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Scott W. Corzine obtained his PhD from the University of California, Santa Barbara, Department of Electrical and Computer Engineering, for his work on vertical-cavity surface-emitting lasers (VCSELs). He worked for ten years at HP/Agilent Laboratories in Palo Alto, California, on VCSELs, externally modulated lasers, and quantum cascade lasers. He is currently with Infinera in Sunnyvale, California, working on photonic integrated circuits.
Milan L. Mashanovitch obtained his PhD in the field of photonic integrated circuits at the University of California, Santa Barbara (UCSB), in 2004. He has since been with UCSB as a scientist working on tunable photonic integrated circuits and as an adjunct professor, and with Freedom Photonics LLC, Santa Barbara, which he cofounded in 2005, working on photonic integrated circuits.
Acknowledgments xxi
List of Fundamental Constants xxiii
1 Ingredients 1
1.1 Introduction 1
1.2 Energy Levels and Bands in Solids 5
1.3 Spontaneous and Stimulated Transitions: The Creation of Light 7
1.4 Transverse Confinement of Carriers and Photons in Diode Lasers: The Double Heterostructure 10
1.5 Semiconductor Materials for Diode Lasers 13
1.6 Epitaxial Growth Technology 20
1.7 Lateral Confinement of Current, Carriers, and Photons for Practical Lasers 24
1.8 Practical Laser Examples 31
References 39
Reading List 40
Problems 40
2 A Phenomenological Approach to Diode Lasers 45
2.1 Introduction 45
2.2 Carrier Generation and Recombination in Active Regions 46
2.3 Spontaneous Photon Generation and LEDs 49
2.4 Photon Generation and Loss in Laser Cavities 52
2.5 Threshold or Steady-State Gain in Lasers 55
2.6 Threshold Current and Power Out Versus Current 60
2.6.1 Basic P–I Characteristics 60
2.6.2 Gain Models and Their Use in Designing Lasers 64
2.7 Relaxation Resonance and Frequency Response 70
2.8 Characterizing Real Diode Lasers 74
2.8.1 Internal Parameters for In-Plane Lasers: αi , ηi , and g versus J 75
2.8.2 Internal Parameters for VCSELs: ηi and g versus J , αi , and αm 78
2.8.3 Efficiency and Heat Flow 79
2.8.4 Temperature Dependence of Drive Current 80
2.8.5 Derivative Analysis 84
References 86
Reading List 87
Problems 87
3 Mirrors and Resonators for Diode Lasers 91
3.1 Introduction 91
3.2 Scattering Theory 92
3.3 S and T Matrices for Some Common Elements 95
3.3.1 The Dielectric Interface 96
3.3.2 Transmission Line with No Discontinuities 98
3.3.3 Dielectric Segment and the Fabry–Perot Etalon 100
3.3.4 S-Parameter Computation Using Mason’s Rule 104
3.3.5 Fabry–Perot Laser 105
3.4 Three- and Four-Mirror Laser Cavities 107
3.4.1 Three-Mirror Lasers 107
3.4.2 Four-Mirror Lasers 111
3.5 Gratings 113
3.5.1 Introduction 113
3.5.2 Transmission Matrix Theory of Gratings 115
3.5.3 Effective Mirror Model for Gratings 121
3.6 Lasers Based on DBR Mirrors 123
3.6.1 Introduction 123
3.6.2 Threshold Gain and Power Out 124
3.6.3 Mode Selection in DBR-Based Lasers 127
3.6.4 VCSEL Design 128
3.6.5 In-Plane DBR Lasers and Tunability 135
3.6.6 Mode Suppression Ratio in DBR Laser 139
3.7 DFB Lasers 141
3.7.1 Introduction 141
3.7.2 Calculation of the Threshold Gains and Wavelengths 143
3.7.3 On Mode Suppression in DFB Lasers 149
References 151
Reading List 151
Problems 151
4 Gain and Current Relations 157
4.1 Introduction 157
4.2 Radiative Transitions 158
4.2.1 Basic Definitions and Fundamental Relationships 158
4.2.2 Fundamental Description of the Radiative Transition Rate 162
4.2.3 Transition Matrix Element 165
4.2.4 Reduced Density of States 170
4.2.5 Correspondence with Einstein’s Stimulated Rate Constant 174
4.3 Optical Gain 174
4.3.1 General Expression for Gain 174
4.3.2 Lineshape Broadening 181
4.3.3 General Features of the Gain Spectrum 185
4.3.4 Many-Body Effects 187
4.3.5 Polarization and Piezoelectricity 190
4.4 Spontaneous Emission 192
4.4.1 Single-Mode Spontaneous Emission Rate 192
4.4.2 Total Spontaneous Emission Rate 193
4.4.3 Spontaneous Emission Factor 198
4.4.4 Purcell Effect 198
4.5 Nonradiative Transitions 199
4.5.1 Defect and Impurity Recombination 199
4.5.2 Surface and Interface Recombination 202
4.5.3 Auger Recombination 211
4.6 Active Materials and Their Characteristics 218
4.6.1 Strained Materials and Doped Materials 218
4.6.2 Gain Spectra of Common Active Materials 220
4.6.3 Gain versus Carrier Density 223
4.6.4 Spontaneous Emission Spectra and Current versus Carrier Density 227
4.6.5 Gain versus Current Density 229
4.6.6 Experimental Gain Curves 233
4.6.7 Dependence on Well Width, Doping, and Temperature 234
References 238
Reading List 240
Problems 240
5 Dynamic Effects 247
5.1 Introduction 247
5.2 Review of Chapter 2 248
5.2.1 The Rate Equations 249
5.2.2 Steady-State Solutions 250
Case (i): Well Below Threshold 251
Case (ii): Above Threshold 252
Case (iii): Below and Above Threshold 253
5.2.3 Steady-State Multimode Solutions 255
5.3 Differential Analysis of the Rate Equations 257
5.3.1 Small-Signal Frequency Response 261
5.3.2 Small-Signal Transient Response 266
5.3.3 Small-Signal FM Response or Frequency Chirping 270
5.4 Large-Signal Analysis 276
5.4.1 Large-Signal Modulation: Numerical Analysis of the Multimode Rate Equations 277
5.4.2 Mode Locking 279
5.4.3 Turn-On Delay 283
5.4.4 Large-Signal Frequency Chirping 286
5.5 Relative Intensity Noise and Linewidth 288
5.5.1 General Definition of RIN and the Spectral Density Function 288
5.5.2 The Schawlow–Townes Linewidth 292
5.5.3 The Langevin Approach 294
5.5.4 Langevin Noise Spectral Densities and RIN 295
5.5.5 Frequency Noise 301
5.5.6 Linewidth 303
5.6 Carrier Transport Effects 308
5.7 Feedback Effects and Injection Locking 311
5.7.1 Optical Feedback Effects—Static Characteristics 311
5.7.2 Injection Locking—Static Characteristics 317
5.7.3 Injection and Feedback Dynamic Characteristics and Stability 320
5.7.4 Feedback Effects on Laser Linewidth 321
References 328
Reading List 329
Problems 329
6 Perturbation, Coupled-Mode Theory, Modal Excitations, and Applications 335
6.1 Introduction 335
6.2 Guided-Mode Power and Effective Width 336
6.3 Perturbation Theory 339
6.4 Coupled-Mode Theory: Two-Mode Coupling 342
6.4.1 Contradirectional Coupling: Gratings 342
6.4.2 DFB Lasers 353
6.4.3 Codirectional Coupling: Directional Couplers 356
6.4.4 Codirectional Coupler Filters and Electro-optic Switches 370
6.5 Modal Excitation 376
6.6 Two Mode Interference and Multimode Interference 378
6.7 Star Couplers 381
6.8 Photonic Multiplexers, Demultiplexers and Routers 382
6.8.1 Arrayed Waveguide Grating De/Multiplexers and Routers 383
6.8.2 Echelle Grating based De/Multiplexers and Routers 389
6.9 Conclusions 390
References 390
Reading List 391
Problems 391
7 Dielectric Waveguides 395
7.1 Introduction 395
7.2 Plane Waves Incident on a Planar Dielectric Boundary 396
7.3 Dielectric Waveguide Analysis Techniques 400
7.3.1 Standing Wave Technique 400
7.3.2 Transverse Resonance 403
7.3.3 WKB Method for Arbitrary Waveguide Profiles 410
7.3.4 2-D Effective Index Technique for Buried Rib Waveguides 418
7.3.5 Analysis of Curved Optical Waveguides using Conformal Mapping 421
7.3.6 Numerical Mode Solving Methods for Arbitrary Waveguide Profiles 424
7.4 Numerical Techniques for Analyzing PICs 427
7.4.1 Introduction 427
7.4.2 Implicit Finite-Difference Beam-Propagation Method 429
7.4.3 Calculation of Propagation Constants in a z -invariant Waveguide from a Beam Propagation Solution 432
7.4.4 Calculation of Eigenmode Profile from a Beam Propagation Solution 434
7.5 Goos–Hanchen Effect and Total Internal Reflection Components 434
7.5.1 Total Internal Reflection Mirrors 435
7.6 Losses in Dielectric Waveguides 437
7.6.1 Absorption Losses in Dielectric Waveguides 437
7.6.2 Scattering Losses in Dielectric Waveguides 438
7.6.3 Radiation Losses for Nominally Guided Modes 438
References 445
Reading List 446
Problems 446
8 Photonic Integrated Circuits 451
8.1 Introduction 451
8.2 Tunable, Widely Tunable, and Externally Modulated Lasers 452
8.2.1 Two- and Three-Section In-plane DBR Lasers 452
8.2.2 Widely Tunable Diode Lasers 458
8.2.3 Other Extended Tuning Range Diode Laser Implementations 463
8.2.4 Externally Modulated Lasers 474
8.2.5 Semiconductor Optical Amplifiers 481
8.2.6 Transmitter Arrays 484
8.3 Advanced PICs 484
8.3.1 Waveguide Photodetectors 485
8.3.2 Transceivers/Wavelength Converters and Triplexers 488
8.4 PICs for Coherent Optical Communications 491
8.4.1 Coherent Optical Communications Primer 492
8.4.2 Coherent Detection 495
8.4.3 Coherent Receiver Implementations 495
8.4.4 Vector Transmitters 498
References 499
Reading List 503
Problems 503
APPENDICES
1 Review of Elementary Solid-State Physics 509
A1.1 A Quantum Mechanics Primer 509
A1.1.1 Introduction 509
A1.1.2 Potential Wells and Bound Electrons 511
A1.2 Elements of Solid-State Physics 516
A1.2.1 Electrons in Crystals and Energy Bands 516
A1.2.2 Effective Mass 520
A1.2.3 Density of States Using a Free-Electron (Effective Mass) Theory 522
References 527
Reading List 527
2 Relationships between Fermi Energy and Carrier Density and Leakage 529
A2.1 General Relationships 529
A2.2 Approximations for Bulk Materials 532
A2.3 Carrier Leakage Over Heterobarriers 537
A2.4 Internal Quantum Efficiency 542
References 544
Reading List 544
3 Introduction to Optical Waveguiding in Simple Double-Heterostructures 545
A3.1 Introduction 545
A3.2 Three-Layer Slab Dielectric Waveguide 546
A3.2.1 Symmetric Slab Case 547
A3.2.2 General Asymmetric Slab Case 548
A3.2.3 Transverse Confinement Factor, x 550
A3.3 Effective Index Technique for Two-Dimensional Waveguides 551
A3.4 Far Fields 555
References 557
Reading List 557
4 Density of Optical Modes, Blackbody Radiation, and Spontaneous Emission Factor 559
A4.1 Optical Cavity Modes 559
A4.2 Blackbody Radiation 561
A4.3 Spontaneous Emission Factor, βsp 562
Reading List 563
5 Modal Gain, Modal Loss, and Confinement Factors 565
A5.1 Introduction 565
A5.2 Classical Definition of Modal Gain 566
A5.3 Modal Gain and Confinement Factors 568
A5.4 Internal Modal Loss 570
A5.5 More Exact Analysis of the Active/Passive Section Cavity 571
A5.5.1 Axial Confinement Factor 572
A5.5.2 Threshold Condition and Differential Efficiency 573
A5.6 Effects of Dispersion on Modal Gain 576
6 Einstein’s Approach to Gain and Spontaneous Emission 579
A6.1 Introduction 579
A6.2 Einstein A and B Coefficients 582
A6.3 Thermal Equilibrium 584
A6.4 Calculation of Gain 585
A6.5 Calculation of Spontaneous Emission Rate 589
Reading List 592
7 Periodic Structures and the Transmission Matrix 593
A7.1 Introduction 593
A7.2 Eigenvalues and Eigenvectors 593
A7.3 Application to Dielectric Stacks at the Bragg Condition 595
A7.4 Application to Dielectric Stacks Away from the Bragg Condition 597
A7.5 Correspondence with Approximate Techniques 600
A7.5.1 Fourier Limit 601
A7.5.2 Coupled-Mode Limit 602
A7.6 Generalized Reflectivity at the Bragg Condition 603
Reading List 605
Problems 605
8 Electronic States in Semiconductors 609
A8.1 Introduction 609
A8.2 General Description of Electronic States 609
A8.3 Bloch Functions and the Momentum Matrix Element 611
A8.4 Band Structure in Quantum Wells 615
A8.4.1 Conduction Band 615
A8.4.2 Valence Band 616
A8.4.3 Strained Quantum Wells 623
References 627
Reading List 628
9 Fermi’s Golden Rule 629
A9.1 Introduction 629
A9.2 Semiclassical Derivation of the Transition Rate 630
A9.2.1 Case I: The Matrix Element-Density of Final States Product is a Constant 632
A9.2.2 Case II: The Matrix Element-Density of Final States Product is a Delta Function 635
A9.2.3 Case III: The Matrix Element-Density of Final States Product is a Lorentzian 636
Reading List 637
Problems 638
10 Transition Matrix Element 639
A10.1 General Derivation 639
A10.2 Polarization-Dependent Effects 641
A10.3 Inclusion of Envelope Functions in Quantum Wells 645
Reading List 646
11 Strained Bandgaps 647
A11.1 General Definitions of Stress and Strain 647
A11.2 Relationship Between Strain and Bandgap 650
A11.3 Relationship Between Strain and Band Structure 655
References 656
12 Threshold Energy for Auger Processes 657
A12.1 CCCH Process 657
A12.2 CHHS and CHHL Processes 659
13 Langevin Noise 661
A13.1 Properties of Langevin Noise Sources 661
A13.1.1 Correlation Functions and Spectral Densities 661
A13.1.2 Evaluation of Langevin Noise Correlation Strengths 664
A13.2 Specific Langevin Noise Correlations 665
A13.2.1 Photon Density and Carrier Density Langevin Noise Correlations 665
A13.2.2 Photon Density and Output Power Langevin Noise Correlations 666
A13.2.3 Photon Density and Phase Langevin Noise Correlations 667
A13.3 Evaluation of Noise Spectral Densities 669
A13.3.1 Photon Noise Spectral Density 669
A13.3.2 Output Power Noise Spectral Density 670
A13.3.3 Carrier Noise Spectral Density 671
References 672
Problems 672
14 Derivation Details for Perturbation Formulas 675
Reading List 676
15 Multimode Interference 677
A15.1 Multimode Interference-Based Couplers 677
A15.2 Guided-Mode Propagation Analysis 678
A15.2.1 General Interference 679
A15.2.2 Restricted Multimode Interference 681
A15.3 MMI Physical Properties 682
A15.3.1 Fabrication 682
A15.3.2 Imaging Quality 682
A15.3.3 Inherent Loss and Optical Bandwidth 682
A15.3.4 Polarization Dependence 683
A15.3.5 Reflection Properties 683
Reference 683
16 The Electro-Optic Effect 685
References 692
Reading List 692
17 Solution of Finite Difference Problems 693
A17.1 Matrix Formalism 693
A17.2 One-Dimensional Dielectric Slab Example 695
Reading List 696
Index 697