# Diode Lasers and Photonic Integrated Circuits

Wiley Series in Microwave and Optical Engineering (Series Nr. 1)

2. Edition April 2012

752 Pages, Hardcover*Professional Book*

**978-0-470-48412-8**

### Short Description

Optical communication technology, like diode lasers used in optical storage devices, is vital to the optoelectronics industry. Since the first edition, Diode Lasers and Photonic Integrated Circuits presents up-to-date information on optical communication technology principles and theories. By expanding the appendices, at least twenty-five percent of new information is added on topics like quantum-dot issues. As the only book on diode lasers, this resource, which includes examples, end-of-the-chapter homework problems, and a solution manual, is essential for students and engineers in comprehending optical communication technology.

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.

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

2.7 Relaxation Resonance and Frequency Response 70

2.8 Characterizing Real Diode Lasers 74

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

3.4 Three- and Four-Mirror Laser Cavities 107

3.5 Gratings 113

3.6 Lasers Based on DBR Mirrors 123

3.7 DFB Lasers 141

References 151

Reading List 151

Problems 151

4 Gain and Current Relations 157

4.1 Introduction 157

4.2 Radiative Transitions 158

4.3 Optical Gain 174

4.4 Spontaneous Emission 192

4.5 Nonradiative Transitions 199

4.6 Active Materials and Their Characteristics 218

References 238

Reading List 240

Problems 240

5 Dynamic Effects 247

5.1 Introduction 247

5.2 Review of Chapter 2 248

Case (i): Well Below Threshold 251

Case (ii): Above Threshold 252

Case (iii): Below and Above Threshold 253

5.3 Differential Analysis of the Rate Equations 257

5.4 Large-Signal Analysis 276

5.5 Relative Intensity Noise and Linewidth 288

5.6 Carrier Transport Effects 308

5.7 Feedback Effects and Injection Locking 311

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

6.5 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

6.9 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

7.4 Numerical Techniques for Analyzing PICs 427

7.5 Goos-Hanchen Effect and Total Internal Reflection Components 434

7.6 Losses in Dielectric Waveguides 437

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

8.3 Advanced PICs 484

8.4 PICs for Coherent Optical Communications 491

References 499

Reading List 503

Problems 503

APPENDICES

1 Review of Elementary Solid-State Physics 509

A1.1 A Quantum Mechanics Primer 509

A1.2 Elements of Solid-State Physics 516

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

A3.3 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, ²sp 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

A5.6 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

A7.6 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

References 627

Reading List 628

9 Fermi's Golden Rule 629

A9.1 Introduction 629

A9.2 Semiclassical Derivation of the Transition Rate 630

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

A13.2 Specific Langevin Noise Correlations 665

A13.3 Evaluation of Noise Spectral Densities 669

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

A15.3 MMI Physical Properties 682

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

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.