Nonlinear Fiber Optics - 4 ed. Agrawal

Chapter 5
Optical Solitons
A fascinating manifestation of the fiber nonlinearity occurs through optical solitons,
formed as a result of the interplay between the dispersive and nonlinear effects. The
word soliton refers to special kinds of wave packets that can propagate undistorted
over long distances. Solitons have been discovered in many branches of physics. In
the context of optical fibers, not only are solitons of fundamental interest but they
have also found practical applications in the field of fiber-optic communications. This
chapter is devoted to the study of pulse propagation in optical fibers in the regime in
which both the group-velocity dispersion (GVD) and self-phase modulation (SPM) are
equally important and must be considered simultaneously.
The chapter is organized as follows. Section 5.1 considers the phenomenon of modulation
instability and shows that propagation of a continuous-wave (CW) beam inside
optical fibers is inherently unstable because of the nonlinear phenomenon of SPM and
leads to formation of a pulse train in the anomalous-dispersion regime of optical fibers.
Section 5.2 discusses the inverse-scattering method and uses it to obtain soliton solutions
of the underlying wave-propagation equation. The properties of the fundamental
and higher-order solitons are considered in this section. Section 5.3 is devoted to other
kinds of solitons forming in optical fibers, with emphasis on dark solitons. Section 5.4
considers the effects of external perturbations on solitons. Perturbations discussed include
fiber losses, amplification of solitons, and noise introduced by optical amplifiers.
Higher-order nonlinear effects such as self-steepening and intrapulse Raman scattering
are the focus of Section 5.5.
5.1 Modulation Instability
Many nonlinear systems exhibit an instability that leads to modulation of the steady
state as a result of an interplay between the nonlinear and dispersive effects. This phenomenon
is referred to as the modulation instability and it was studied during the 1960s
in such diverse fields as fluid dynamics [1], nonlinear optics [2]–[4] and plasma physics
[5]–[7]. In the context of optical fibers, modulation instability requires anomalous dispersion
and manifests itself as breakup of the CW or quasi-CW radiation into a train
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