nergy, hv3 and hv4. Nonlinear Optical Transmission The FWM process can be regarded in a number of equivalent ways. One of them is as a nonlinear scattering process in which there is momentum conservation that can be expressed in terms of the fiber's propagation constants at the four participating frequencies: (6.37) By recalling that the phase change experienced by a guided wave is the product of the propagation constant and the fiber length, L, it is clear that equation 6.37 is the phase-match- ing condition for the FWM process. The participating frequencies are related by the energy conservation condition: (6.38) When many channel frequencies are present, large numbers of "mixing products" are generated that satisfy equation 6.38. The process is complicated by the fact that some of these products lie on top of the channel frequencies and others do not. Moreover, the fre- quencies that create the FWM (V1) V4 in equation 6.38) do not all need to be distinct. When two of them are identical, we have "degenerate FWM," in which only two new fre- quencies are generated. A central requirement for FWM is the condition necessary for the phase matching. FWM can only occur efficiently if the fiber's chromatic dispersion allows equation 6.37 to be satisfied (at least approximately). Therefore, FWM is most efficient (and thus most prob- lematic) when operating at or near the wavelength of zero dispersion. When there is nonzero dispersion, the channels "walk off" from each other but their spatial overlap increases as |D| approaches zero. For the same reason, when the frequency separations of the channels are small they travel at similar velocities in the fiber, which increases the interactions between them. FWM depends on the presence of at least two channels for the degenerate interaction or three for the nondegenerate case; in all circumstances it has a power-cubed dependence and consequently is sensitive to the launched channel powers. The magnitude of the mixing products increases with the fiber's effective length, and th