Chapter 7 - Cross-phase modulation

Abstract

When two or more optical fields having different wavelengths propagate simultaneously inside a fiber, they interact with each other through cross-phase modulation (XPM). The XPM-induced coupling among multiple optical fields gives rise to a number of interesting nonlinear effects in optical fibers. The coupling between two fields of different wavelengths is considered in Section 7.1, where a set of two coupled nonlinear Schrödinger equations is derived, assuming that each wave maintains its state of polarization. These equations are used in Section 7.2 to discuss how the XPM affects the phenomenon of modulation instability. Similar to the analysis in Section 6.4, this instability can occur even in the normal-dispersion regime of an optical fiber. Section 7.3 focuses on soliton pairs whose members support each other through XPM. The effects of XPM on the shape and the spectrum of copropagating ultrashort pulses are described in Section 7.4. Several applications of XPM-induced coupling in optical fibers are discussed in Section 7.5. A vector theory of XPM is developed in Section 7.6 and is used to discuss several new effects such as polarization-dependent spectral broadening, pulse trapping, and optical wave breaking. Section 7.7 extends this theory to the case of birefringent fibers. A pump–probe configuration is used to reveal that random changes in the birefringence of a fiber along its length lead to the phenomenon of intrapulse depolarization.