Nonlinear Optics

by Robert W. Boyd

Overview

Nonlinear Optics, Fourth Edition, is a tutorial-based introduction to nonlinear optics that is suitable for graduate-level courses in electrical and electronic engineering, and for electronic and computer engineering departments, physics departments, and as a reference for industry practitioners of nonlinear optics. It will appeal to a wide audience of optics, physics and electrical and electronic engineering students, as well as practitioners in related fields, such as materials science and chemistry.

Product Details

ISBN-13:	9780128110027
Publisher:	Elsevier Science
Publication date:	03/31/2020
Edition description:	4th ed.
Pages:	634
Product dimensions:	7.30(w) x 9.20(h) x 1.20(d)

About the Author

Robert W. Boyd was born in Buffalo, New York. He received the B.S. degree in physics from the Massachusetts Institute of Technology and the Ph.D. degree in physics in 1977 from the University of California at Berkeley. His Ph.D. thesis was supervised by Professor Charles H. Townes and involved the use of nonlinear optical techniques in infrared detection for astronomy. Professor Boyd joined the faculty of the Institute of Optics of the University of Rochester in 1977 and since 1987 has held the position of Professor of Optics. Since July 2001 he has also held the position of the M. Parker Givens Professor of Optics. His research interests include studies of nonlinear optical interactions, studies of the nonlinear optical properties of materials, the development of photonic devices including photonic biosensors, and studies of the quantum statistical properties of nonlinear optical interactions. Professor Boyd has written two books, co-edited two anthologies, published over 200 research papers, and has been awarded five patents. He is a fellow of the Optical Society of America and of the American Physical Society and is the past chair of the Division of Laser Science of the American Physical Society.

Table of Contents

Preface to the Fourth Edition xv

Preface to the Third Edition xvii

Preface to the Second Edition xix

Preface to the First Edition xxi

Chapter 1 The Nonlinear Optical Susceptibility 1

1.1 Introduction to Nonlinear Optics 1

1.2 Descriptions of Nonlinear Optical Processes 4

1.2.1 Second-Harmonic Generation 4

1.2.2 Sum- and Difference-Frequency Generation 6

1.2.3 Sum-Frequency Generation 7

1.2.4 Difference-Frequency Generation 8

1.2.5 Optical Parametric Oscillation 9

1.2.6 Third-Order Nonlinear Optical Processes 10

1.2.7 Third-Harmonic Generation 10

1.2.8 Intensity-Dependent Refractive Index 11

1.2.9 Third-Order Interactions (General Case) 11

1.2.10 Parametric versus Nonparametric Processes 13

1.2.11 Saturable Absorption 14

1.2.12 Two-Photon Absorption 15

1.2.13 Stimulated Raman Scattering 16

1.3 Formal Definition of the Nonlinear Susceptibility 16

1.4 Nonlinear Susceptibility of a Classical Anharmonic Oscillator 20

1.4.1 Noncentrosymmetric Media 21

1.4.2 Miller's Rule 26

1.4.3 Centrosymmetric Media 27

1.5 Properties of the Nonlinear Susceptibility 32

1.5.1 Reality of the Fields 33

1.5.2 Intrinsic Permutation Symmetry 34

1.5.3 Symmetries for Lossless Media 34

1.5.4 Field Energy Density for a Nonlinear Medium 35

1.5.5 Kleinman's Symmetry 37

1.5.6 Contracted Notation 38

1.5.7 Effective Value of d (d_eff) 40

1.5.8 Spatial Symmetry of the Nonlinear Medium 41

1.5.9 Influence of Spatial Symmetry on the Linear Optical Properties of a Material Medium 41

1.5.10 Influence of Inversion Symmetry on the Second-Order Nonlinear Response 42

1.5.11 Influence of Spatial Symmetry on the Second-Order Susceptibility 44

1.5.12 Number of Independent Elements of X²_ijk(ω3, ω2, ω1) 45

1.5.13 Distinction between Noncentrosymmetric and Cubic Crystal Classes 45

1.5.14 Distinction between Noncentrosymmetric and Polar Crystal Classes 50

1.5.15 Influence of Spatial Symmetry on the Third-Order Nonlinear Response 50

1.6 Time-Domain Description of Optical Nonlinearities 50

1.7 Kramers-Kronig Relations in Linear and Nonlinear Optics 56

1.7.1 Kramers-Kronig Relations in Linear Optics 56

1.7.2 Kramers-Kronig Relations in Nonlinear Optics 59

Problems 61

References 63

Chapter 2 Wave-Equation Description of Nonlinear Optical interactions 65

2.1 The Wave Equation for Nonlinear Optical Media 65

2.2 The Coupled-Wave Equations for Sum-Frequency Generation 70

2.2.1 Phase-Matching Considerations 72

2.3 Phase Matching 74

2.4 Quasi-Phase-Matching (QPM) 79

2.5 The Manley-Rowe Relations 83

2.6 Sum-Frequency Generation 86

2.7 Second-Harmonic Generation 91

2.7.1 Applications of Second-Harmonic Generation 98

2.8 Difference-Frequency Generation and Parametric Amplification 100

2.9 Optical Parametric Oscillators 102

2.9.1 Influence of Cavity Mode Structure on OPO Tuning 105

2.10 Nonlinear Optical Interactions with Focused Gaussian Beams 109

2.10.1 Paraxial Wave Equation 109

2.10.2 Gaussian Beams 110

2.10.3 Harmonic Generation Using Focused Gaussian Beams 112

2.11 Nonlinear Optics at an Interface 116

2.12 Advanced Phase Matching Methods 121

Problems 130

References 134

Chapter 3 Quantum-Mechanical Theory of the Nonlinear Optical Susceptibility 137

3.1 Introduction 137

3.2 Schrödinger Equation Calculation of the Nonlinear Optical Susceptibility 138

3.2.1 Energy Eigenstates 139

3.2.2 Perturbation Solution to Schrödinger's Equation 140

3.2.3 Linear Susceptibility 142

3.2.4 Second-Order Susceptibility 144

3.2.5 Third-Order Susceptibility 146

3.2.6 Third-Harmonic Generation in Alkali Metal Vapors 148

3.3 Density Matrix Formulation of Quantum Mechanics 151

3.3.1 Example: Two-Level Atom 158

3.4 Perturbation Solution of the Density Matrix Equation of Motion 159

3.5 Density Matrix Calculation of the Linear Susceptibility 161

3.5.1 Linear Response Theory 164

3.6 Density Matrix Calculation of the Second-Order Susceptibility 169

3.6.1 χ⁽²⁾ in the Limit of Nonresonant Excitation 178

3.7 Density Matrix Calculation of the Third-Order Susceptibility 179

3.8 Electromagnetically Induced Transparency 184

3.9 Local-Field Effects in the Nonlinear Optics 192

3.9.1 Local-Field Effects in Linear Optics 192

3.9.2 Local-Field Effects in Nonlinear Optics 194

Problems 198

References 201

Chapter 4 The Intensity-Dependent Refractive Index 203

4.1 Descriptions of the Intensity-Dependent Refractive Index 203

4.2 Tensor Nature of the Third-Order Susceptibility 209

4.2.1 Propagation through Isotropic Nonlinear Media 213

4.3 Nonresonant Electronic Nonlinearities 217

4.3.1 Classical, Anharmonic Oscillator Model of Electronic Nonlinearities 218

4.3.2 Quantum-Mechanical Model of Nonresonant Electronic Nonlinearities 218

4.3.3 χ⁽³⁾ in the Low-Frequency Limit 222

4.4 Nonlinearities Due to Molecular Orientation 223

4.4.1 Tensor Properties of χ⁽³⁾ for the Molecular Orientation Effect 229

4.5 Thermal Nonlinear Optical Effects 231

4.5.1 Thermal Nonlinearities with Continuous-Wave Laser Beams 233

4.5.2 Thermal Nonlinearities with Pulsed Laser Beams 234

4.6 Semiconductor Nonlinearities 235

4.6.1 Nonlinearities Resulting from Band-to-Band Transitions 235

4.6.2 Nonlinearities Involving Virtual Transitions 241

4.7 Concluding Remarks 243

Problems 245

References 247

Chapter 5 Molecular Origin of the Nonlinear Optical Response 249

5.1 Nonlinear Susceptibilities Calculated Using Time-Independent Perturbation Theory 249

5.1.1 Hydrogen Atom 250

5.1.2 General Expression for the Nonlinear Susceptibility in the Quasi-Static Limit 251

5.2 Semiempirical Models of the Nonlinear Optical Susceptibility 255

Model of Boling, Glass, and Owyoung 256

5.3 Nonlinear Optical Properties of Conjugated Polymers 257

5.4 Bond-Charge Model of Nonlinear Optical Properties 259

5.5 Nonlinear Optics of Chiral Media 264

5.6 Nonlinear Optics of Liquid Crystals 266

Problems 269

References 269

Chapter 6 Nonlinear Optics in the Two-Level Approximation 273

6.1 Introduction 273

6.2 Density Matrix Equations of Motion for a Two-Level Atom 274

6.2.1 Closed Two-Level Atom 276

6.2.2 Open Two-Level Atom 279

6.2.3 Two-Level Atom with a Non-Radiatively Coupled Third Level 279

6.3 Steady-State Response of a Two-Level Atom to a Monochromatic Field 280

6.4 Optical Bloch Equations 288

6.4.1 Harmonic Oscillator Form of the Density Matrix Equations 291

6.4.2 Adiabatic-Following Limit 293

6.5 Rabi Oscillations and Dressed Atomic States 295

6.5.1 Rabi Solution of the Schrodinger Equation 296

6.5.2 Solution for an Atom Initially in the Ground State 298

6.5.3 Dressed States 302

6.5.4 Inclusion of Relaxation Phenomena 305

6.6 Optical Wave Mixing in Two-Level Systems 307

6.6.1 Solution of the Density Matrix Equations for a Two-Level Atom in the Presence of Pump and Probe Fields 308

6.6.2 Nonlinear Susceptibility and Coupled-Amplitude Equations 315

Problems 319

References 320

Chapter 7 Processes Resulting from the Intensity-Dependent Refractive Index 321

7.1 Self-Focusing of Light and Other Self-Action Effects 321

7.1.1 Self-Trapping of Light 324

7.1.2 Mathematical Description of Self-Action Effects 327

7.1.3 Laser Beam Breakup into Many Filaments 328

7.1.4 Self-Action Effects with Pulsed Laser Beams 333

7.2 Optical Phase Conjugation 334

7.2.1 Aberration Correction by Phase Conjugation 336

7.2.2 Phase Conjugation by Degenerate Four-Wave Mixing 338

7.2.3 Polarization Properties of Phase Conjugation 345

7.3 Optical Bistability and Optical Switching 349

7.3.1 Absorptive Bistability 351

7.3.2 Refractive Bistability 354

7.3.3 Optical Switching 356

7.4 Two-Beam Coupling 359

7.5 Pulse Propagation and Temporal Solitons 365

7.5.1 Self-Phase Modulation 365

7.5.2 Pulse Propagation Equation 368

7.5.3 Temporal Optical Solitons 372

Problems 374

References 379

Chapter 8 Spontaneous Light Scattering and Acoustooptics 381

8.1 Features of Spontaneous Light Scattering 381

8.1.1 Fluctuations as the Origin of Light Scattering 382

8.1.2 Scattering Coefficient 384

8.1.3 Scattering Cross Section 385

8.2 Microscopic Theory of Light Scattering 386

8.3 Thermodynamic Theory of Scalar Light Scattering 392

8.3.1 Ideal Gas 394

8.3.2 Spectrum of the Scattered Light 395

8.3.3 Brillouin Scattering 395

8.3.4 Stokes Scattering (First Term in Eq. (8.3.36)) 398

8.3.5 Anti-Stokes Scattering (Second Term in Eq. (8.3.36)) 400

8.3.6 Rayleigh Center Scattering 402

8.4 Acoustooptics 403

8.4.1 Bragg Scattering of Light by Sound Waves 403

8.4.2 Raman-Nath Effect 412

Problems 416

References 417

Chapter 9 Stimulated Brillouin and Stimulated Rayleigh Scattering 419

9.1 Stimulated Scattering Processes 419

9.2 Electrostriction 421

9.3 Stimulated Brillouin Scattering (Induced by Electrostriction) 425

9.3.1 Pump Depletion Effects in SBS 431

9.3.2 SBS Generator 433

9.3.3 Transient and Dynamical Features of SBS 436

9.4 Phase Conjugation by Stimulated Brillouin Scattering 437

9.5 Stimulated Brillouin Scattering in Gases 441

9.6 General Theory of Stimulated Brillouin and Stimulated Rayleigh Scattering 443

9.6.1 Appendix: Definition of the Viscosity Coefficients 454

Problems 456

References 457

Chapter 10 Stimulated Raman Scattering and Stimulated Rayleigh-Wing Scattering 459

10.1 The Spontaneous Raman Effect 459

10.2 Spontaneous versus Stimulated Raman Scattering 460

10.3 Stimulated Raman Scattering Described by the Nonlinear Polarization 465

10.4 Stokes-Anti-Stokes Coupling in Stimulated Raman Scattering 474

10.4.1 Dispersionless, Nonlinear Medium without Gain or Loss 478

10.4.2 Medium without a Nonlinearity 479

10.4.3 Stokes-Anti-Stokes Coupling in Stimulated Raman Scattering 480

10.5 Coherent Anti-Stokes Raman Scattering 483

10.6 Stimulated Rayleigh-Wing Scattering 486

10.6.1 Polarization Properties of Stimulated Rayleigh-Wing Scattering 490

Problems 492

References 492

Chapter 11 The Electrooptic and Photorefractive Effects 495

11.1 Introduction to the Electrooptic Effect 495

11.2 Linear Electrooptic Effect 496

11.3 Electrooptic Modulators 500

11.4 Introduction to the Photorefractive Effect 507

11.5 Photorefractive Equations of Kukhtarev et al 508

11.6 Two-Beam Coupling in Photorefractive Materials 511

11.7 Four-Wave Mixing in Photorefractive Materials 518

11.7.1 Externally Self-Pumped Phase-Conjugate Mirror 519

11.7.2 Internally Self-Pumped Phase-Conjugate Mirror 519

11.7.3 Double Phase-Conjugate Mirror 520

11.7.4 Other Applications of Photorefractive Nonlinear Optics 521

Problems 521

References 521

Chapter 12 Optically Induced Damage and Multiphoton Absorption 523

12.1 Introduction to Optical Damage 523

12.2 Avalanche-Breakdown Model 524

12.3 Influence of Laser Pulse Duration 526

12.4 Direct Photoionization 528

12.5 Multiphoton Absorption and Multiphoton Ionization 528

12.5.1 Theory of Single- and Multiphoton Absorption and Fermi's Golden Rule 530

12.5.2 Linear (One-Photon) Absorption 532

12.5.3 Two-Photon Absorption 535

12.5.4 Multiphoton Absorption 538

Problems 538

References 538

Chapter 13 Ultra fast and Intense-Field Nonlinear Optics 541

13.1 Introduction 541

13.2 Ultrashort-Pulse Propagation Equation 541

13.3 Interpretation of the Ultrashort-Pulse Propagation Equation 547

13.3.1 Self-Steepening 548

13.3.2 Space-Time Coupling 550

13.3.3 Supercontinuum Generation 551

13.4 Intense-Field Nonlinear Optics 552

13.5 Motion of a Free Electron in a Laser Field 553

13.6 High-Harmonic Generation 555

13.7 Tunnel Ionization and the Keldysh Model 559

13.8 Nonlinear Optics of Plasmas and Relativistic Nonlinear Optics 560

13.9 Nonlinear Quantum Electrodynamics 565

Problem 567

References 567

Chapter 14 Nonlinear Optics of Plasmonic Systems 569

14.1 Introduction to Plasmonics 569

14.2 Simple Derivation of the Plasma Frequency 569

14.3 The Drude Model 571

14.4 Optical Properties of Gold 574

14.5 Surface Plasmon Polaritons 576

14.6 Electric Field Enhancement in Plasmonic Systems 579

Problems 581

References 581

Appendices 583

Appendix A The SI System of Units 583

A.1 Energy Relations and Poynting's Theorem 586

A.2 The Wave Equation 586

A.3 Boundary Conditions 588

Appendix B The Gaussian System of Units 590

Appendix C Systems of Units in Nonlinear Optics 594

C.1 Conversion between the Systems 595

Appendix D Relationship between Intensity and Field Strength 596

Appendix E Physical Constants 597

References 599

Index 601

What People are Saying About This

From the Publisher

Presents the most updated edition of this classic, respected reference on nonlinear optics, with a new chapter on quantum optics

Editorial Reviews

"This comprehensive lecture-based book is pleasant and contains careful discussions on a large number of topics dealing with the multifaceted aspects of nonlinear optics. The fourth edition has been updated to capture the latest and most up-to-date research on the nonlinear optics of plasmonic systems. The target audience for Boyd’s book is clearly graduate students of engineering and science, and optical engineers and designers. But anyone concerned with the field of optical physics from the perspective of nonlinear optics will profit from reading this book." —The Optical Society: Optics and Photonics News

From the Publisher

An introduction to the field at the level of a beginning graduate student. Fundamental aspects are stressed, with applications and experimental results included only as necessary illustrations. Many of the topics included are those of particular historical value. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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