Nonlinear Fiber Optics - 4 ed. Agrawal

Chapter 6
Polarization Effects
As discussed in Section 2.3, a major simplification made in the derivation of the nonlinear
Schrödinger (NLS) equation consists of assuming that the polarization state of
the incident light is preserved during its propagating inside an optical fiber. This is
not really the case in practice. In this chapter we focus on the polarization effects
and consider the coupling between the two orthogonally polarized components of an
optical field induced by the nonlinear phenomenon known as cross-phase modulation
(XPM). The XPM is always accompanied with self-phase modulation (SPM) and can
also occur between two optical fields of different wavelengths. The nondegenerate case
involving different wavelengths is discussed in Chapter 7.
The chapter is organized as follows. The origin of nonlinear birefringence is discussed
first in Section 6.1 and is followed by the derivation of a set of two coupled
NLS equations that describes evolution of the two orthogonally polarized components
of an optical field. The XPM-induced nonlinear birefringence has several practical
applications discussed in Section 6.2. The next section considers nonlinear polarization
changes with focus on polarization instability. Section 6.4 is devoted to the vector
modulation instability occurring in birefringent fibers. In contrast with the scalar
case discussed in Section 5.1, the vector modulation instability can occur even in the
normal-dispersion regime of a birefringent fiber. Section 6.5 considers the effects of
birefringence on solitons. The last section focuses on polarization-mode dispersion
(PMD) occurring in fibers with randomly varying birefringence along their length and
its implications for lightwave systems.
6.1 Nonlinear Birefringence
As mentioned in Section 2.2, even a single-mode fiber, in fact, supports two orthogonally
polarized modes with the same spatial distribution. The two modes are degenerate
in an ideal fiber (maintaining perfect cylindrical symmetry along its entire length) in
the sense that their effective refractive indices, n x and n y , are identical. In practice, all
fibers exhibit some modal birefringence (n x ≠ n y ) because of unintentional variations
in the core shape and anisotropic stresses along the fiber length. Moreover, the de-
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