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**Nonlinear optics.**
*(English)*
Zbl 1054.78001

Boulder, CO: Westview Press (ISBN 0-8133-4118-3/pbk). x, 440 p. (2004).

The subject of Nonlinear optics, the interaction of high-intensity light with matter, is treated as a system of oscillators of light and of matter in this book.

In Chapter 1, the Introduction, some historical remarks are given. Starting from Maxwell’s equations the authors point out that several observations (e.g. photoelectric effect, radioactivity) could not be explained by the wave theory and that the corpuscular nature of light has to be taken into account. Based on these effects the rapid progress in Nonlinear optics is outlined step by step in form of an overview.

The explicit description of the theory starts in Chapter 2. The subject is the propagation of light waves in linear and weakly nonlinear (so-called Kerr) dielectrics. The nonlinear Schrödinger equation is introduced, which describes the evolution of wavepackets through a Kerr medium. The Raman and Brillouin scattering are treated in connection with the three- and four-wave interaction equations. The double refraction in isotropic media (so-called nonlinear birefringence) is introduced.

Chapter 3 discusses the role of the soliton of the nonlinear Schrödinger equation for monomode, polarizations preserving optical fibers. The use of nonlinear pulses as information bits in optical fibers communication is demonstrated. The transmission and reflection of light beams at interfaces are treated on the basis of Snell’s law. The modes of nonlinear waveguides and the shapes of the guided waves are introduced.

Compared to the previous chapters the oscillations of matter are taken into account in Chapter 4. They become active field variables and the Maxwell-Bloch and the Maxwell-Debye equations are derived, useful for lasers and delayed response in transparent materials, respectively. The Born-Oppenheimer approximation is reviewed in order to declare the simplifications in derivations made in this chapter.

Chapter 5 deals with practical applications (e.g. lasers, coherent pulse propagation, optical bistable cavities, Raman and Brillouin scattering).

Chapter 6 is about mathematical and computational methods that are used in the analysis of optics. The sections are related to the other chapters. The sine-Gordon equation and the Ginzburg-Landau equation are considered. Ideas of the perturbation theory, asymptotic expansion, multiple scales, solitons, numerical methods and the use of software packages are treated.

First of all, the well-written book is indended for students. The reader should have some knowledge in Fourier analysis, vector calculus, ordinary and partial differential equations and electromagnetic theory.

In Chapter 1, the Introduction, some historical remarks are given. Starting from Maxwell’s equations the authors point out that several observations (e.g. photoelectric effect, radioactivity) could not be explained by the wave theory and that the corpuscular nature of light has to be taken into account. Based on these effects the rapid progress in Nonlinear optics is outlined step by step in form of an overview.

The explicit description of the theory starts in Chapter 2. The subject is the propagation of light waves in linear and weakly nonlinear (so-called Kerr) dielectrics. The nonlinear Schrödinger equation is introduced, which describes the evolution of wavepackets through a Kerr medium. The Raman and Brillouin scattering are treated in connection with the three- and four-wave interaction equations. The double refraction in isotropic media (so-called nonlinear birefringence) is introduced.

Chapter 3 discusses the role of the soliton of the nonlinear Schrödinger equation for monomode, polarizations preserving optical fibers. The use of nonlinear pulses as information bits in optical fibers communication is demonstrated. The transmission and reflection of light beams at interfaces are treated on the basis of Snell’s law. The modes of nonlinear waveguides and the shapes of the guided waves are introduced.

Compared to the previous chapters the oscillations of matter are taken into account in Chapter 4. They become active field variables and the Maxwell-Bloch and the Maxwell-Debye equations are derived, useful for lasers and delayed response in transparent materials, respectively. The Born-Oppenheimer approximation is reviewed in order to declare the simplifications in derivations made in this chapter.

Chapter 5 deals with practical applications (e.g. lasers, coherent pulse propagation, optical bistable cavities, Raman and Brillouin scattering).

Chapter 6 is about mathematical and computational methods that are used in the analysis of optics. The sections are related to the other chapters. The sine-Gordon equation and the Ginzburg-Landau equation are considered. Ideas of the perturbation theory, asymptotic expansion, multiple scales, solitons, numerical methods and the use of software packages are treated.

First of all, the well-written book is indended for students. The reader should have some knowledge in Fourier analysis, vector calculus, ordinary and partial differential equations and electromagnetic theory.

Reviewer: Georg Hebermehl (Berlin)

### MSC:

78-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to optics and electromagnetic theory |

78A60 | Lasers, masers, optical bistability, nonlinear optics |