Diode lasers and photonic integrated circuits

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Diode lasers and photonic integrated circuits

Larry A. Coldren, Scott W. Corzine, Milan L. Mašanović

（Wiley series in microwave and optical engineering / Kai Chang, editor）

Wiley, c2012

2nd ed

Available at  / 13 libraries

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Includes index

Description and Table of Contents

Description

Diode Lasers and Photonic Integrated Circuits, Second Edition provides a comprehensive treatment of optical communication technology, its principles and theory, treating students as well as experienced engineers to an in-depth exploration of this field. Diode lasers are still of significant importance in the areas of optical communication, storage, and sensing. Using the the same well received theoretical foundations of the first edition, the Second Edition now introduces timely updates in the technology and in focus of the book. After 15 years of development in the field, this book will offer brand new and updated material on GaN-based and quantum-dot lasers, photonic IC technology, detectors, modulators and SOAs, DVDs and storage, eye diagrams and BER concepts, and DFB lasers. Appendices will also be expanded to include quantum-dot issues and more on the relation between spontaneous emission and gain.

Table of Contents

Preface xvii 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: < i>, i , and g versus J 75 2.8.2 Internal Parameters for VCSELs: i and g versus J, < i>, and m 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, sp 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

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