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Solitons in optical communications. (English) Zbl 0840.35092

Oxford Series in Optical and Imaging Sciences. 7. Oxford: Clarendon Press. xiv, 320 p. (1995).
This book is a fundamental monograph which summarizes recent theoretical and experimental results on use of solitons for long-haul data transmission by means of nonlinear optical fibers. The solitons are self-sustained stable localized pulses of light, which exist due to a balance between the linear dispersion and nonlinear self-attraction of light in the fiber. The balance is possible in the case when the mean wave length of the carrier electromagnetic wave belongs to the spectral region in which the dispersion is negative, i.e., the fiber-guided electromagnetic waves with larger frequencies have a larger group velocity. The self-attracting nonlinearity is produced by the so-called Kerr effect in the silica. In the lowest approximation, evolution of a complex envelope of the electromagnetic field in the fiber is governed by the nonlinear Schrödinger (NLS) equation, which is a celebrated equation amenable to an exact solution by means of the inverse scattering transform. However, light propagation in real fibers is complicated by various factors, the most important of which being dissipative losses. The losses can be compensated by periodically reshaping the solitons by means of the Erbium-doped fiber amplifiers, which however, gives rise to another fundamental problem – noise generation. The solitons, interacting with the noise, will undergo an effective random walk (jitter), which is expected to randomly change temporal delays between the solitons and thus to lead to loss of the information coded in terms of the delays. This effect, in turn, may be suppressed by means of specially tuned optical filters.
In the book, the authors present systematic analysis of these and other physical effects, based, chiefly, on various forms of the perturbed NLS equation (or coupled NLS equations; the latter case is very important for description of effects of the light polarization). The analysis is based on a combination of analytical and numerical methods. In particular, the authors develop their own method based on the guiding-center approximation for soliton propagation in a very long fiber with periodic reshaping, which is a most fundamental approach to this problem for the so-called picosecond solitons (i.e., not extremely short ones). The authors are well-known leaders of research in the field of the nonlinear guided light propagation. In particular, A. Hasegawa was, together with F. Tappert, a coauthor of a theoretical paper in which the optical solitons were first predicted in 1973; their first experimental observation was reported in 1980.

MSC:

35Q51 Soliton equations
35Q55 NLS equations (nonlinear Schrödinger equations)
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
94A05 Communication theory
78-02 Research exposition (monographs, survey articles) pertaining to optics and electromagnetic theory
78A60 Lasers, masers, optical bistability, nonlinear optics
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