Nonlinear optics

Front Cover -- Nonlinear Optics -- Copyright -- Contents -- Preface to the Fourth Edition -- Preface to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- 1 The Nonlinear Optical Susceptibility -- 1.1 Introduction to Nonlinear Optics -- 1.2 Descriptions of Nonlinear Optical Processes -- 1.2.1 Second-Harmonic Generation -- 1.2.2 Sum- and Difference-Frequency Generation -- 1.2.3 Sum-Frequency Generation -- 1.2.4 Difference-Frequency Generation -- 1.2.5 Optical Parametric Oscillation -- 1.2.6 Third-Order Nonlinear Optical Processes Contents......Page 7 Preface to the Fourth Edition......Page 15 Preface to the Third Edition......Page 17 Preface to the Second Edition......Page 19 Preface to the First Edition......Page 21 1.1 Introduction to Nonlinear Optics......Page 24 1.2.1 Second-Harmonic Generation......Page 27 1.2.2 Sum- and Difference-Frequency Generation......Page 29 1.2.3 Sum-Frequency Generation......Page 30 1.2.4 Difference-Frequency Generation......Page 31 1.2.5 Optical Parametric Oscillation......Page 32 1.2.7 Third-Harmonic Generation......Page 33 1.2.9 Third-Order Interactions (General Case)......Page 34 1.2.10 Parametric versus Nonparametric Processes......Page 36 Optical Bistability......Page 37 1.2.12 Two-Photon Absorption......Page 38 1.3 Formal Definition of the Nonlinear Susceptibility......Page 39 1.4 Nonlinear Susceptibility of a Classical Anharmonic Oscillator......Page 43 1.4.1 Noncentrosymmetric Media......Page 44 1.4.2 Miller's Rule......Page 49 1.4.3 Centrosymmetric Media......Page 50 1.5 Properties of the Nonlinear Susceptibility......Page 55 1.5.1 Reality of the Fields......Page 56 1.5.3 Symmetries for Lossless Media......Page 57 1.5.4 Field Energy Density for a Nonlinear Medium......Page 58 1.5.5 Kleinman's Symmetry......Page 60 1.5.6 Contracted Notation......Page 61 1.5.7 Effective Value of d (deff)......Page 63 1.5.9 Influence of Spatial Symmetry on the Linear Optical Properties of a Material Medium......Page 64 1.5.10 Influence of Inversion Symmetry on the Second-Order Nonlinear Response......Page 65 1.5.11 Influence of Spatial Symmetry on the Second-Order Susceptibility......Page 67 1.5.13 Distinction between Noncentrosymmetric and Cubic Crystal Classes......Page 68 1.6 Time-Domain Description of Optical Nonlinearities......Page 73 1.7.1 Kramers-Kronig Relations in Linear Optics......Page 79 1.7.2 Kramers-Kronig Relations in Nonlinear Optics......Page 82 Problems......Page 84 Further Reading on Nonlinear Optics......Page 86 Suggested Further Reading on Kramers-Kronig Relations......Page 87 2.1 The Wave Equation for Nonlinear Optical Media......Page 88 2.2 The Coupled-Wave Equations for Sum-Frequency Generation......Page 93 2.2.1 Phase-Matching Considerations......Page 95 2.3 Phase Matching......Page 97 Angle Tuning......Page 100 2.4 Quasi-Phase-Matching (QPM)......Page 102 2.5 The Manley–Rowe Relations......Page 106 2.6 Sum-Frequency Generation......Page 109 2.7 Second-Harmonic Generation......Page 114 Surface Nonlinear Optics......Page 121 Nonlinear Optical Microscopy......Page 122 2.8 Difference-Frequency Generation and Parametric Amplification......Page 123 2.9 Optical Parametric Oscillators......Page 125 Threshold for Parametric Oscillation......Page 127 2.9.1 Influence of Cavity Mode Structure on OPO Tuning......Page 128 2.10.1 Paraxial Wave Equation......Page 132 2.10.2 Gaussian Beams......Page 133 2.10.3 Harmonic Generation Using Focused Gaussian Beams......Page 135 2.11 Nonlinear Optics at an Interface......Page 139 Types of Phase Matching......Page 144 Phase Matching of Spontaneous Parametric Down Conversion (SPDC)......Page 147 Tilted-Pulse-Front Method for the Generation of THz Radiation......Page 150 Problems......Page 153 Section 7: Applications of Second-Harmonic Generation......Page 157 Suggested Further Readings on THz Pulse Generation......Page 158 3.1 Introduction......Page 159 3.2 Schrödinger Equation Calculation of the Nonlinear Optical Susceptibility......Page 160 3.2.1 Energy Eigenstates......Page 161 3.2.2 Perturbation Solution to Schrödinger's Equation......Page 162 3.2.3 Linear Susceptibility......Page 164 3.2.4 Second-Order Susceptibility......Page 166 3.2.5 Third-Order Susceptibility......Page 168 3.2.6 Third-Harmonic Generation in Alkali Metal Vapors......Page 170 3.3 Density Matrix Formulation of Quantum Mechanics......Page 173 3.3.1 Example: Two-Level Atom......Page 180 3.4 Perturbation Solution of the Density Matrix Equation of Motion......Page 181 3.5 Density Matrix Calculation of the Linear Susceptibility......Page 183 3.5.1 Linear Response Theory......Page 186 3.6 Density Matrix Calculation of the Second-Order Susceptibility......Page 191 3.6.1 χ(2) in the Limit of Nonresonant Excitation......Page 200 3.7 Density Matrix Calculation of the Third-Order Susceptibility......Page 201 3.8 Electromagnetically Induced Transparency......Page 206 3.9.1 Local-Field Effects in Linear Optics......Page 214 3.9.2 Local-Field Effects in Nonlinear Optics......Page 216 Problems......Page 220 Further Reading on Quantum-Mechanical Models of the Nonlinear Optical Susceptibility......Page 223 Local-Field Effects in Nonlinear Optics......Page 224 4.1 Descriptions of the Intensity-Dependent Refractive Index......Page 225 4.2 Tensor Nature of the Third-Order Susceptibility......Page 231 4.2.1 Propagation through Isotropic Nonlinear Media......Page 235 4.3 Nonresonant Electronic Nonlinearities......Page 239 4.3.2 Quantum-Mechanical Model of Nonresonant Electronic Nonlinearities......Page 240 4.3.3 χ(3) in the Low-Frequency Limit......Page 244 4.4 Nonlinearities Due to Molecular Orientation......Page 245 4.4.1 Tensor Properties of χ(3) for the Molecular Orientation Effect......Page 251 4.5 Thermal Nonlinear Optical Effects......Page 253 4.5.1 Thermal Nonlinearities with Continuous-Wave Laser Beams......Page 255 4.5.2 Thermal Nonlinearities with Pulsed Laser Beams......Page 256 4.6.1 Nonlinearities Resulting from Band-to-Band Transitions......Page 257 Free-Electron Response......Page 258 Modification of Optical Properties by Plasma Screening Effects......Page 259 Change of Optical Properties Due to Band-Filling Effects......Page 262 4.6.2 Nonlinearities Involving Virtual Transitions......Page 263 4.7 Concluding Remarks......Page 265 Problems......Page 267 Semiconductor Nonlinearities......Page 269 Concluding Remarks......Page 270 5.1 Nonlinear Susceptibilities Calculated Using Time-Independent Perturbation Theory......Page 271 5.1.1 Hydrogen Atom......Page 272 5.1.2 General Expression for the Nonlinear Susceptibility in the Quasi-Static Limit......Page 273 5.2 Semiempirical Models of the Nonlinear Optical Susceptibility......Page 277 Model of Boling, Glass, and Owyoung......Page 278 5.3 Nonlinear Optical Properties of Conjugated Polymers......Page 279 5.4 Bond-Charge Model of Nonlinear Optical Properties......Page 281 5.5 Nonlinear Optics of Chiral Media......Page 286 5.6 Nonlinear Optics of Liquid Crystals......Page 288 Suggested Books on Molecular Nonlinear Optics for Further Reading......Page 291 Section 5.6. Liquid Crystal Nonlinear Optics......Page 292 6.1 Introduction......Page 294 6.2 Density Matrix Equations of Motion for a Two-Level Atom......Page 295 6.2.1 Closed Two-Level Atom......Page 297 6.2.3 Two-Level Atom with a Non-Radiatively Coupled Third Level......Page 300 6.3 Steady-State Response of a Two-Level Atom to a Monochromatic Field......Page 301 6.4 Optical Bloch Equations......Page 309 6.4.1 Harmonic Oscillator Form of the Density Matrix Equations......Page 312 6.4.2 Adiabatic-Following Limit......Page 314 6.5 Rabi Oscillations and Dressed Atomic States......Page 316 6.5.1 Rabi Solution of the Schrödinger Equation......Page 317 6.5.2 Solution for an Atom Initially in the Ground State......Page 319 6.5.3 Dressed States......Page 323 6.5.4 Inclusion of Relaxation Phenomena......Page 326 6.6 Optical Wave Mixing in Two-Level Systems......Page 328 6.6.1 Solution of the Density Matrix Equations for a Two-Level Atom in the Presence of Pump and Probe Fields......Page 329 6.6.2 Nonlinear Susceptibility and Coupled-Amplitude Equations......Page 336 Problems......Page 340 References......Page 341 7.1 Self-Focusing of Light and Other Self-Action Effects......Page 342 7.1.1 Self-Trapping of Light......Page 345 7.1.2 Mathematical Description of Self-Action Effects......Page 348 7.1.3 Laser Beam Breakup into Many Filaments......Page 349 Conditions for the Occurrence of Nonlinear Beam Breakup......Page 353 Moving Focus Model......Page 354 7.2 Optical Phase Conjugation......Page 355 7.2.1 Aberration Correction by Phase Conjugation......Page 357 7.2.2 Phase Conjugation by Degenerate Four-Wave Mixing......Page 359 7.2.3 Polarization Properties of Phase Conjugation......Page 366 7.3 Optical Bistability and Optical Switching......Page 370 7.3.1 Absorptive Bistability......Page 372 7.3.2 Refractive Bistability......Page 375 7.3.3 Optical Switching......Page 377 7.4 Two-Beam Coupling......Page 380 7.5.1 Self-Phase Modulation......Page 386 7.5.2 Pulse Propagation Equation......Page 389 7.5.3 Temporal Optical Solitons......Page 393 Problems......Page 395 Suggested Additional Reading on Self-Action Effects......Page 400 Section 7.5 Pulse Propagation and Temporal Solitons......Page 401 8.1 Features of Spontaneous Light Scattering......Page 402 8.1.1 Fluctuations as the Origin of Light Scattering......Page 403 8.1.2 Scattering Coefficient......Page 405 8.1.3 Scattering Cross Section......Page 406 8.2 Microscopic Theory of Light Scattering......Page 407 8.3 Thermodynamic Theory of Scalar Light Scattering......Page 413 8.3.1 Ideal Gas......Page 415 8.3.3 Brillouin Scattering......Page 416 8.3.4 Stokes Scattering (First Term in Eq. (8.3.36))......Page 419 8.3.5 Anti-Stokes Scattering (Second Term in Eq. (8.3.36))......Page 421 8.3.6 Rayleigh Center Scattering......Page 423 8.4.1 Bragg Scattering of Light by Sound Waves......Page 424 8.4.2 Raman-Nath Effect......Page 433 Problems......Page 437 Recommended Further Reading on Light Scattering and Acoustooptics......Page 438 9.1 Stimulated Scattering Processes......Page 439 9.2 Electrostriction......Page 441 9.3 Stimulated Brillouin Scattering (Induced by Electrostriction)......Page 445 9.3.1 Pump Depletion Effects in SBS......Page 451 9.3.2 SBS Generator......Page 453 9.3.3 Transient and Dynamical Features of SBS......Page 456 9.4 Phase Conjugation by Stimulated Brillouin Scattering......Page 457 9.5 Stimulated Brillouin Scattering in Gases......Page 461 9.6 General Theory of Stimulated Brillouin and Stimulated Rayleigh Scattering......Page 463 9.6.1 Appendix: Definition of the Viscosity Coefficients......Page 474 Problems......Page 476 Suggested Further Reading on Stimulated Light Scattering......Page 477 Stimulated Brillouin Scattering......Page 478 10.1 The Spontaneous Raman Effect......Page 479 10.2 Spontaneous versus Stimulated Raman Scattering......Page 480 10.3 Stimulated Raman Scattering Described by the Nonlinear Polarization......Page 485 10.4 Stokes-Anti-Stokes Coupling in Stimulated Raman Scattering......Page 494 10.4.1 Dispersionless, Nonlinear Medium without Gain or Loss......Page 498 10.4.2 Medium without a Nonlinearity......Page 499 10.4.3 Stokes-Anti-Stokes Coupling in Stimulated Raman Scattering......Page 500 10.5 Coherent Anti-Stokes Raman Scattering......Page 503 10.6 Stimulated Rayleigh-Wing Scattering......Page 506 10.6.1 Polarization Properties of Stimulated Rayleigh-Wing Scattering......Page 510 Stimulated Raman Scattering......Page 512 Stimulated Rayleigh-Wing Scattering......Page 513 11.1 Introduction to the Electrooptic Effect......Page 514 11.2 Linear Electrooptic Effect......Page 515 11.3 Electrooptic Modulators......Page 519 11.4 Introduction to the Photorefractive Effect......Page 526 11.5 Photorefractive Equations of Kukhtarev et al.......Page 527 11.6 Two-Beam Coupling in Photorefractive Materials......Page 530 11.7 Four-Wave Mixing in Photorefractive Materials......Page 537 11.7.2 Internally Self-Pumped Phase-Conjugate Mirror......Page 538 11.7.3 Double Phase-Conjugate Mirror......Page 539 Electrooptic Effect......Page 540 Photorefractive Effect......Page 541 12.1 Introduction to Optical Damage......Page 542 12.2 Avalanche-Breakdown Model......Page 543 12.3 Influence of Laser Pulse Duration......Page 545 12.5 Multiphoton Absorption and Multiphoton Ionization......Page 547 12.5.1 Theory of Single- and Multiphoton Absorption and Fermi's Golden Rule......Page 549 12.5.2 Linear (One-Photon) Absorption......Page 551 12.5.3 Two-Photon Absorption......Page 554 Optical Damage......Page 557 Multiphoton Absorption......Page 558 13.2 Ultrashort-Pulse Propagation Equation......Page 559 13.3 Interpretation of the Ultrashort-Pulse Propagation Equation......Page 565 13.3.1 Self-Steepening......Page 566 13.3.2 Space-Time Coupling......Page 568 13.3.3 Supercontinuum Generation......Page 569 13.4 Intense-Field Nonlinear Optics......Page 570 13.5 Motion of a Free Electron in a Laser Field......Page 571 13.6 High-Harmonic Generation......Page 573 13.7 Tunnel Ionization and the Keldysh Model......Page 577 13.8 Nonlinear Optics of Plasmas and Relativistic Nonlinear Optics......Page 578 13.9 Nonlinear Quantum Electrodynamics......Page 583 Sections 13.1 through 13.3: Ultrafast Nonlinear Optics......Page 585 Section 13.9: Nonlinear Quantum Electrodynamics......Page 586 14.2 Simple Derivation of the Plasma Frequency......Page 587 14.3 The Drude Model......Page 589 14.4 Optical Properties of Gold......Page 592 14.5 Surface Plasmon Polaritons......Page 594 14.6 Electric Field Enhancement in Plasmonic Systems......Page 597 Plasma Frequency and Drude Model......Page 599 Electric Field Enhancement in Plasmonic Systems......Page 600 Appendix A The SI System of Units......Page 601 A.2 The Wave Equation......Page 604 A.3 Boundary Conditions......Page 606 Appendix B The Gaussian System of Units......Page 608 Appendix C Systems of Units in Nonlinear Optics......Page 612 C.1 Conversion between the Systems......Page 613 Appendix D Relationship between Intensity and Field Strength......Page 614 Appendix E Physical Constants......Page 615 References......Page 617 Index......Page 618

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.

• Presents an introduction to the entire field of optical physics from the perspective of nonlinear optics
• Combines first-rate pedagogy with a treatment of the fundamental aspects of nonlinear optics
• Covers all the latest topics and technology in this ever-evolving industry
• Contains a strong emphasis on fundamentals