Diode Lasers and Photonic Integrated Circuits

Transcription

1 Diode Lasers and Photonic Integrated Circuits L. A. COLDREN S. W. CORZINE University of California Santa Barbara, California A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC. NEW YORK / CHICHESTER / BRISBANE / TORONTO / SINGAPORE

2 Contents PREFACE ACKNOWLEDGEMENTS LIST OF FUNDAMENTAL CONSTANTS xvii xxi xxiii 1 Ingredients Introduction Energy Levels and Bands in Solids Spontaneous and Stimulated Transitions: the Creation of Light Transverse Confinement of Carriers and Photons in Diode Lasers: the Double Heterostructure Semiconductor Materials for Diode Lasers Epitaxial Growth Technology Lateral Confinement of Current, Carriers, and Photons for Practical Lasers 17 References 24 Reading List 25 Problems 25 2 A Phenomenological Approach to Diode Lasers Introduction Carrier Generation and Recombination in Active Regions Spontaneous Photon Generation and LEDs Photon Generation and Loss in Laser Cavities Threshold or Steady-State Gain in Lasers Threshold Current and Power Out vs. Current Basic PI Characteristics Relation of Laser Drive Current to Mirror Reflectivity and Cavity Length 44

3 VIII CONTENTS 2.7 Relaxation Resonance and Frequency Response Characterizing Real Diode Lasers Internal Parameters for In-Plane Lasers: a h r\ b and g vs. J Internal Parameters for VCSELs: r\ { and g vs. J, щ, and a. m Efficiency and Heat Flow Temperature Dependence of Drive Current Derivative Analysis 59 References 61 Reading List 61 Problems 62 3 Mirrors and Resonators for Diode Lasers Introduction Scattering Theory S and T Matrices for some Common Elements The Dielectric Interface Transmission Line with no Discontinuities Dielectric Segment and the Fabry-Perot Etalon Fabry-Perot Laser Three- and Four-Mirror Laser Cavities Three-Mirror Lasers Four-Mirror Lasers Gratings Introduction Transmission Matrix Theory Effective Mirror Model for Gratings DBR Lasers Introduction Threshold Gain and Power Out Mode Selection and Tunability DFB Lasers Mode Suppression Ratio in Single-Frequency Lasers 106 Reading List 108 Problems Gain and Current Relations Introduction Radiative Transitions Basic Definitions and Fundamental Relationships 112

4 CONTENTS ix Fundamental Description of the Radiative Transition Rate Transition Matrix Element Reduced Density of States Correspondence with Einstein's Stimulated Rate Constant Optical Gain General Expression for Gain Lineshape Broadening General Features of the Gain Spectrum Many-Body Effects Spontaneous Emission Single-Mode Spontaneous Emission Rate Total Spontaneous Emission Rate Spontaneous Emission Factor Nonradiative Transitions Defect and Impurity Recombination Surface and Interface Recombination Auger Recombination Active Materials and their Characteristics Strained Materials and Doped Materials Gain Spectra of Common Active Materials Gain vs. Carrier Density Spontaneous Emission Spectra and Current vs. Carrier Density Gain vs. Current Density Experimental Gain Curves Dependence on Well Width, Doping, and Temperature 174 References 178 Reading List 179 Problems Dynamic Effects Introduction Review of Chapter The Rate Equations Steady-State Solutions Steady-State Multimode Solutions Differential Analysis of the Rate Equations Small-Signal Frequency Response Small-Signal Transient Response Small-Signal FM Response or Frequency Chirping 207

5 X CONTENTS 5.4 Large-Signal Analysis Large-Signal Modulation: Numerical Analysis of the Multimode Rate Equations Turn-On Delay Large-Signal Frequency Chirping Relative Intensity Noise and Linewidth General Definition of RIN and the Spectral Density Function The Schawlow-Townes Linewidth The Langevin Approach Langevin Noise Spectral Densities and RIN Frequency Noise Linewidth Carrier Transport Effects Feedback Effects Static Characteristics Dynamic Characteristics and Linewidth 252 References 257 Reading List 258 Problems Perturbation and Coupled-Mode Theory Introduction Perturbation Theory Uniform Dielectric Perturbations Quantum-Well Laser Modal Gain and Index Perturbation: an Example Coupled-Mode Theory: Two-Mode Coupling Contradirectional Coupling: Gratings DFB Lasers Codirectional Coupling: Directional Couplers The Four-Port Directional Coupler Codirectional Coupler Filters and Electro-optic Switches Modal Excitation Conclusions 298 References 299 Reading List 299 Problems Dielectric Waveguides Introduction Plane Waves Incident on a Planar Dielectric Boundary 303

6 CONTENTS XI 7.3 Dielectric Waveguide Analysis Techniques Standing Wave Technique Transverse Resonance Cutoff and "Leaky" or "Quasi Modes" Radiation Modes Multilayer Waveguides WKB Method for Arbitrary Waveguide Profiles Review of Effective Index Technique for Channel Waveguides Numerical Solutions to the Wave Equation Guided-Mode Power and Effective Width Radiation Losses for Nominally Guided Modes 331 References 338 Reading List 338 Problems Photonic Integrated Circuits Introduction Tunable Lasers and Laser-Modulators with In-Line Grating Reflectors Two- and Three-Section DBR Lasers Two-Section Example Problem Extended Tuning Range Four-Section DBR Laser-Modulator or Amplifier Laser-Modulator Example Problem PICs using Directional Couplers for Output Coupling and Signal Combining Ring Laser with a Directional Coupler Output Tap Integrated Heterodyne Receiver PICs using Codirectionally Coupled Filters The Grating-Assisted Codirectionally Coupled Filter and Related Devices Numerical Techniques for Analyzing PICs Introduction Implicit Finite-Difference Beam-Propagation Method Calculation of Propagation Constants in a z-invariant Waveguide from a Beam Propagation Solution Calculation of Eigenmode Profile from a Beam Propagation Solution 387 References 387 Reading List 388 Problems 388

7 xii CONTENTS APPENDICES 1 Review of Elementary Solid-State Physics 392 A 1.1 A Quantum Mechanics Primer 392 A Introduction 392 A Potential Wells and Bound Electrons 393 A 1.2 Elements of Solid-State Physics 399 A Electrons in Crystals and Energy Bands 399 A Effective Mass 403 A Density of States using a Free-Electron (Effective Mass) Theory 405 References 411 Reading List Relationships between Fermi Energy and Carrier Density and Leakage 412 A2.1 General Relationships 412 A2.2 Approximations for Bulk Materials 415 A2.3 Carrier Leakage over Heterobarriers 421 A2.4 Internal Quantum Efficiency 425 References 427 Reading List Introduction to Optical Waveguiding in Simple Double- Heterostructures 428 A3.1 Introduction 428 A3.2 Three-Layer Slab Dielectric Waveguide 429 A3.2.1 Symmetric Slab Case 430 A3.2.2 General Asymmetric Slab Case 431 A3.2.3 Transverse Confinement Factor, Г х 432 АЗ.З Effective Index Technique for Two-Dimensional Waveguides 433 A3.4 Far Fields 438 Reference 440 Reading List Density of Optical Modes, Blackbody Radiation, and Spontaneous Emission Factor 441 A4.1 Optical Cavity Modes 441 A4.2 Blackbody Radiation 443 A4.3 Spontaneous Emission Factor, ß sp AAA Reading List 445

8 CONTENTS xiii 5 Modal Gain, Modal Loss, and Confinement Factors 446 A5.1 Introduction 446 A5.2 Classical Definition of Modal Gain 447 A5.3 Modal Gain and Confinement Factors 449 A5.4 Internal Modal Loss 451 A5.5 More Exact Analysis of the Active/Passive Section Cavity 452 A5.5.1 Axial Confinement Factor 453 A5.5.2 Threshold Condition and Differential Efficiency 455 A5.6 Effects of Dispersion on Modal Gain Einstein's Approach to Gain and Spontaneous Emission 459 A6.1 Introduction 459 A6.2 Einstein A and В Coefficients 462 A6.3 Thermal Equilibrium 464 A6.4 Calculation of Gain 465 A6.5 Calculation of Spontaneous Emission Rate 469 Reading List Periodic Structures and the Transmission Matrix 473 A7.1 Introduction 473 A7.2 Eigenvalues and Eigenvectors 473 A7.3 Application to Dielectric Stacks at the Bragg Condition 475 A7.4 Application to Dielectric Stacks away from the Bragg Condition 477 A7.5 Correspondence with Approximate Techniques 481 A7.5.1 Fourier Limit 481 A7.5.2 Coupled-Mode Limit 482 A7.6 Generalized Reflectivity at the Bragg Condition 484 Reading List 485 Problems Electronic States in Semiconductors 488 A8.1 Introduction 488 A8.2 General Description of Electronic States 488 A8.3 Bloch Functions and the Momentum Matrix Element 490 A8.4 Band Structure in Quantum Wells 494 A8.4.1 Conduction Band 494 A8.4.2 Valance Band 495 A8.4.3 Strained Quantum Wells 502 References 507 Reading List 507

9 xiv CONTENTS 9 Fermi's Golden Rule 508 A9.1 Introduction 508 A9.2 Semiclassical Derivation of the Transition Rate 508 A9.2.1 Case I: the Matrix Element-Density of Final States Product is a Constant 511 A9.2.2 Case II: the Matrix Element-Density of Final States Product is a Delta Function 514 A9.2.3 Case III: the Matrix Element-Density of Final States Product is a Lorentzian 515 Reading List 516 Problems Transition Matrix Element 518 A 10.1 General Derivation 518 A 10.2 Polarization-Dependent Effects 521 A10.3 Inclusion of Envelope Functions in Quantum Wells 524 Reading List Strained Bandgaps 527 Al 1.1 General Definitions of Stress and Strain 527 Al 1.2 Relationship between Strain and Bandgap 530 Al 1.3 Relationship between Strain and Band Structure 535 References Threshold Energy for Auger Processes 537 A12.1 CCCH Process 537 A12.2 CHHS and CHHL Processes Langevin Noise 540 Al3.1 Properties of Langevin Noise Sources 540 A Correlation Functions and Spectral Densities 540 A Evaluation of Langevin Noise Correlation Strengths 542 A 13.2 Specific Langevin Noise Correlations 544 A Photon Density and Carrier Density Langevin Noise Correlations 544 Al3.2.2 Photon Density and Output Power Langevin Noise Correlations 545 A Photon Density and Phase Langevin Noise Correlations 547

10 CONTENTS XV A 13.3 Evaluation of Noise Spectral Densities 548 A Photon Noise Spectral Density 548 A Output Power Noise Spectral Density 549 A Carrier Noise Spectral Density 550 References 551 Problems Derivation Details for Perturbation Formulas 553 Reading List The Electro-Optic Effect 555 References 562 Reading List Solution of Finite Difference Problems 563 A 16.1 Matrix Formalism 563 A 16.2 One-Dimensional Dielectric Slab Example 565 Reading List Optimizing Laser Cavity Designs 568 A 17.1 General Approach 568 A17.2 Specific Cases 570 A Case Al: Optimize L a for a Fixed L (a ia = <x ip ) 570 A Case A2: Optimize L a for a Fixed L (a ia ф a ip ) 571 A Case Bl: Optimize L a for a Fixed L p (L p = 0) 572 A Case B2: Optimize L a for a Fixed L p (L p Ф 0) 572 A Case C: Optimize L a for a Fixed L p /L a 573 A Case D: Optimize N w for Fixed L a and L p (In-Plane Laser) 574 A Case E: Optimize N w for Fixed L (VCSEL) 575 A Summary of Cases A through E? 576 A 17.3 Optimum Operating Point on the Gain Curve 577 A 17.4 Shifted Optimum Operating Points on the Gain Curve 579 A17.5 Other Design Considerations 580 A High-Speed Designs 580 A Heating Effects 581 Reading List 582 Index 583