Optoelectronics

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 17
1.2 The postulates of quantum mechanics......Page 21
1.3.1 Stationary states......Page 26
1.3.2 Calculation of stationary states in a one-dimensional potential......Page 27
1.4.1 The general case......Page 28
(1) Even solutions......Page 31
(2) Odd solutions......Page 32
1.4.2 The infinite square well......Page 34
1.5 Time-independent perturbation theory......Page 35
1st order......Page 36
2nd order......Page 37
1.6.1 The general case......Page 38
qth-order term......Page 39
1.6.2 Sinusoidal perturbation......Page 40
Case 1: transitions induced between discrete levels by single frequency excitation......Page 41
Case 2: transitions induced between a discrete level and a continuum state by single frequency excitation......Page 42
1.7 The density matrix......Page 43
1.7.2 Mixed quantum ensembles......Page 44
(a) Diagonal elements......Page 45
1.7.3 Density matrix and relaxation time for a two-level system......Page 46
FURTHER READING......Page 48
1.A Problems posed by continuums: the fictitious quantum box and the density of states......Page 49
1.B Perturbation on a degenerate state......Page 53
1.C The quantum confined Stark effect......Page 57
1.D The harmonic oscillator......Page 61
1.E Transition probabilities and Rabi oscillations......Page 70
FURTHER READING......Page 75
2.2 Maxwell’s equations in reciprocal space......Page 76
2.3 Properties of the Fourier transform......Page 78
2.4 Quantization of electromagnetic waves......Page 81
2.5 The photon......Page 83
2.6 The coherent state......Page 87
2.7 Blackbody radiation......Page 91
FURTHER READING......Page 95
2.A Radiation field for an oscillating charge: the Lorentz gauge......Page 96
2.B Thermography......Page 104
FURTHER READING......Page 110
3.2 Dipolar interaction Hamiltonian for electrons and photons......Page 111
Coulomb gauge......Page 112
3.3 Linear optical susceptibility obtained by the density matrix......Page 113
3.4 Linear optical susceptibility: absorption and optical gain......Page 116
3.5.1 Adiabatic approximation and corpuscular interpretation......Page 120
3.5.2 Stimulated emission......Page 121
3.5.3 Absorption saturation......Page 122
3.6.1 Spontaneous emission......Page 124
3.6.2 The rate equations including spontaneous emission......Page 129
3.7 Polychromatic transitions and Einstein’s equations......Page 130
3.8 Rate equations revisited......Page 131
3.8.1 Monochromatic single-mode waves......Page 132
3.8.2 Multimode monochromatic waves......Page 133
FURTHER READING......Page 134
3.A Homogeneous and inhomogeneous broadening: coherence of light......Page 135
1b Broadening due to elastic collisions: temporal coherence......Page 136
3.A.2 Inhomogeneous broadening......Page 140
FURTHER READING......Page 142
3.B Second-order time-dependent perturbations......Page 143
3.C Einstein coefficients in two limiting cases: quasi-monochromatic and broadband optical transitions......Page 151
3.D Equivalence of the A·p and D·E Hamiltonians and the Thomas–Reiche–Kuhn sum rule......Page 153
4.2.1 Population inversion......Page 159
4.2.2 Optical amplification and gain saturation......Page 161
4.3 Three-and four-level systems......Page 163
4.4 Optical resonators and laser threshold......Page 166
Gain condition......Page 168
Phase condition......Page 169
4.5.1 Internal laser characteristics and gain clamping......Page 170
4.5.2 Output power......Page 172
4.5.3 Spectral characteristics......Page 174
Homogeneous gain spectrum (see Complement 3.A)......Page 175
4.6 Cavity rate equations and the dynamic behaviour of lasers......Page 176
4.6.1 Damped oscillations......Page 178
4.6.2 Laser cavity dumping by loss modulation (Q-switching)......Page 179
4.6.3 Mode locking......Page 183
FURTHER READING......Page 186
4.A The effect of spontaneous emission and photon condensation......Page 187
4.B Saturation in laser amplifiers......Page 191
4.C Electrodynamic laser equations: electromagnetic foundations for mode locking......Page 198
4.D The Schawlow–Townes limit and Langevin-noise force......Page 205
4.E A case study: diode pumped lasers......Page 213
FURTHER READING......Page 218
5.2 Crystal structures, Bloch functions, and the Brillouin zone......Page 219
5.3 Energy bands......Page 224
5.4 Effective mass and density of states......Page 226
5.5 Dynamic interpretation of effective mass and the concept of holes......Page 230
5.6.1 Fermi statistics and the Fermi level......Page 236
Occupied Fermi level: degenerate system (Fig.5.15)......Page 237
Unoccupied Fermi level (Fig.5.16)......Page 238
5.6.2 Intrinsic semiconductors......Page 241
5.6.3 Doped semiconductors......Page 242
5.6.4 Quasi-Fermi level in a non-equilibrium system......Page 244
Semiconductors......Page 246
5.A The nearly free electron model......Page 247
5.B Linear combination of atomic orbitals: the tight binding model......Page 250
5.C Kane’s k · p method......Page 254
FURTHER READING......Page 261
5.D Deep defects in semiconductors......Page 262
FURTHER READING......Page 264
6.2 Boltzmann’s equation......Page 265
6.3 Scattering mechanisms......Page 271
6.4.1 Warm electrons......Page 277
6.4.2 Hot electrons: saturation velocity......Page 278
6.4.3 Hot electrons: negative differential velocity......Page 280
6.5 Recombination......Page 281
6.6 Transport equations in a semiconductor......Page 286
FURTHER READING......Page 290
6.A The Hall effect......Page 291
6.B.1 Phonons......Page 293
6.B.2 The Fröhlich interaction......Page 300
6.C Avalanche breakdown......Page 305
6.D Auger recombination......Page 309
FURTHER READING......Page 315
7.2 Dipolar elements in direct gap semiconductors......Page 316
7.3 Optical susceptibility of a semiconductor......Page 321
7.4 Absorption and spontaneous emission......Page 326
7.5 Bimolecular recombination coefficient......Page 333
7.6 Conditions for optical amplification in semiconductors......Page 336
FURTHER READING......Page 340
7.A The Franz–Keldysh-effect electromodulator......Page 341
7.B Optical index of semiconductors......Page 348
7.B.1 Mid- and far-infrared regions......Page 349
7.B.2 Near gap regime......Page 350
7.C Free-carrier absorption......Page 353
Strong conductivity (Sigma » EpsilonOmega)......Page 354
Weak conductivity (Sigma « EpsilonOmega)......Page 355
FURTHER READING......Page 361
8.1 Introduction......Page 362
8.2 Envelope function formalism......Page 364
8.3 The quantum well......Page 370
8.4 Density of states and statistics in a quantum well......Page 374
8.5.1 Hole states in the valence bands......Page 378
8.5.2 Optical transitions between the valence and conduction bands......Page 379
8.6 Optical intersubband transitions in a quantum well......Page 385
8.7.1 Summary for interband and intersubband transition rates......Page 389
8.7.2 Influence of the angle of incidence......Page 390
FURTHER READING......Page 396
8.A Quantum wires and boxes......Page 397
8.B Excitons......Page 400
8.B.1 Three-dimensional excitons......Page 401
8.B.2 Two-dimensional excitons......Page 405
8.C Quantum confined Stark effect and the SEED electromodulator......Page 408
8.D Valence subbands......Page 412
9.2 A geometrical approach to waveguides......Page 416
9.3 An oscillatory approach to waveguides......Page 420
Transverse electric (TE) waves......Page 422
Transverse magnetic(TM) waves......Page 426
9.4 Optical confinement......Page 427
9.5 Coupling between guided modes: coupled mode theory......Page 430
FURTHER READING......Page 433
9.A Optical coupling between guides: electro-optic switches......Page 434
FURTHER READING......Page 440
9.B Bragg waveguides......Page 441
FURTHER READING......Page 446
9.C.1 TE mode in–TE mode out......Page 447
Quasi-phase matching......Page 450
9.C.2 TE mode in–TM mode out......Page 452
9.D Fabry–Pérot cavities and Bragg reflectors......Page 454
9.D.1 The Fabry–Pérot cavity......Page 457
9.D.2 Bragg mirrors......Page 462
FURTHER READING......Page 466
10.1 Introduction......Page 467
10.2 Surface phenomena......Page 468
10.3 The Schottky junction......Page 471
10.4 The p–n junction......Page 476
FURTHER READING......Page 485
10.A.1 p–n heterojunction diode......Page 486
10.A.2 The p–i–n diode......Page 487
10.B Diode leakage current......Page 490
11.2 Distribution of carriers in a photoexcited semiconductor......Page 495
11.3.1 Photoconduction gain......Page 501
11.3.2 Photoconductor detectivity......Page 504
11.3.3 Time response of a photoconductor......Page 506
11.4 Photovoltaic detectors......Page 508
11.4.1 Photodiode detectivity......Page 512
11.4.2 Time response of a photodiode......Page 514
11.5 Internal emission photodetector......Page 517
11.6 Quantum well photodetectors (QWIPs)......Page 520
11.7 Avalanche photodetectors......Page 529
FURTHER READING......Page 532
11.A Detector noise......Page 533
11.A.1 Fluctuations......Page 534
11.A.3 Thermal noise......Page 538
11.A.4 Generation–recombination noise......Page 541
11.A.5 Multiplication noise......Page 545
11.B Detectivity limits: performance limits due to background (BLIP)......Page 550
FURTHER READING......Page 557
12.2 A mechanical description for second harmonic frequency generation......Page 558
12.3 An electromagnetic description of quadratic non-linear optical interaction......Page 563
12.4 Optical second harmonic generation......Page 566
12.5 Manley–Rowe relations......Page 570
12.6 Parametric amplification......Page 571
12.7.1 Simply resonant optical parametric oscillators (SROPOs)......Page 574
12.7.2 Doubly resonant optical parametric oscillator (DROPO)......Page 577
Difference frequency generation (DFG) 4…......Page 580
Parametric oscillation......Page 582
FURTHER READING......Page 584
12.A A quantum model for quadratic non-linear susceptibility......Page 585
12.B Methods for achieving phase matching in semiconductors......Page 592
12.B.1 Birefringent phase matching......Page 593
12.B.2 Quasi-phase matching......Page 599
12.C Pump depletion in parametric interactions......Page 602
12.D Spectral and temporal characteristics of optical parametric oscillators......Page 607
12.E Parametric interactions in laser cavities......Page 616
12.F Continuous wave optical parametric oscillator characteristics......Page 622
12.F.1 Singly resonant OPO......Page 623
12.F.2 Doubly resonant OPO: the balanced DROPO......Page 628
12.F.3 Doubly resonant OPO: the general case......Page 630
FURTHER READING......Page 632
13.2 Electrical injection and non-equilibrium carrier densities......Page 633
13.3.1 Electroluminescence......Page 637
13.3.2 Internal and external efficiencies for LEDs......Page 639
13.3.3 A few device issues......Page 643
13.4 Optical amplification in heterojunction diodes......Page 644
13.5.1 Laser threshold......Page 649
13.5.2 Output power......Page 654
13.6.1 Optical amplification in a quantum well structure: general case......Page 657
13.6.2 Transparency threshold......Page 661
13.6.3 Laser threshold for a quantum well laser......Page 667
13.6.4 Scaling rules for multi-quantum well lasers......Page 669
13.7 Dynamic aspects of laser diodes......Page 672
13.8.1 Spectral distribution......Page 675
13.8.2 Spatial distribution......Page 676
FURTHER READING......Page 679
13.A Distributed feedback (DFB) lasers......Page 680
13.B Strained quantum well lasers......Page 685
13.C.1 Conditions for achieving threshold in a VCSEL......Page 691
13.C.2 VCSEL performance......Page 695
13.D Thermal aspects of laser diodes and high power devices......Page 696
Emissive surface in an infinite medium: transient response......Page 697
Thermal dissipation on both sides of the junction under continuous operation......Page 700
13.E Spontaneous emission in semiconductor lasers......Page 703
13.F Gain saturation and the K factor......Page 710
13.G Laser diode noise and linewidth......Page 716
13.G.1 Linewidth broadening......Page 720
13.G.2 Relative intensity noise (RIN) and optical link budget......Page 721
13.H Unipolar quantum cascade lasers......Page 724
13.I Mode competition: cross gain modulators......Page 728
FURTHER READING......Page 732
Index......Page 733