the axial coordinate Z and effective generation of the new frequency happens only when the infinitesimal contributions generated in correspondence of each fiber section add together to form a sizeable optical power. In order to have this superposition, the term depending on t in (4.43) has to vanish SO that fixing selection rules for the frequencies where macroscopic FWM can be observed: they are all the frequencies where at least Wi appears with the opposite sign with respect to the other angular frequencies. In this case, the time dependent term in the phase matching expression vanishes with a suitable choice of Wj and the phase matching condition becomes (4.44) In order to satisfy this condition, chromatic dispersion has to be negligible. The evolution of the FWM generated waves, besides that of the waves injected at the fiber input, can be derived by solving the nonlinear wave equation. Following the method of the coupled waves equations it can be decomposed in a set of coupled wave equations, one for each wave, containing the coupling terms that derives from the nonlinear interaction. In the so-called nondepleted pump condition, that is, when the nonlinear interaction is very low and the coupling terms in the equations describing the evolution of the injected waves can be neglected, the coupled waves equations can be analytically solved. Assuming to have three waves at the fiber input, the power of the jth FWM wave is given by [23] (4.45) where Le indicates the characteristic length defined in Equation 4.36 de is the so-called degeneracy factor that is equal to 3 in case of degenerate FWM, when two interacting photons have the same frequency, and 6 in the other cases Technology for Telecommunications: Optical Fibers, Amplifiers, and Passive Devices y is the so-called nonlinear coefficient n is the FWM efficiency, that is, the parameter that represents the effectiveness of the nonlinear effect The FWM efficiency n can be written as follows [23]: (4.46) The dependence of the FWM efficiency on dispersion is cle