Nonlinear Fiber Optics - 4 ed. Agrawal

18 Chapter 1. Introduction
diameter so that w 0 is reduced [97]. It is also possible to use nonlinear materials for
which n 2 is larger than silica. Optical fibers made with lead silicate glasses have n 2
values larger by about a factor of ten [98]. Even larger values (n 2 = 4.2×10 −18 m 2 /W)
have been measured in chalcogenide and other nonsilica fibers [99]. Such fibers are
attracting attention and may become important for nonlinear fiber optics [100]–[104].
1.4 Overview
This book is intended to provide a comprehensive account of the nonlinear phenomena
in optical fibers. Broadly speaking, Chapters 1–3 provide the background material and
the mathematical tools needed for understanding the various nonlinear effects. Chapters
4–7 discuss the nonlinear effects that lead to spectral and temporal changes in an
optical wave without changing its energy. Chapters 8–12 consider the nonlinear effects
that generate new optical waves through an energy transfer from the incident waves.
The applications of nonlinear fiber optics are not covered fully as a separate volume is
devoted to them [105].
Chapter 2 provides the mathematical framework needed for a theoretical understanding
of the nonlinear phenomena in optical fibers. Starting from Maxwell’s equations,
the wave equation in a nonlinear dispersive medium is used to discuss the fiber
modes and to obtain a basic propagation equation satisfied by the amplitude of the
pulse envelope. The procedure emphasizes the various approximations made in the
derivation of this equation. The numerical methods used to solve the basic propagation
equation are then discussed with emphasis on the split-step Fourier method, also
known as the beam-propagation method.
Chapter 3 focuses on the dispersive effects that occur when the incident power and
the fiber length are such that the nonlinear effects are negligible. The main effect of
GVD is to broaden an optical pulse as it propagates through the fiber. Such dispersioninduced
broadening is considered for several pulse shapes with particular attention
paid to the effects of the frequency chirp imposed on the input pulse. The higher-order
dispersive effects, important near the zero-dispersion wavelength of fibers, are also
discussed.
Chapter 4 considers the nonlinear phenomenon of SPM occurring as a result of the
intensity dependence of the refractive index. The main effect of SPM is to broaden
the spectrum of optical pulses propagating through the fiber. The pulse shape is also
affected if SPM and GVD act together to influence the optical pulse. The features of
SPM-induced spectral broadening with and without the GVD effects are discussed in
separate sections. The higher-order nonlinear and dispersive effects are also considered
in this chapter.
Chapter 5 is devoted to the study of optical solitons, a topic that has drawn considerable
attention because of its fundamental nature as well as potential applications
for optical fiber communications. The modulation instability is considered first to emphasize
the importance of the interplay between the dispersive and nonlinear effects
that can occur in the anomalous-GVD regime of optical fibers. The fundamental and
higher-order solitons are then introduced together with the inverse scattering method
used to solve the nonlinear Schrödinger equation. Dark solitons are also discussed