Nonlinear Optics -  Robert W. Boyd

Nonlinear Optics (eBook)

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2008 | 3. Auflage
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Elsevier Science (Verlag)
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Nonlinear optics is the study of the interaction of intense laser light with matter. The third edition of this textbook has been rewritten to conform to the standard SI system of units and includes comprehensively updated material on the latest developments in the field.
The book presents an introduction to the entire field of optical physics and specifically the area of nonlinear optics, covering fundamental issues and applied aspects of this exciting area.
Nonlinear Optics will have lasting appeal to a wide audience of physics, optics, and electrical engineering students, as well as to working researchers and engineers. Those in related fields, such as materials science and chemistry, will also find this book of particular interest.
* Presents an introduction to the entire field of optical physics from the perspective of nonlinear optics
* Combines first-rate pedagogy with a treatment of fundamental aspects of nonlinear optics
* Covers all the latest topics and technology in this ever-evolving industry
* Strong emphasis on the fundamentals

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.
Nonlinear optics is the study of the interaction of intense laser light with matter. The third edition of this textbook has been rewritten to conform to the standard SI system of units and includes comprehensively updated material on the latest developments in the field. The book presents an introduction to the entire field of optical physics and specifically the area of nonlinear optics, covering fundamental issues and applied aspects of this exciting area. Nonlinear Optics will have lasting appeal to a wide audience of physics, optics, and electrical engineering students, as well as to working researchers and engineers. Those in related fields, such as materials science and chemistry, will also find this book of particular interest. - Presents an introduction to the entire field of optical physics from the perspective of nonlinear optics- Combines first-rate pedagogy with a treatment of fundamental aspects of nonlinear optics- Covers all the latest topics and technology in this ever-evolving industry- Strong emphasis on the fundamentals

Front cover 1
Nonlinear Optics 4
Copyright page 5
Contents 8
Preface to the Third Edition 14
Preface to the Second Edition 16
Preface to the First Edition 18
Chapter 1. The Nonlinear Optical Susceptibility 22
1.1. Introduction to Nonlinear Optics 22
1.2. Descriptions of Nonlinear Optical Processes 25
1.3. Formal Definition of the Nonlinear Susceptibility 38
1.4. Nonlinear Susceptibility of a Classical Anharmonic Oscillator 42
1.5. Properties of the Nonlinear Susceptibility 54
1.6. Time-Domain Description of Optical Nonlinearities 73
1.7. Kramers-Kronig Relations in Linear and Nonlinear Optics 79
Problems 84
References 86
Chapter 2. Wave-Equation Description of Nonlinear Optical Interactions 90
2.1. The Wave Equation for Nonlinear Optical Media 90
2.2. The Coupled-Wave Equations for Sum-Frequency Generation 95
2.3. Phase Matching 100
2.4. Quasi-Phase-Matching 105
2.5. The Manley-Rowe Relations 109
2.6. Sum-Frequency Generation 112
2.7. Second-Harmonic Generation 117
2.8. Difference-Frequency Generation and Parametric Amplification 126
2.9. Optical Parametric Oscillators 129
2.10. Nonlinear Optical Interactions with Focused Gaussian Beams 137
2.11. Nonlinear Optics at an Interface 143
Problems 149
References 153
Chapter 3. Quantum-Mechanical Theory of the Nonlinear Optical Susceptibility 156
3.1. Introduction 156
3.2. Schrödinger Calculation of Nonlinear Optical Susceptibility 158
3.3. Density Matrix Formulation of Quantum Mechanics 171
3.4. Perturbation Solution of the Density Matrix Equation of Motion 179
3.5. Density Matrix Calculation of the Linear Susceptibility 182
3.6. Density Matrix Calculation of the Second-Order Susceptibility 191
3.7. Density Matrix Calculation of the Third-Order Susceptibility 201
3.8. Electromagnetically Induced Transparency 206
3.9. Local-Field Corrections to the Nonlinear Optical Susceptibility 215
Problems 222
References 225
Chapter 4. The Intensity-Dependent Refractive Index 228
4.1. Descriptions of the Intensity-Dependent Refractive Index 228
4.2. Tensor Nature of the Third-Order Susceptibility 232
4.3. Nonresonant Electronic Nonlinearities 242
4.4. Nonlinearities Due to Molecular Orientation 249
4.5. Thermal Nonlinear Optical Effects 256
4.6. Semiconductor Nonlinearities 261
4.7. Concluding Remarks 268
References 272
Chapter 5. Molecular Origin of the Nonlinear Optical Response 274
5.1. Nonlinear Susceptibilities Calculated Using Time-Independent Perturbation Theory 274
5.2. Semiempirical Models of the Nonlinear Optical Susceptibility 280
Model of Boling, Glass, and Owyoung 281
5.3. Nonlinear Optical Properties of Conjugated Polymers 283
5.4. Bond-Charge Model of Nonlinear Optical Properties 285
5.5. Nonlinear Optics of Chiral Media 289
5.6. Nonlinear Optics of Liquid Crystals 292
Problems 294
References 295
Chapter 6. Nonlinear Optics in the Two-Level Approximation 298
6.1. Introduction 298
6.2. Density Matrix Equations of Motion for a Two-Level Atom 299
6.3. Steady-State Response of a Two-Level Atom to a Monochromatic Field 306
6.4. Optical Bloch Equations 314
6.5. Rabi Oscillations and Dressed Atomic States 322
6.6. Optical Wave Mixing in Two-Level Systems 334
Problems 347
References 348
Chapter 7. Processes Resulting from the Intensity-Dependent Refractive Index 350
7.1. Self-Focusing of Light and Other Self-Action Effects 350
7.2. Optical Phase Conjugation 363
7.3. Optical Bistability and Optical Switching 380
7.4. Two-Beam Coupling 390
7.5. Pulse Propagation and Temporal Solitons 396
Problems 404
References 409
Chapter 8. Spontaneous Light Scattering and Acoustooptics 412
8.1. Features of Spontaneous Light Scattering 412
8.2. Microscopic Theory of Light Scattering 417
8.3 Thermodynamic Theory of Scalar Light Scattering 423
8.4. Acoustooptics 434
Problems 448
References 449
Chapter 9. Stimulated Brillouin and Stimulated Rayleigh Scattering 450
9.1. Stimulated Scattering Processes 450
9.2. Electrostriction 452
9.3. Stimulated Brillouin Scattering (Induced by Electrostriction) 457
9.4. Phase Conjugation by Stimulated Brillouin Scattering 469
9.5. Stimulated Brillouin Scattering in Gases 474
9.6. Stimulated Brillouin and Stimulated Rayleigh Scattering 476
Problems 489
References 491
Chapter 10. Stimulated Raman Scattering and Stimulated Rayleigh-Wing Scattering 494
10.1. The Spontaneous Raman Effect 494
10.2. Spontaneous versus Stimulated Raman Scattering 495
10.3. Stimulated Raman Scattering Described by the Nonlinear Polarization 500
10.4. Stokes-Anti-Stokes Coupling in Stimulated Raman Scattering 509
10.5. Coherent Anti-Stokes Raman Scattering 520
10.6. Stimulated Rayleigh-Wing Scattering 522
Problems 529
References 529
Chapter 11. The Electrooptic and Photorefractive Effects 532
11.1. Introduction to the Electrooptic Effect 532
11.2. Linear Electrooptic Effect 533
11.3. Electrooptic Modulators 537
11.4. Introduction to the Photorefractive Effect 544
11.5 Photorefractive Equations of Kukhtarev et al. 547
11.6. Two-Beam Coupling in Photorefractive Materials 549
11.7. Four-Wave Mixing in Photorefractive Materials 557
Problems 561
References 561
Chapter 12. Optically Induced Damage and Multiphoton Absorption 564
12.1. Introduction to Optical Damage 564
12.2. Avalanche-Breakdown Model 565
12.3. Influence of Laser Pulse Duration 567
12.4. Direct Photoionization 569
12.5. Multiphoton Absorption and Multiphoton Ionization 570
Problems 580
References 580
Chapter 13. Ultrafast and Intense-Field Nonlinear Optics 582
13.1. Introduction 582
13.2. Ultrashort Pulse Propagation Equation 582
13.3. Interpretation of the Ultrashort-Pulse Propagation Equation 588
13.4. Intense-Field Nonlinear Optics 592
13.5. Motion of a Free Electron in a Laser Field 593
13.6. High-Harmonic Generation 596
13.7. Nonlinear Optics of Plasmas and Relativistic Nonlinear Optics 600
13.8. Nonlinear Quantum Electrodynamics 604
Problem 607
References 607
Appendices 610
Appendix A. The SI System of Units 610
Further reading 617
Appendix B. The Gaussian System of Units 617
Further reading 621
Appendix C. Systems of Units in Nonlinear Optics 621
Appendix D. Relationship between Intensity and Field Strength 623
Appendix E. Physical Constants 624
Index 626

Chapter 1 The Nonlinear Optical Susceptibility

1.1. Introduction to Nonlinear Optics


Nonlinear optics is the study of phenomena that occur as a consequence of the modification of the optical properties of a material system by the presence of light. Typically, only laser light is sufficiently intense to modify the optical properties of a material system. The beginning of the field of nonlinear optics is often taken to be the discovery of second-harmonic generation by Franken et al. (1961), shortly after the demonstration of the first working laser by Maiman in 1960.* Nonlinear optical phenomena are “nonlinear” in the sense that they occur when the response of a material system to an applied optical field depends in a nonlinear manner on the strength of the optical field. For example, second-harmonic generation occurs as a result of the part of the atomic response that scales quadratically with the strength of the applied optical field. Consequently, the intensity of the light generated at the second-harmonic frequency tends to increase as the square of the intensity of the applied laser light.

In order to describe more precisely what we mean by an optical nonlinear-ity, let us consider how the dipole moment per unit volume, or polarization (t), of a material system depends on the strength (t) of an applied optical field.* In the case of conventional (i.e., linear) optics, the induced polarization depends linearly on the electric field strength in a manner that can often be described by the relationship

where the constant of proportionality χ(1) is known as the linear susceptibility and ε0 is the permittivity of free space. In nonlinear optics, the optical response can often be described by generalizing Eq. (1.1.1) by expressing the polarization (t) as a power series in the field strength (t) as

The quantities χ(2) and χ(3) are known as the second- and third-order nonlinear optical susceptibilities, respectively. For simplicity, we have taken the fields (t) and (t) to be scalar quantities in writing Eqs. (1.1.1) and (1.1.2). In Section 1.3 we show how to treat the vector nature of the fields; in such a case χ(1) becomes a second-rank tensor, χ(2) becomes a third-rank tensor, and so on. In writing Eqs. (1.1.1) and (1.1.2) in the forms shown, we have also assumed that the polarization at time t depends only on the instantaneous value of the electric field strength. The assumption that the medium responds instantaneously also implies (through the Kramers-Kronig relations) that the medium must be lossless and dispersionless. We shall see in Section 1.3 how to generalize these equations for the case of a medium with dispersion and loss. In general, the nonlinear susceptibilities depend on the frequencies of the applied fields, but under our present assumption of instantaneous response, we take them to be constants.

We shall refer to as the second-order nonlinear polarization and to as the third-order nonlinear polarization. We shall see later in this section that physical processes that occur as a result of the second-order polarization (2) tend to be distinct from those that occur as a result of the third-order polarization (3). In addition, we shall show in Section 1.5 that second-order nonlinear optical interactions can occur only in noncentrosymmetric crystals—that is, in crystals that do not display inversion symmetry. Since liquids, gases, amorphous solids (such as glass), and even many crystals display inversion symmetry, χ(2) vanishes identically for such media, and consequently such materials cannot produce second-order nonlinear optical interactions. On the other hand, third-order nonlinear optical interactions (i.e., those described by a χ(3) susceptibility) can occur for both centrosymmetric and noncentrosymmetric media.

We shall see in later sections of this book how to calculate the values of the nonlinear susceptibilities for various physical mechanisms that lead to optical nonlinearities. For the present, we shall make a simple order-of-magnitude estimate of the size of these quantities for the common case in which the non-linearity is electronic in origin (see, for instance, Armstrong et al., 1962). One might expect that the lowest-order correction term (2) would be comparable to the linear response (1) when the amplitude of the applied field is of the order of the characteristic atomic electric field strength , where —e is the charge of the electron and is the Bohr radius of the hydrogen atom (here is Planck’s constant divided by 2π, and m is the mass of the electron). Numerically, we find that Eat = 5.14 × 1011 V/m.* We thus expect that under conditions of nonresonant excitation the second-order susceptibility χ(2) will be of the order of χ(1)/Eat. For condensed matter χ(1) is of the order of unity, and we hence expect that χ(2) will be of the order of 1/Eat, or that

Similarly, we expect χ(3) to be of the order of χ(1)/E2at, which for condensed matter is of the order of

These predictions are in fact quite accurate, as one can see by comparing tnese values with actual measured values of χ(2) (see, for instance, Table 1.5.3) and χ(3) (see, for instance, Table 4.3.1).

For certain purposes, it is useful to express the second- and third-order susceptibilities in terms of fundamental physical constants. As just noted, for condensed matter χ(1) is of the order of unity. This result can be justified either as an empirical fact or can be justified more rigorously by noting that χ(1) is the product of atomic number density and atomic polarizability. The number density N of condensed matter is of the order of (a0)−3, and the nonresonant polarizability is of the order of (a0)3. We thus deduce that χ(1) is of the order of unity. We then find that χ(2) (4π ε0)34/m2e5 and χ(3) (4π ε0)68/m4e10. See Boyd (1999) for further details.

The most usual procedure for describing nonlinear optical phenomena is based on expressing the polarization (t) in terms of the applied electric field strength (t), as we have done inEq. (1.1.2). The reason why the polarization plays a key role in the description of nonlinear optical phenomena is that a time-varying polarization can act as the source of new components of the electromagnetic field. For example, we shall see in Section 2.1 that the wave equation in nonlinear optical media often has the form

where n is the usual linear refractive index and c is the speed of light in vacuum. We can interpret this expression as an inhomogeneous wave equation in which the polarization NL associated with the nonlinear response drives the electric field . Since ∂2NL/∂t2 is a measure of the acceleration of the charges that constitute the medium, this equation is consistent with Larmor’s theorem of electromagnetism which states that accelerated charges generate electromagnetic radiation.

It should be noted that the power series expansion expressed by Eq. (1.1.2) need not necessarily converge. In such circumstances the relationship between the material response and the applied electric field amplitude must be expressed using different procedures. One such circumstance is that of resonant excitation of an atomic system, in which case an appreciable fraction of the atoms can be removed from the ground state. Saturation effects of this sort can be described by procedures developed in Chapter 6. Even under nonreso-nant conditions, Eq. (1.1.2) loses its validity if the applied laser field strength becomes comparable to the characteristic atomic field strength Eat, because of strong photoionization that can occur under these conditions. For future reference, we note that the laser intensity associated with a peak field strength of Eat is given by

We shall see later in this book (see especially Chapter 13) how nonlinear optical processes display qualitatively distinct features when excited by such super-intense fields.

1.2. Descriptions of Nonlinear Optical Processes


In the present section, we present brief qualitative descriptions of a number of nonlinear optical processes. In addition, for those processes that can occur in a lossless medium, we indicate how they can be described in terms of the nonlinear contributions to the polarization described by Eq. (1.1.2).* Our motivation is to provide an indication of the variety of nonlinear optical phenomena that can occur. These interactions are described in greater detail in later sections of this book. In this section we also introduce some notational conventions and some of the basic concepts of nonlinear optics.

FIGURE 1.2.1 (a) Geometry of second-harmonic generation, (b) Energy-level diagram describing second-harmonic generation.

1.2.1 Second-Harmonic Generation


As an example of a nonlinear optical interaction, let us consider the process of second-harmonic generation, which is illustrated schematically in Fig. 1.2.1. Here a laser beam whose electric field strength is represented as

is incident upon a crystal for which the second-order susceptibility χ(2) is nonzero. The nonlinear...

Erscheint lt. Verlag 13.5.2008
Co-Autor Debbie Prato
Sprache englisch
Themenwelt Mathematik / Informatik Mathematik
Naturwissenschaften Physik / Astronomie
Technik Elektrotechnik / Energietechnik
ISBN-10 0-08-048596-0 / 0080485960
ISBN-13 978-0-08-048596-6 / 9780080485966
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