nd SO by equation 6.35 the peak experiences greater nonlinear phase delays. In other words, each channel under- goes a phase modulation that is induced by its own intensity (Bayvel & Killey, 2002). For this reason, the effect is called "Self-Phase Modulation" (SPM). In terms of the wavelength domain, SPM creates chirped pulses. It occurs whether operation is single channel or WDM, and it follows from equation 6.35 that it is greatest when the launched signal powers are high and in fibers with a small effective area. Chapter 6 Optical Fiber Transmission An influence that is not apparent from equation 6.35 is that of chromatic dispersion. When both the dispersion and its slope are negligible (e.g., when operating at 20 in a low- dispersion-slope fiber) and we use direct detection, SPM has no influence on the system's BER. The phase-insensitive nature of the optical-to-electrical bit conversion is not affected by the chirped pulses. However, there is a more complicated interaction between the phase changes resulting from SPM and nonzero values of fiber dispersion. The overall influence depends on the sign of the dispersion and causes pulse broadening when D is negative (the normal dispersion region) but causes pulse narrowing when D is positive (the anomalous dispersion region). When the pulses broaden beyond their own bitslots there is an increase in the BER. The overall behavior is described mathematically by the "nonlinear Schrödinger equation" (NLSE), which is a partial differential equation in the length and time domains that is for- mulated in terms of complex electric fields to account for both phase and amplitude changes. The details of the NLSE are outside the scope of this chapter, but they can be found in Agrawal (2001) and Butcher and Cotter (1990), for example. Cross-Phase Modulation Other nonlinear phenomena occur in WDM operation because the channels can interact in many ways. An important contributor is called "Cross-Phase Modulation" (XPM), and its influence on the pulse streams can be mathematicall