Fundamentals of Nonlinear Optics , Peter E.Powers, CRC Press/Taylor & Francis, Boca Raton, FL, 2011. $79.95 (311 pp.). ISBN 978-1-4200-9351-3

Nonlinear optics is usually considered a difficult subject because it relies heavily on electromagnetic theory, quantum mechanics, and advanced mathematical concepts from vector analysis, tensor algebra, symmetry, and group theory. In Fundamentals of Nonlinear Optics, Peter Powers’s rigorous but simple description of a difficult field keeps the reader’s attention throughout.

Fundamentals of Nonlinear Optics begins with a short introduction to the subject’s history and its foundational concepts. It then provides a primer on key linear optical phenomena, such as the propagation of electromagnetic waves in anisotropic media, birefringence, dispersion, and the propagation of Gaussian and near-Gaussian beams—phenomena essential for a solid understanding of nonlinear effects. In subsequent chapters, the author explains the core concepts of nonlinear-induced polarization and nonlinear susceptibility. He describes details of the second- and third-order phenomena in nonlinear optics, in which the nonlinear susceptibility is basically defined by the symmetry properties of the sample.

The author dedicates chapters 3 throughout 7 to the second-order or χ(2) phenomena, discussing details about second-harmonic generation, three-wave-mixing processes, and phase-matching and quasi-phase-matching conditions. Included in his discussion are practical designs of such modern χ(2) devices as harmonic generators, optical parametric amplifiers, and optical parametric generators; also covered are suggestions for improving the tuning capabilities, phase-matching requirements, efficiency, and other performance metrics of all those devices.

Chapters 8 and 9 refer to third-order, or χ(3), nonlinear phenomena, including wave propagation, nonlinear absorption, optical bistability, and cross-phase modulation. In particular, chapter 9, on Raman and Brillouin scattering, goes into detail about spontaneous and stimulated Raman scattering and its importance in optical-fiber amplifiers, and the chapter later explains the diffraction of light on acoustic waves. Chapter 10, the final one, deals with spatial and temporal propagation effects that result from diffraction and dispersion of light; the author obtains and solves realistic propagation equations using analytic and numerical approximations. The book ends with four appendixes that include computational programming techniques and an estimation of optical properties of common nonlinear optical crystals.

All chapters contain a list of references and large numbers of practice examples to be worked through. Among the recommended literature are other textbooks, handbooks, and carefully selected scientific communications that should be in the library of any professional or student working or studying in the field. By carefully working through the proposed problems, students will develop a sound understanding of the fundamental principles and applications. Solutions to the problems are not included, but their formulations facilitate step-by-step resolution. Some of the proposed problems require the use of numerical algorithms in their resolution, since most nonlinear optical problems of practical importance cannot be solved otherwise. Computers and advanced software are becoming essential components of the modern nonlinear optics course. The author’s remarkable use of programming techniques makes the book a good resource for instructors moving in that direction.

Some aspects of nonlinear optics, such as the quantum theory of nonlinear susceptibility and multi-photon ionization, fall beyond the scope of the book. However, the book serves perfectly for an introductory-level course for second- and third-order nonlinear optical phenomena. The author’s writing style is refreshing and original. I expect that Fundamentals of Nonlinear Optics will fast become popular among students, professors, and professionals interested in basic and applied research in the field. I intend to add it to the list of references for my nonlinear optics course and related courses that I teach.