomy School of the Southampton University Dr Guillaume Malpuech

CNRS researcher, head of group at the Blaise Pascal University, Clermont-Ferrand, France Dr Fabrice Laussy

Postdoctoral research associate at the University of Sheffield

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Table of Contents

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
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