Nonlinear optical waves
It is impossible to review a solid work of over 600 pages in detail and accordingly a list of chapter titles will be given and attention will be drawn to some of the most interesting matters in them. According to the preface, the authors who come from the Moscow State Engineering Physics Institute state that they will dwell on basic theory, analytical methods and non-dissipative phenomena for waves in one dimension. The book is divided into nine chapters, each chapter having an introduction to its contents and closing with a summary. The first chapter is entitled Basic Equations and provides a general introduction to the subject, paying particular attention to the Maxwell-Bloch equations. The second chapter, on coherent transient phenomena, pays particular attention to photon echoes and discusses also super flourescence and optical nutation. The third chapter deals with the inverse scattering transform method. Amongst the topics discussed therein are reflectionless potentials and scattering data. The fourth chapter is concerned with the ideas associated with self induced transparency, and involves topics such as Bäcklund transformations, polaritons and two-photon resonances. The subject matter of the fifth chapter is coherent pulse propagation. In this particular attention is paid to Kerr-type media and to the propagation of ultra-short pulses. The sixth chapter on optical solutions in fibres is a long one. In this nonlinear Schrödinger equations receive particular attention, picosecond and femtosecond solitons are considered and the concept of a vector soliton is introduced. Parametric interaction of optical waves is the subject of the seventh chapter. In this three-wave and four wave interaction is considered. Nonlinear waveguide structures is the subject of the eighth chapter. Surface waves and their dispersion relations are considered and there is a discussion of the Thirring thin films of resonant atoms in which one and two photon resonance are considered. There are also four appendices: the density matrix equations of a system in broadband thermostat, the density matrix equation for a gas medium, adiabatic following approximation, relation between exactly integrable models in resonance optics. The various chapters are followed by lists of references, the total of which is more than 900. This is a substantial work and there is much of interest in it. One difficulty in reading it is that in many cases brackets and bars in fractions have come out very faintly. It would also be very helpful if all equations were numbered. The price is very high and will be out of reach for many University libraries, and almost certainly individuals. Should a further edition be required, perhaps thought to be given to splitting it into two or three parts. There are a few ``Russisms'' which should have been edited out, but the book on the whole reads well, and it can be recommended.
scientific article; zbMATH DE number 1540709