Nonlinear optics

Cover
Nonlinear Optics
Copyright
Dedication
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
		1.2.7 Third-Harmonic Generation
		1.2.8 Intensity-Dependent Refractive Index
			Self-Focusing
		1.2.9 Third-Order Interactions (General Case)
		1.2.10 Parametric versus Nonparametric Processes
		1.2.11 Saturable Absorption
			Optical Bistability
		1.2.12 Two-Photon Absorption
		1.2.13 Stimulated Raman Scattering
	1.3 Formal Definition of the Nonlinear Susceptibility
	1.4 Nonlinear Susceptibility of a Classical Anharmonic Oscillator
		1.4.1 Noncentrosymmetric Media
		1.4.2 Miller\'s Rule
		1.4.3 Centrosymmetric Media
	1.5 Properties of the Nonlinear Susceptibility
		1.5.1 Reality of the Fields
		1.5.2 Intrinsic Permutation Symmetry
		1.5.3 Symmetries for Lossless Media
		1.5.4 Field Energy Density for a Nonlinear Medium
		1.5.5 Kleinman\'s Symmetry
		1.5.6 Contracted Notation
		1.5.7 Effective Value of d (deff)
		1.5.8 Spatial Symmetry of the Nonlinear Medium
		1.5.9 Influence of Spatial Symmetry on the Linear Optical Properties of a Material Medium
		1.5.10 Influence of Inversion Symmetry on the Second-Order Nonlinear Response
		1.5.11 Influence of Spatial Symmetry on the Second-Order Susceptibility
		1.5.12 Number of Independent Elements of χ(2)ijk ( ω3, ω2, ω1)
		1.5.13 Distinction between Noncentrosymmetric and Cubic Crystal Classes
		1.5.14 Distinction between Noncentrosymmetric and Polar Crystal Classes
		1.5.15 Influence of Spatial Symmetry on the Third-Order Nonlinear Response
	1.6 Time-Domain Description of Optical Nonlinearities
	1.7 Kramers-Kronig Relations in Linear and Nonlinear Optics
		1.7.1 Kramers-Kronig Relations in Linear Optics
		1.7.2 Kramers-Kronig Relations in Nonlinear Optics
	Problems
	References
		General References
		Further Reading on Nonlinear Optics
		Further Reading on Group Theory and Crystal Symmetry
		Suggested Further Reading on Kramers-Kronig Relations
2 Wave-Equation Description of Nonlinear Optical Interactions
	2.1 The Wave Equation for Nonlinear Optical Media
	2.2 The Coupled-Wave Equations for Sum-Frequency Generation
		2.2.1 Phase-Matching Considerations
	2.3 Phase Matching
		Angle Tuning
		Temperature Tuning
	2.4 Quasi-Phase-Matching (QPM)
	2.5 The Manley–Rowe Relations
	2.6 Sum-Frequency Generation
	2.7 Second-Harmonic Generation
		2.7.1 Applications of Second-Harmonic Generation
			Surface Nonlinear Optics
			Nonlinear Optical Microscopy
	2.8 Difference-Frequency Generation and Parametric Amplification
	2.9 Optical Parametric Oscillators
		Threshold for Parametric Oscillation
		Wavelength Tuning of an OPO
			2.9.1 Influence of Cavity Mode Structure on OPO Tuning
	2.10 Nonlinear Optical Interactions with Focused Gaussian Beams
		2.10.1 Paraxial Wave Equation
		2.10.2 Gaussian Beams
		2.10.3 Harmonic Generation Using Focused Gaussian Beams
	2.11 Nonlinear Optics at an Interface
	2.12 Advanced Phase Matching Methods
		Types of Phase Matching
		Phase Matching of Spontaneous Parametric Down Conversion (SPDC)
		Tilted-Pulse-Front Method for the Generation of THz Radiation
	Problems
	References
		General References
		Section 3: Phase-Matching
		Section 4: Quasi-Phase-Matching
		Section 7: Applications of Second-Harmonic Generation
		Section 9: Optical Parametric Oscillators
		Section 10: Nonlinear Optical Interactions with Focused Gaussian Beams
		Section 11: Nonlinear Optics at an Interface
		Recommended Textbooks on Quantum Nonlinear Optics
		Books that Treat Crystal Optics
		Recommended Further Reading on Quantum Nonlinear Optics
		Suggested Further Readings on THz Pulse Generation
3 Quantum-Mechanical Theory of the Nonlinear Optical Susceptibility
	3.1 Introduction
	3.2 Schrödinger Equation Calculation of the Nonlinear Optical Susceptibility
		3.2.1 Energy Eigenstates
		3.2.2 Perturbation Solution to Schrödinger\'s Equation
		3.2.3 Linear Susceptibility
		3.2.4 Second-Order Susceptibility
		3.2.5 Third-Order Susceptibility
		3.2.6 Third-Harmonic Generation in Alkali Metal Vapors
	3.3 Density Matrix Formulation of Quantum Mechanics
		3.3.1 Example: Two-Level Atom
	3.4 Perturbation Solution of the Density Matrix Equation of Motion
	3.5 Density Matrix Calculation of the Linear Susceptibility
		3.5.1 Linear Response Theory
	3.6 Density Matrix Calculation of the Second-Order Susceptibility
		3.6.1 χ(2) in the Limit of Nonresonant Excitation
	3.7 Density Matrix Calculation of the Third-Order Susceptibility
	3.8 Electromagnetically Induced Transparency
	3.9 Local-Field Effects in the Nonlinear Optics
		3.9.1 Local-Field Effects in Linear Optics
		3.9.2 Local-Field Effects in Nonlinear Optics
	Problems
	References
		Books on Quantum Mechanics
		Quantum-Mechanical Models of the Nonlinear Optical Susceptibility
		Further Reading on Quantum-Mechanical Models of the Nonlinear Optical Susceptibility
		Electromagnetically Induced Transparency (EIT)
		Suggested Furth Reading: Reviews of EIT
		Local-Field Effects in Nonlinear Optics
4 The Intensity-Dependent Refractive Index
	4.1 Descriptions of the Intensity-Dependent Refractive Index
	4.2 Tensor Nature of the Third-Order Susceptibility
		4.2.1 Propagation through Isotropic Nonlinear Media
	4.3 Nonresonant Electronic Nonlinearities
		4.3.1 Classical, Anharmonic Oscillator Model of Electronic Nonlinearities
		4.3.2 Quantum-Mechanical Model of Nonresonant Electronic Nonlinearities
		4.3.3 χ(3) in the Low-Frequency Limit
	4.4 Nonlinearities Due to Molecular Orientation
		4.4.1 Tensor Properties of χ(3) for the Molecular Orientation Effect
	4.5 Thermal Nonlinear Optical Effects
		4.5.1 Thermal Nonlinearities with Continuous-Wave Laser Beams
		4.5.2 Thermal Nonlinearities with Pulsed Laser Beams
	4.6 Semiconductor Nonlinearities
		4.6.1 Nonlinearities Resulting from Band-to-Band Transitions
			Free-Electron Response
			Modification of Optical Properties by Plasma Screening Effects
			Change of Optical Properties Due to Band-Filling Effects
			Change in Optical Properties Due to Band-Gap Renormalization
		4.6.2 Nonlinearities Involving Virtual Transitions
	4.7 Concluding Remarks
	Problems
	References
		General References
			Recommended Additional Reading
		Tensor Nature of the Third-Order Susceptibility
		Thermal Nonlinear Optical Effects
		Semiconductor Nonlinearities
			Recommended Additional Reading
		Concluding Remarks
5 Molecular Origin of the Nonlinear Optical Response
	5.1 Nonlinear Susceptibilities Calculated Using Time-Independent Perturbation Theory
		5.1.1 Hydrogen Atom
		5.1.2 General Expression for the Nonlinear Susceptibility in the Quasi-Static Limit
	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
		Suggested Books on Molecular Nonlinear Optics for Further Reading
		Section 5.1.  Nonlinear Susceptibility …Time-Independent Perturbation Theory
		Section 5.2. Semiempirical Models
		Section 5.3. Nonlinear Optics of Conjugated Polymers
		Section 5.4. Bond Charge Model
		Section 5.5. Nonlinear Optics of Chiral Media
		Section 5.6. Liquid Crystal Nonlinear Optics
6 Nonlinear Optics in the Two-Level Approximation
	6.1 Introduction
	6.2 Density Matrix Equations of Motion for a Two-Level Atom
		6.2.1 Closed Two-Level Atom
		6.2.2 Open Two-Level Atom
		6.2.3 Two-Level Atom with a Non-Radiatively Coupled Third Level
	6.3 Steady-State Response of a Two-Level Atom to a Monochromatic Field
	6.4 Optical Bloch Equations
		6.4.1 Harmonic Oscillator Form of the Density Matrix Equations
		6.4.2 Adiabatic-Following Limit
	6.5 Rabi Oscillations and Dressed Atomic States
		6.5.1 Rabi Solution of the Schrödinger Equation
		6.5.2 Solution for an Atom Initially in the Ground State
		6.5.3 Dressed States
		6.5.4 Inclusion of Relaxation Phenomena
	6.6 Optical Wave Mixing in Two-Level Systems
		6.6.1 Solution of the Density Matrix Equations for a Two-Level Atom in the Presence of Pump and Probe Fields
		6.6.2 Nonlinear Susceptibility and Coupled-Amplitude Equations
	Problems
	References
7 Processes Resulting from the Intensity-Dependent Refractive Index
	7.1 Self-Focusing of Light and Other Self-Action Effects
		7.1.1 Self-Trapping of Light
		7.1.2 Mathematical Description of Self-Action Effects
		7.1.3 Laser Beam Breakup into Many Filaments
			Conditions for the Occurrence of Nonlinear Beam Breakup
		7.1.4 Self-Action Effects with Pulsed Laser Beams
			Moving Focus Model
			Transient Self-Focusing
	7.2 Optical Phase Conjugation
		7.2.1 Aberration Correction by Phase Conjugation
		7.2.2 Phase Conjugation by Degenerate Four-Wave Mixing
		7.2.3 Polarization Properties of Phase Conjugation
	7.3 Optical Bistability and Optical Switching
		7.3.1 Absorptive Bistability
		7.3.2 Refractive Bistability
		7.3.3 Optical Switching
	7.4 Two-Beam Coupling
	7.5 Pulse Propagation and Temporal Solitons
		7.5.1 Self-Phase Modulation
		7.5.2 Pulse Propagation Equation
		7.5.3 Temporal Optical Solitons
	Problems
	References
		Section 7.1 Self-Focusing of Light and Other Self-Action Effect
			Suggested Additional Reading on Self-Action Effects
		Section 7.2 Optical Phase Conjugation
			Polarization Properties of Phase Conjugation
		Section 7.3 Optical Bistability
		Section 7.4 Two-Beam Coupling
		Section 7.5 Pulse Propagation and Temporal Solitons
8 Spontaneous Light Scattering and Acoustooptics
	8.1 Features of Spontaneous Light Scattering
		8.1.1 Fluctuations as the Origin of Light Scattering
		8.1.2 Scattering Coefficient
		8.1.3 Scattering Cross Section
	8.2 Microscopic Theory of Light Scattering
	8.3 Thermodynamic Theory of Scalar Light Scattering
		8.3.1 Ideal Gas
		8.3.2 Spectrum of the Scattered Light
		8.3.3 Brillouin Scattering
		8.3.4 Stokes Scattering (First Term in Eq. (8.3.36))
		8.3.5 Anti-Stokes Scattering (Second Term in Eq. (8.3.36))
		8.3.6 Rayleigh Center Scattering
	8.4 Acoustooptics
		8.4.1 Bragg Scattering of Light by Sound Waves
		8.4.2 Raman-Nath Effect
	Problems
	References
		Recommended Further Reading on Light Scattering and Acoustooptics
9 Stimulated Brillouin and Stimulated Rayleigh Scattering
	9.1 Stimulated Scattering Processes
	9.2 Electrostriction
	9.3 Stimulated Brillouin Scattering (Induced by Electrostriction)
		9.3.1 Pump Depletion Effects in SBS
		9.3.2 SBS Generator
		9.3.3 Transient and Dynamical Features of SBS
	9.4 Phase Conjugation by Stimulated Brillouin Scattering
	9.5 Stimulated Brillouin Scattering in Gases
	9.6 General Theory of Stimulated Brillouin and Stimulated Rayleigh Scattering
		9.6.1 Appendix: Definition of the Viscosity Coefficients
	Problems
	References
		Suggested Further Reading on Stimulated Light Scattering
		Stimulated Brillouin Scattering
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
		10.4.1 Dispersionless, Nonlinear Medium without Gain or Loss
		10.4.2 Medium without a Nonlinearity
		10.4.3 Stokes-Anti-Stokes Coupling in Stimulated Raman Scattering
	10.5 Coherent Anti-Stokes Raman Scattering
	10.6 Stimulated Rayleigh-Wing Scattering
		10.6.1 Polarization Properties of Stimulated Rayleigh-Wing Scattering
	Problems
	References
		Stimulated Raman Scattering
		Tensor Properties of Stimulated Raman Scattering
		Coherent Anti-Stokes Raman Scattering
		Stimulated Rayleigh-Wing Scattering
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
		11.7.1 Externally Self-Pumped Phase-Conjugate Mirror
		11.7.2 Internally Self-Pumped Phase-Conjugate Mirror
		11.7.3 Double Phase-Conjugate Mirror
		11.7.4 Other Applications of Photorefractive Nonlinear Optics
	Problems
	References
		Electrooptic Effect
		Photorefractive Effect
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
		12.5.1 Theory of Single- and Multiphoton Absorption and Fermi\'s Golden Rule
		12.5.2 Linear (One-Photon) Absorption
		12.5.3 Two-Photon Absorption
		12.5.4 Multiphoton Absorption
	Problems
	References
		Optical Damage
		Reviews of Optical Damage
		Optical Damage with Femtosecond Laser Pulses
		Multiphoton Absorption
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
		13.3.1 Self-Steepening
		13.3.2 Space-Time Coupling
		13.3.3 Supercontinuum Generation
	13.4 Intense-Field Nonlinear Optics
	13.5 Motion of a Free Electron in a Laser Field
	13.6 High-Harmonic Generation
	13.7 Tunnel Ionization and the Keldysh Model
	13.8 Nonlinear Optics of Plasmas and Relativistic Nonlinear Optics
	13.9 Nonlinear Quantum Electrodynamics
	Problem
	References
		Sections 13.1 through 13.3: Ultrafast Nonlinear Optics
		Sections 13.4 and 13.5: Intense-Field Nonlinear Optics and Motion of a Free Electron
		Section 13.6: High-Harmonic Generation
		Section 13.7: Tunnel Ionization and the Keldysh Mechanism
		Section 13.9: Nonlinear Quantum Electrodynamics
14 Nonlinear Optics of Plasmonic Systems
	14.1 Introduction to Plasmonics
	14.2 Simple Derivation of the Plasma Frequency
	14.3 The Drude Model
	14.4 Optical Properties of Gold
	14.5 Surface Plasmon Polaritons
	14.6 Electric Field Enhancement in Plasmonic Systems
	Problems
	References
		Plasma Frequency and Drude Model
		Optical Properties of Gold
		Surface Plasmon Polaritons
		Electric Field Enhancement in Plasmonic Systems
Appendices
	Appendix A The SI System of Units
		A.1 Energy Relations and Poynting\'s Theorem
		A.2 The Wave Equation
		A.3 Boundary Conditions
	Appendix B The Gaussian System of Units
	Appendix C Systems of Units in Nonlinear Optics
		C.1 Conversion between the Systems
	Appendix D Relationship between Intensity and Field Strength
	Appendix E Physical Constants
	References
Index
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