Diode Lasers and Photonic Integrated Circuits

Larry A. Coldren is the Fred Kavli Professor of Optoelectronics and Sensors at the University of California, Santa Barbara. He has authored or coauthored over a thousand journal and conference papers, seven book chapters, and a textbook, and has been issued sixty-three patents. He is a Fellow of the IEEE, OSA, and IEE, the recipient of the 2004 John Tyndall and 2009 Aron Kressel Awards, and a member of the National Academy of Engineering. 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.

• Preface xviiAcknowledgments xxiList of Fundamental Constants xxiii1 Ingredients 11.1 Introduction 11.2 Energy Levels and Bands in Solids 51.3 Spontaneous and Stimulated Transitions: The Creation of Light 71.4 Transverse Confinement of Carriers and Photons in Diode Lasers: The Double Heterostructure 101.5 Semiconductor Materials for Diode Lasers 131.6 Epitaxial Growth Technology 201.7 Lateral Confinement of Current, Carriers, and Photons for Practical Lasers 241.8 Practical Laser Examples 31References 39Reading List 40Problems 402 A Phenomenological Approach to Diode Lasers 452.1 Introduction 452.2 Carrier Generation and Recombination in Active Regions 462.3 Spontaneous Photon Generation and LEDs 492.4 Photon Generation and Loss in Laser Cavities 522.5 Threshold or Steady-State Gain in Lasers 552.6 Threshold Current and Power Out Versus Current 602.6.1 Basic P–I Characteristics 602.6.2 Gain Models and Their Use in Designing Lasers 642.7 Relaxation Resonance and Frequency Response 702.8 Characterizing Real Diode Lasers 742.8.1 Internal Parameters for In-Plane Lasers: ‹αi›, ηi , and g versus J 752.8.2 Internal Parameters for VCSELs: ηi and g versus J, ‹αi›, and αm 782.8.3 Efficiency and Heat Flow 792.8.4 Temperature Dependence of Drive Current 802.8.5 Derivative Analysis 84References 86Reading List 87Problems 873 Mirrors and Resonators for Diode Lasers 913.1 Introduction 913.2 Scattering Theory 923.3 S and T Matrices for Some Common Elements 953.3.1 The Dielectric Interface 963.3.2 Transmission Line with No Discontinuities 983.3.3 Dielectric Segment and the Fabry–Perot Etalon 1003.3.4 S-Parameter Computation Using Mason’s Rule 1043.3.5 Fabry–Perot Laser 1053.4 Three- and Four-Mirror Laser Cavities 1073.4.1 Three-Mirror Lasers 1073.4.2 Four-Mirror Lasers 1113.5 Gratings 1133.5.1 Introduction 1133.5.2 Transmission Matrix Theory of Gratings 1153.5.3 Effective Mirror Model for Gratings 1213.6 Lasers Based on DBR Mirrors 1233.6.1 Introduction 1233.6.2 Threshold Gain and Power Out 1243.6.3 Mode Selection in DBR-Based Lasers 1273.6.4 VCSEL Design 1283.6.5 In-Plane DBR Lasers and Tunability 1353.6.6 Mode Suppression Ratio in DBR Laser 1393.7 DFB Lasers 1413.7.1 Introduction 1413.7.2 Calculation of the Threshold Gains and Wavelengths 1433.7.3 On Mode Suppression in DFB Lasers 149References 151Reading List 151Problems 1514 Gain and Current Relations 1574.1 Introduction 1574.2 Radiative Transitions 1584.2.1 Basic Definitions and Fundamental Relationships 1584.2.2 Fundamental Description of the Radiative Transition Rate 1624.2.3 Transition Matrix Element 1654.2.4 Reduced Density of States 1704.2.5 Correspondence with Einstein’s Stimulated Rate Constant 1744.3 Optical Gain 1744.3.1 General Expression for Gain 1744.3.2 Lineshape Broadening 1814.3.3 General Features of the Gain Spectrum 1854.3.4 Many-Body Effects 1874.3.5 Polarization and Piezoelectricity 1904.4 Spontaneous Emission 1924.4.1 Single-Mode Spontaneous Emission Rate 1924.4.2 Total Spontaneous Emission Rate 1934.4.3 Spontaneous Emission Factor 1984.4.4 Purcell Effect 1984.5 Nonradiative Transitions 1994.5.1 Defect and Impurity Recombination 1994.5.2 Surface and Interface Recombination 2024.5.3 Auger Recombination 2114.6 Active Materials and Their Characteristics 2184.6.1 Strained Materials and Doped Materials 2184.6.2 Gain Spectra of Common Active Materials 2204.6.3 Gain versus Carrier Density 2234.6.4 Spontaneous Emission Spectra and Current versus Carrier Density 2274.6.5 Gain versus Current Density 2294.6.6 Experimental Gain Curves 2334.6.7 Dependence on Well Width, Doping, and Temperature 234References 238Reading List 240Problems 2405 Dynamic Effects 2475.1 Introduction 2475.2 Review of Chapter 2 2485.2.1 The Rate Equations 2495.2.2 Steady-State Solutions 250Case (i): Well Below Threshold 251Case (ii): Above Threshold 252Case (iii): Below and Above Threshold 2535.2.3 Steady-State Multimode Solutions 2555.3 Differential Analysis of the Rate Equations 2575.3.1 Small-Signal Frequency Response 2615.3.2 Small-Signal Transient Response 2665.3.3 Small-Signal FM Response or Frequency Chirping 2705.4 Large-Signal Analysis 2765.4.1 Large-Signal Modulation: Numerical Analysis of the Multimode Rate Equations 2775.4.2 Mode Locking 2795.4.3 Turn-On Delay 2835.4.4 Large-Signal Frequency Chirping 2865.5 Relative Intensity Noise and Linewidth 2885.5.1 General Definition of RIN and the Spectral Density Function 2885.5.2 The Schawlow–Townes Linewidth 2925.5.3 The Langevin Approach 2945.5.4 Langevin Noise Spectral Densities and RIN 2955.5.5 Frequency Noise 3015.5.6 Linewidth 3035.6 Carrier Transport Effects 3085.7 Feedback Effects and Injection Locking 3115.7.1 Optical Feedback Effects—Static Characteristics 3115.7.2 Injection Locking—Static Characteristics 3175.7.3 Injection and Feedback Dynamic Characteristics and Stability 3205.7.4 Feedback Effects on Laser Linewidth 321References 328Reading List 329Problems 3296 Perturbation, Coupled-Mode Theory, Modal Excitations, and Applications 3356.1 Introduction 3356.2 Guided-Mode Power and Effective Width 3366.3 Perturbation Theory 3396.4 Coupled-Mode Theory: Two-Mode Coupling 3426.4.1 Contradirectional Coupling: Gratings 3426.4.2 DFB Lasers 3536.4.3 Codirectional Coupling: Directional Couplers 3566.4.4 Codirectional Coupler Filters and Electro-optic Switches 3706.5 Modal Excitation 3766.6 Two Mode Interference and Multimode Interference 3786.7 Star Couplers 3816.8 Photonic Multiplexers, Demultiplexers and Routers 3826.8.1 Arrayed Waveguide Grating De/Multiplexers and Routers 3836.8.2 Echelle Grating based De/Multiplexers and Routers 3896.9 Conclusions 390References 390Reading List 391Problems 3917 Dielectric Waveguides 3957.1 Introduction 3957.2 Plane Waves Incident on a Planar Dielectric Boundary 3967.3 Dielectric Waveguide Analysis Techniques 4007.3.1 Standing Wave Technique 4007.3.2 Transverse Resonance 4037.3.3 WKB Method for Arbitrary Waveguide Profiles 4107.3.4 2-D Effective Index Technique for Buried Rib Waveguides 4187.3.5 Analysis of Curved Optical Waveguides using Conformal Mapping 4217.3.6 Numerical Mode Solving Methods for Arbitrary Waveguide Profiles 4247.4 Numerical Techniques for Analyzing PICs 4277.4.1 Introduction 4277.4.2 Implicit Finite-Difference Beam-Propagation Method 4297.4.3 Calculation of Propagation Constants in a z–invariant Waveguide from a Beam Propagation Solution 4327.4.4 Calculation of Eigenmode Profile from a Beam Propagation Solution 4347.5 Goos–Hanchen Effect and Total Internal Reflection Components 4347.5.1 Total Internal Reflection Mirrors 4357.6 Losses in Dielectric Waveguides 4377.6.1 Absorption Losses in Dielectric Waveguides 4377.6.2 Scattering Losses in Dielectric Waveguides 4387.6.3 Radiation Losses for Nominally Guided Modes 438References 445Reading List 446Problems 4468 Photonic Integrated Circuits 4518.1 Introduction 4518.2 Tunable, Widely Tunable, and Externally Modulated Lasers 4528.2.1 Two- and Three-Section In-plane DBR Lasers 4528.2.2 Widely Tunable Diode Lasers 4588.2.3 Other Extended Tuning Range Diode Laser Implementations 4638.2.4 Externally Modulated Lasers 4748.2.5 Semiconductor Optical Amplifiers 4818.2.6 Transmitter Arrays 4848.3 Advanced PICs 4848.3.1 Waveguide Photodetectors 4858.3.2 Transceivers/Wavelength Converters and Triplexers 4888.4 PICs for Coherent Optical Communications 4918.4.1 Coherent Optical Communications Primer 4928.4.2 Coherent Detection 4958.4.3 Coherent Receiver Implementations 4958.4.4 Vector Transmitters 498References 499Reading List 503Problems 503Appendices1 Review of Elementary Solid-State Physics 509A1.1 A Quantum Mechanics Primer 509A1.1.1 Introduction 509A1.1.2 Potential Wells and Bound Electrons 511A1.2 Elements of Solid-State Physics 516A1.2.1 Electrons in Crystals and Energy Bands 516A1.2.2 Effective Mass 520A1.2.3 Density of States Using a Free-Electron (Effective Mass) Theory 522References 527Reading List 5272 Relationships between Fermi Energy and Carrier Density and Leakage 529A2.1 General Relationships 529A2.2 Approximations for Bulk Materials 532A2.3 Carrier Leakage Over Heterobarriers 537A2.4 Internal Quantum Efficiency 542References 544Reading List 5443 Introduction to Optical Waveguiding in Simple Double-Heterostructures 545A3.1 Introduction 545A3.2 Three-Layer Slab Dielectric Waveguide 546A3.2.1 Symmetric Slab Case 547A3.2.2 General Asymmetric Slab Case 548A3.2.3 Transverse Confinement Factor, Γx 550A3.3 Effective Index Technique for Two-Dimensional Waveguides 551A3.4 Far Fields 555References 557Reading List 5574 Density of Optical Modes, Blackbody Radiation, and Spontaneous Emission Factor 559A4.1 Optical Cavity Modes 559A4.2 Blackbody Radiation 561A4.3 Spontaneous Emission Factor, βsp 562Reading List 5635 Modal Gain, Modal Loss, and Confinement Factors 565A5.1 Introduction 565A5.2 Classical Definition of Modal Gain 566A5.3 Modal Gain and Confinement Factors 568A5.4 Internal Modal Loss 570A5.5 More Exact Analysis of the Active/Passive Section Cavity 571A5.5.1 Axial Confinement Factor 572A5.5.2 Threshold Condition and Differential Efficiency 573A5.6 Effects of Dispersion on Modal Gain 5766 Einstein’s Approach to Gain and Spontaneous Emission 579A6.1 Introduction 579A6.2 Einstein A and B Coefficients 582A6.3 Thermal Equilibrium 584A6.4 Calculation of Gain 585A6.5 Calculation of Spontaneous Emission Rate 589Reading List 5927 Periodic Structures and the Transmission Matrix 593A7.1 Introduction 593A7.2 Eigenvalues and Eigenvectors 593A7.3 Application to Dielectric Stacks at the Bragg Condition 595A7.4 Application to Dielectric Stacks Away from the Bragg Condition 597A7.5 Correspondence with Approximate Techniques 600A7.5.1 Fourier Limit 601A7.5.2 Coupled-Mode Limit 602A7.6 Generalized Reflectivity at the Bragg Condition 603Reading List 605Problems 6058 Electronic States in Semiconductors 609A8.1 Introduction 609A8.2 General Description of Electronic States 609A8.3 Bloch Functions and the Momentum Matrix Element 611A8.4 Band Structure in Quantum Wells 615A8.4.1 Conduction Band 615A8.4.2 Valence Band 616A8.4.3 Strained Quantum Wells 623References 627Reading List 6289 Fermi’s Golden Rule 629A9.1 Introduction 629A9.2 Semiclassical Derivation of the Transition Rate 630A9.2.1 Case I: The Matrix Element-Density of Final States Product is a Constant 632A9.2.2 Case II: The Matrix Element-Density of Final States Product is a Delta Function 635A9.2.3 Case III: The Matrix Element-Density of Final States Product is a Lorentzian 636Reading List 637Problems 63810 Transition Matrix Element 639A10.1 General Derivation 639A10.2 Polarization-Dependent Effects 641A10.3 Inclusion of Envelope Functions in Quantum Wells 645Reading List 64611 Strained Bandgaps 647A11.1 General Definitions of Stress and Strain 647A11.2 Relationship Between Strain and Bandgap 650A11.3 Relationship Between Strain and Band Structure 655References 65612 Threshold Energy for Auger Processes 657A12.1 CCCH Process 657A12.2 CHHS and CHHL Processes 65913 Langevin Noise 661A13.1 Properties of Langevin Noise Sources 661A13.1.1 Correlation Functions and Spectral Densities 661A13.1.2 Evaluation of Langevin Noise Correlation Strengths 664A13.2 Specific Langevin Noise Correlations 665A13.2.1 Photon Density and Carrier Density Langevin Noise Correlations 665A13.2.2 Photon Density and Output Power Langevin Noise Correlations 666A13.2.3 Photon Density and Phase Langevin Noise Correlations 667A13.3 Evaluation of Noise Spectral Densities 669A13.3.1 Photon Noise Spectral Density 669A13.3.2 Output Power Noise Spectral Density 670A13.3.3 Carrier Noise Spectral Density 671References 672Problems 67214 Derivation Details for Perturbation Formulas 675Reading List 67615 Multimode Interference 677A15.1 Multimode Interference-Based Couplers 677A15.2 Guided-Mode Propagation Analysis 678A15.2.1 General Interference 679A15.2.2 Restricted Multimode Interference 681A15.3 MMI Physical Properties 682A15.3.1 Fabrication 682A15.3.2 Imaging Quality 682A15.3.3 Inherent Loss and Optical Bandwidth 682A15.3.4 Polarization Dependence 683A15.3.5 Reflection Properties 683Reference 68316 The Electro-Optic Effect 685References 692Reading List 69217 Solution of Finite Difference Problems 693A17.1 Matrix Formalism 693A17.2 One-Dimensional Dielectric Slab Example 695Reading List 696Index 697

“The book is very clearly written and has many demonstrated examples. It is a valuable resource for anyone who wants to learn about basic optoelectronic devices with every-day applications.”  (Optics and Photonics News, 4 January 2013)