nonlinear optics.pdf

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Preface to the Third Edition

Preface to the Second Edition

Preface to the First Edition

The Nonlinear Optical Susceptibility

Introduction to Nonlinear Optics

Descriptions of Nonlinear Optical Processes

Formal Definition of the Nonlinear Susceptibility

Nonlinear Susceptibility of a Classical Anharmonic Oscillator

Properties of the Nonlinear Susceptibility

Time-Domain Description of Optical Nonlinearities

Kramers-Kronig Relations in Linear and Nonlinear Optics

Problems

References

Wave-Equation Description of Nonlinear Optical Interactions

The Wave Equation for Nonlinear Optical Media

The Coupled-Wave Equations for Sum-Frequency Generation

Phase Matching

Quasi-Phase-Matching

The Manley-Rowe Relations

Sum-Frequency Generation

Second-Harmonic Generation

Difference-Frequency Generation and Parametric Amplification

Optical Parametric Oscillators

Nonlinear Optical Interactions with Focused Gaussian Beams

Nonlinear Optics at an Interface

Problems

References

Quantum-Mechanical Theory of the Nonlinear Optical Susceptibility

Introduction

Schrödinger Calculation of Nonlinear Optical Susceptibility

Density Matrix Formulation of Quantum Mechanics

Perturbation Solution of the Density Matrix Equation of Motion

Density Matrix Calculation of the Linear Susceptibility

Density Matrix Calculation of the Second-Order Susceptibility

Density Matrix Calculation of the Third-Order Susceptibility

Electromagnetically Induced Transparency

Local-Field Corrections to the Nonlinear Optical Susceptibility

Problems

References

The Intensity-Dependent Refractive Index

Descriptions of the Intensity-Dependent Refractive Index

Tensor Nature of the Third-Order Susceptibility

Nonresonant Electronic Nonlinearities

Nonlinearities Due to Molecular Orientation

Thermal Nonlinear Optical Effects

Semiconductor Nonlinearities

Concluding Remarks

References

Molecular Origin of the Nonlinear Optical Response

Nonlinear Susceptibilities Calculated Using Time-Independent Perturbation Theory

Semiempirical Models of the Nonlinear Optical Susceptibility

Model of Boling, Glass, and Owyoung

Nonlinear Optical Properties of Conjugated Polymers

Bond-Charge Model of Nonlinear Optical Properties

Nonlinear Optics of Chiral Media

Nonlinear Optics of Liquid Crystals

Problems

References

Nonlinear Optics in the Two-Level Approximation

Introduction

Density Matrix Equations of Motion for a Two-Level Atom

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

Optical Bloch Equations

Rabi Oscillations and Dressed Atomic States

Optical Wave Mixing in Two-Level Systems

Problems

References

Processes Resulting from the Intensity-Dependent Refractive Index

Self-Focusing of Light and Other Self-Action Effects

Optical Phase Conjugation

Optical Bistability and Optical Switching

Two-Beam Coupling

Pulse Propagation and Temporal Solitons

Problems

References

Spontaneous Light Scattering and Acoustooptics

Features of Spontaneous Light Scattering

Microscopic Theory of Light Scattering

Thermodynamic Theory of Scalar Light Scattering

Acoustooptics

Problems

References

Stimulated Brillouin and Stimulated Rayleigh Scattering

Stimulated Scattering Processes

Electrostriction

Stimulated Brillouin Scattering (Induced by Electrostriction)

Phase Conjugation by Stimulated Brillouin Scattering

Stimulated Brillouin Scattering in Gases

Stimulated Brillouin and Stimulated Rayleigh Scattering

Problems

References

Stimulated Raman Scattering and Stimulated Rayleigh-Wing Scattering

The Spontaneous Raman Effect

Spontaneous versus Stimulated Raman Scattering

Stimulated Raman Scattering Described by the Nonlinear Polarization

Stokes-Anti-Stokes Coupling in Stimulated Raman Scattering

Coherent Anti-Stokes Raman Scattering

Stimulated Rayleigh-Wing Scattering

Problems

References

The Electrooptic and Photorefractive Effects

Introduction to the Electrooptic Effect

Linear Electrooptic Effect

Electrooptic Modulators

Introduction to the Photorefractive Effect

Photorefractive Equations of Kukhtarev et al.

Two-Beam Coupling in Photorefractive Materials

Four-Wave Mixing in Photorefractive Materials

Problems

References

Optically Induced Damage and Multiphoton Absorption

Introduction to Optical Damage

Avalanche-Breakdown Model

Influence of Laser Pulse Duration

Direct Photoionization

Multiphoton Absorption and Multiphoton Ionization

Problems

References

Ultrafast and Intense-Field Nonlinear Optics

Introduction

Ultrashort Pulse Propagation Equation

Interpretation of the Ultrashort-Pulse Propagation Equation

Intense-Field Nonlinear Optics

Motion of a Free Electron in a Laser Field

High-Harmonic Generation

Nonlinear Optics of Plasmas and Relativistic Nonlinear Optics

Nonlinear Quantum Electrodynamics

Problem

References

The SI System of Units

Further reading

Systems of Units in Nonlinear Optics

Relationship between Intensity and Field Strength

Physical Constants

Index

for my family

Contents Preface to the Third Edition Preface to the Second Edition Preface to the First Edition 1. The Nonlinear Optical Susceptibility Introduction to Nonlinear Optics 1.1. 1.2. Descriptions of Nonlinear Optical Processes 1.3. Formal Deﬁnition of the Nonlinear Susceptibility 1.4. Nonlinear Susceptibility of a Classical Anharmonic Oscillator 1.5. Properties of the Nonlinear Susceptibility 1.6. Time-Domain Description of Optical Nonlinearities 1.7. Kramers–Kronig Relations in Linear and Nonlinear Optics Problems References xiii xv xvii 1 1 4 17 21 33 52 58 63 65 2. Wave-Equation Description of Nonlinear Optical Interactions 69 2.1. The Wave Equation for Nonlinear Optical Media 2.2. The Coupled-Wave Equations for Sum-Frequency Generation 2.3. Phase Matching 2.4. Quasi-Phase-Matching 2.5. The Manley–Rowe Relations 2.6. Sum-Frequency Generation 2.7. Second-Harmonic Generation 69 74 79 84 88 91 96 vii

viii Contents 2.8. Difference-Frequency Generation and Parametric Ampliﬁcation 2.9. Optical Parametric Oscillators 2.10. Nonlinear Optical Interactions with Focused Gaussian Beams 2.11. Nonlinear Optics at an Interface Problems References 3. Quantum-Mechanical Theory of the Nonlinear Optical Susceptibility 105 108 116 122 128 132 135 Introduction 3.1. 135 3.2. Schrödinger Calculation of Nonlinear Optical Susceptibility 137 3.3. Density Matrix Formulation of Quantum Mechanics 150 3.4. Perturbation Solution of the Density Matrix Equation of Motion 3.5. Density Matrix Calculation of the Linear Susceptibility 3.6. Density Matrix Calculation of the Second-Order 158 161 Susceptibility 170 3.7. Density Matrix Calculation of the Third-Order Susceptibility 180 3.8. Electromagnetically Induced Transparency 185 3.9. Local-Field Corrections to the Nonlinear Optical Susceptibility Problems References 4. The Intensity-Dependent Refractive Index 4.1. Descriptions of the Intensity-Dependent Refractive Index 4.2. Tensor Nature of the Third-Order Susceptibility 4.3. Nonresonant Electronic Nonlinearities 4.4. Nonlinearities Due to Molecular Orientation 4.5. Thermal Nonlinear Optical Effects 4.6. Semiconductor Nonlinearities 4.7. Concluding Remarks References 5. Molecular Origin of the Nonlinear Optical Response 5.1. Nonlinear Susceptibilities Calculated Using Time-Independent Perturbation Theory 194 201 204 207 207 211 221 228 235 240 247 251 253 253

Contents 5.2. Semiempirical Models of the Nonlinear Optical Susceptibility Model of Boling, Glass, and Owyoung 5.3. Nonlinear Optical Properties of Conjugated Polymers 5.4. Bond-Charge Model of Nonlinear Optical Properties 5.5. Nonlinear Optics of Chiral Media 5.6. Nonlinear Optics of Liquid Crystals Problems References 6. Nonlinear Optics in the Two-Level Approximation Introduction 6.1. 6.2. Density Matrix Equations of Motion for a Two-Level Atom 6.3. Steady-State Response of a Two-Level Atom to a Monochromatic Field 6.4. Optical Bloch Equations 6.5. Rabi Oscillations and Dressed Atomic States 6.6. Optical Wave Mixing in Two-Level Systems Problems References 7. Processes Resulting from the Intensity-Dependent Refractive Index 7.1. Self-Focusing of Light and Other Self-Action Effects 7.2. Optical Phase Conjugation 7.3. Optical Bistability and Optical Switching 7.4. Two-Beam Coupling 7.5. Pulse Propagation and Temporal Solitons Problems References 8. Spontaneous Light Scattering and Acoustooptics 8.1. Features of Spontaneous Light Scattering 8.2. Microscopic Theory of Light Scattering 8.3. Thermodynamic Theory of Scalar Light Scattering ix 259 260 262 264 268 271 273 274 277 277 278 285 293 301 313 326 327 329 329 342 359 369 375 383 388 391 391 396 402

x Contents 8.4. Acoustooptics Problems References 9. Stimulated Brillouin and Stimulated Rayleigh Scattering 413 427 428 429 429 9.1. Stimulated Scattering Processes 431 9.2. Electrostriction 9.3. Stimulated Brillouin Scattering (Induced by Electrostriction) 436 448 9.4. Phase Conjugation by Stimulated Brillouin Scattering 453 9.5. Stimulated Brillouin Scattering in Gases 9.6. Stimulated Brillouin and Stimulated Rayleigh Scattering 455 468 470 Problems References 10. Stimulated Raman Scattering and Stimulated Rayleigh-Wing Scattering 10.1. The Spontaneous Raman Effect 10.2. Spontaneous versus Stimulated Raman Scattering 10.3. Stimulated Raman Scattering Described by the Nonlinear Polarization 10.4. Stokes–Anti-Stokes Coupling in Stimulated Raman Scattering 10.5. Coherent Anti-Stokes Raman Scattering 10.6. Stimulated Rayleigh-Wing Scattering Problems References 11. The Electrooptic and Photorefractive Effects 11.1. Introduction to the Electrooptic Effect 11.2. Linear Electrooptic Effect 11.3. Electrooptic Modulators 11.4. Introduction to the Photorefractive Effect 11.5. Photorefractive Equations of Kukhtarev et al. 11.6. Two-Beam Coupling in Photorefractive Materials 11.7. Four-Wave Mixing in Photorefractive Materials Problems References 473 473 474 479 488 499 501 508 508 511 511 512 516 523 526 528 536 540 540

Contents 12. Optically Induced Damage and Multiphoton Absorption 12.1. Introduction to Optical Damage 12.2. Avalanche-Breakdown Model 12.3. Inﬂuence of Laser Pulse Duration 12.4. Direct Photoionization 12.5. Multiphoton Absorption and Multiphoton Ionization Problems References 13. Ultrafast and Intense-Field Nonlinear Optics 13.1. Introduction 13.2. Ultrashort Pulse Propagation Equation 13.3. Interpretation of the Ultrashort-Pulse Propagation Equation 13.4. Intense-Field Nonlinear Optics 13.5. Motion of a Free Electron in a Laser Field 13.6. High-Harmonic Generation 13.7. Nonlinear Optics of Plasmas and Relativistic Nonlinear Optics 13.8. Nonlinear Quantum Electrodynamics Problem References Appendices A. B. C. D. E. The SI System of Units Further reading The Gaussian System of Units Further reading Systems of Units in Nonlinear Optics Relationship between Intensity and Field Strength Physical Constants Index xi 543 543 544 546 548 549 559 559 561 561 561 567 571 572 575 579 583 586 586 589 589 596 596 600 600 602 603 605

Preface to the Third Edition It has been a great pleasure for me to have prepared the latest edition of my book on nonlinear optics. My intrigue in the subject matter of this book is as strong as it was when the ﬁrst edition was published in 1992. The principal changes present in the third edition are as follows: (1) The book has been entirely rewritten using the SI system of units. I personally prefer the elegance of the gaussian system of units, which was used in the ﬁrst two editions, but I realize that most readers would prefer the SI system, and the change was made for this reason. (2) In addition, a large number of minor changes have been made throughout the text to clarify the intended meaning and to make the arguments easier to follow. I am indebted to the countless comments received from students and colleagues both in Rochester and from around the world that have allowed me to improve the writing in this man- ner. (3) Moreover, several sections that treat entirely new material have been added. Applications of harmonic generation, including applications within the ﬁelds of microscopy and biophotonics, are treated in Subsection 2.7.1. Elec- tromagnetically induced transparency is treated in Section 3.8. Some brief but crucial comments regarding limitations to the maximum size of the intensity- induced refractive-index change are made in Section 4.7. The use of nonlinear optical methods for inducing unusual values of the group velocity of light are discussed brieﬂy in Section 3.8 and in Subsection 6.6.2. Spectroscopy based on coherent anti–Stokes Raman scattering (CARS) is discussed in Section 10.5. In addition, the appendix has been expanded to include brief descrip- tions of both the SI and gaussian systems of units and procedures for conver- sion between them. xiii

xiv Preface to the Third Edition The book in its present form contains far too much material to be covered within a conventional one-semester course. For this reason, I am often asked for advice on how to structure a course based on the content of my textbook. Some of my thoughts along these lines are as follows: (1) I have endeavored as much as possible to make each part of the book self-contained. Thus, the sophisticated reader can read the book in any desired order and can read only sections of personal interest. (2) Nonetheless, when using the book as a course text, I suggest starting with Chapters 1 and 2, which present the basic formal- ism of the subject material. At that point, topics of interest can be taught in nearly any order. (3) Special mention should be made regarding Chapters 3 and 6, which deal with quantum mechanical treatments of nonlinear optical phenomena. These chapters are among the most challenging of any within the book. These chapters can be skipped entirely if one is comfortable with estab- lishing only a phenomenological description of nonlinear optical phenomena. Alternatively, these chapters can form the basis of a formal treatment of how the laws of quantum mechanics can be applied to provide detailed descrip- tions of a variety of optical phenomena. (4) From a different perspective, I am sometimes asked for my advice on extracting the essential material from the book—that is, in determining which are topics that everyone should know. This question often arises in the context of determining what material stu- dents should study when preparing for qualifying exams. My best response to questions of this sort is that the essential material is as follows: Chapter 1 in its entirety; Sections 2.1–2.3, 2.4, and 2.10 of Chapter 2; Subsection 3.5.1 of Chapter 3; Sections 4.1, 4.6, and 4.7 of Chapter 4; Chapter 7 in its entirety; Section 8.1 of Chapter 8; and Section 9.1 of Chapter 9. (5) Finally, I often tell my classroom students that my course is in some ways as much a course on optical physics as it is a course on nonlinear optics. I simply use the concept of nonlinear optics as a unifying theme for presenting conceptual issues and practical applications of optical physics. Recognizing that this is part of my perspective in writing, this book could be useful to its readers. I want to express my thanks once again to the many students and colleagues who have given me useful advice and comments regarding this book over the past ﬁfteen years. I am especially indebted to my own graduate students for the assistance and encouragement they have given to me. Robert Boyd Rochester, New York October, 2007

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