y modeled by writing an NLSE for each channel and including the cross-modulation terms that are characteristic of the effect. XPM occurs because the intensity dependence of the refractive index applies to every propagating wave in the fiber. Consequently, each channel modulates the phase of the others, without transferring power between them. XPM is always accompanied by SPM, but its influence via the intensity-dependent refractive index is twice as great in the ideal case when a pair of interacting channels are copolarized. Owing to its influence via the intensity-dependent refractive index, XPM is most pro- nounced in fibers with small effective areas and when the channel powers are high. These features can be seen in equation 6.35. Moreover, the phase shift imposed by XPM is directly proportional to the effective fiber length, as given by equation 6.36. XPM also depends on the spatial overlap of the pulses of the different channels as they travel along the fiber. Therefore, assuming that there is good bit sequence scrambling to eliminate long strings of 1s, the channels "walk off" from each other when there is nonzero chromatic dispersion (of either positive or negative sign). For this reason, (1) the nonlinear phase shift due to XPM is lower in nonzero-dispersion fibers and (2) the extent of the walk-off depends on the channel spacing. Thus, XPM is more marked in very dense WDM operation. Four-Wave Mixing A crucial nonlinear optical effect in WDM systems is Four-Wave Mixing (FWM). We saw that XPM causes each channel to modulate the others without power exchanges. In contrast, FWM does cause power transfer-from each channel to some of the others and/or from each channel to frequencies that are not occupied by channels. In common with the other nonlinear effects, FWM results from the nonlinear response of bound electrons in the fiber's glass, but it differs because it is a parametric process that requires the presence of phase matching. In general, two photons of energy, hv1 and hv2, create two new photons of e