Table of Contents
Preface v
1 Oscillator Model 1
1.1 Optical Susceptibility 2
1.2 Absorption and Refraction 6
1.3 Retarded Green's Function 12
2 Atoms in a Classical Light Field 17
2.1 Atomic Optical Susceptibility 17
2.2 Oscillator Strength 21
2.3 Optical Stark Shift 23
3 Periodic Lattice of Atoms 29
3.1 Reciprocal Lattice, Bloch Theorem 29
3.2 Tight-Binding Approximation 36
3.3 k.p Theory 41
3.4 Degenerate Valence Bands 45
4 Mesoscopic Semiconductor Structures 53
4.1 Envelope Function Approximation 54
4.2 Conduction Band Electrons in Quantum Wells 56
4.3 Degenerate Hole Bands in Quantum Wells 60
5 Free Carrier Transitions 65
5.1 Optical Dipole Transitions 65
5.2 Kinetics of Optical Interband Transitions 69
5.2.1 Quasi-D-Dimensional Semiconductors 70
5.2.2 Quantum Confined Semiconductors with Subband Structure 72
5.3 Coherent Regime: Optical Bloch Equations 74
5.4 Quasi-Equilibrium Regime: Free Carrier Absorption 78
6 Ideal Quantum Gases 89
6.1 Ideal Fermi Gas 90
6.1.1 Ideal Fermi Gas in Three Dimensions 93
6.1.2 Ideal Fermi Gas in Two Dimensions 97
6.2 Ideal Bose Gas 97
6.2.1 Ideal Bose Gas in Three Dimensions 99
6.2.2 Ideal Bose Gas in Two Dimensions 101
6.3 Ideal Quantum Gases in D Dimensions 101
7 Interacting Electron Gas 107
7.1 The Electron Gas Hamiltonian 107
7.2 Three-Dimensional Electron Gas 113
7.3 Two-Dimensional Electron Gas 119
7.4 Multi-Subband Quantum Wells 122
7.5 Quasi-One-Dimensional Electron Gas 123
8 Plasmons and Plasma Screening 129
8.1 Plasmons and Pair Excitations 129
8.2 Plasma Screening 137
8.3 Analysis of the Lindhard Formula 140
8.3.1 Three Dimensions 140
8.3.2 Two Dimensions143
8.3.3 One Dimensions 145
8.4 Plasmon-Pole Approximation 146
9 Retarded Green's Function for Electrons 149
9.1 Definitions 149
9.2 Interacting Electron Gas 152
9.3 Screened Hartree-Fock Approximation 156
10 Excitons 163
10.1 The Interband Polarization 164
10.2 Wannier Equation 169
10.3 Excitons 173
10.3.1 Three- and Two-Dimensional Cases 174
10.3.2 Quasi-One-Dimensional Case 179
10.4 The Ionization Continuum 181
10.4.1 Three- and Two-Dimensional Cases 181
10.4.2 Quasi-One-Dimensional Case 183
10.5 Optical Spectra 184
10.5.1 Three- and Two-Dimensional Cases 186
10.5.2 Quasi-One-Dimensional Case 189
11 Polaritons 193
11.1 Dielectric Theory of Polaritons 193
11.1.1 Polaritions without Spatial Dispersion and Damping 195
11.1.2 Polaritons with Spatial Dispersion and Damping 197
11.2 Hamiltonian Theory of Polaritons 199
11.3 Microcavity Polaritons 206
12 Semiconductor Bloch Equations 211
12.1 Hamiltonian Equations 211
12.2 Multi-Subband Microstructures 219
12.3 Scattering Terms 221
12.3.1 Intraband Relaxation 226
12.3.2 Dephasing of the Interband Polarization 230
12.3.3 Full Mean-Field Evolution of the Phonon-Assisted Density Matrices 231
13 Excitonic Optical Stark Effect 235
13.1 Quasi-Stationary Results 237
13.2 Dynamic Results 246
13.3 Correlation Effects 255
14 Wave-Mixing Spectroscopy 269
14.1 Thin Samples 271
14.2 Semiconductor Photon Echo 275
15 Optical Properties of a Quasi-Equilibrium Electron-Hole Plasma 283
15.1 Numerical Matrix Inversion 287
15.2 High-Density Approximations 293
15.3 Effective Pair-Equation Approximation 296
15.3.1 Bound states 299
15.3.2 Continuum states 300
15.3.3 Optical spectra 300
16 Optical Bistability 305
16.1 The Light Field Equation 306
16.2 The Carrier Equation 309
16.3 Bistability in Semiconductor Resonators 311
16.4 Intrinsic Optical Bistability 316
17 Semiconductor Laser 321
17.1 Material Equations 322
17.2 Field Equations 324
17.3 Quantum Mechanical Langevin Equations 328
17.4 Stochastic Laser Theory 335
17.5 Nonlinear Dynamics with Delayed Feedback 340
18 Electroabsorption 349
18.1 Bulk Semiconductors 349
18.2 Quantum Wells 355
18.3 Exciton Electroabsorption 360
18.3.1 Bulk Semiconductors 360
18.3.2 Quantum Wells 368
19 Magneto-Optics 371
19.1 Single Electron in a Magnetic Field 372
19.2 Bloch Equations for a Magneto-Plasma 375
19.3 Magneto-Luminescence of Quantum Wires 378
20 Quantum Dots 383
20.1 Effective Mass Approximation 383
20.2 Single Particle Properties 386
20.3 Pair States 388
20.4 Dipole Transitions 392
20.5 Bloch Equations 395
20.6 Optical Spectra 396
21 Coulomb Quantum Kinetics 401
21.1 General Formulation 402
21.2 Second Born Approximation 408
21.3 Build-Up of Screening 413
22 Quantum Optical Effects 421
22.1 Quantum Optics for Semiconductors 421
22.2 Cluster Expansion 424
22.2.1 Cluster Expansion for Fermions 424
22.2.2 Quantum Optical Cluster Expansion 428
22.3 Semiconductor Luminescence Equations 429
22.4 Quasi-Stationary Luminescence 432
Appendix A Field Quantization 437
A.1 Lagrange Functional 437
A.2 Canonical Momentum and Hamilton Function 442
A.3 Quantization of the Fields 444
Appendix B Contour-Ordered Green's Functions 451
B.1 Interaction Representation 452
B.2 Langreth Theorem 455
B.3 Equilibrium Electron-Phonon Self-Energy 458
Index 461
