ar from Equation 4.46, since cannot be equal to zero in the presence of sizable chromatic dispersion. Approximating the propagation constants with their second-order approximation and assuming B2 independent from the wavelength, an expression of the FWM efficiency as a function of the dispersion constant can be obtained. The FWM efficiency in the higher-efficiency case (@1 # W2, W1 W2 - W3 = wj) is shown in Figure 4.7 [21] versus the spacing between adjacent injected frequencies Aw = W1 All parameters are evaluated at 1.55 um and two values of D are considered: 16ps/nm/ km (corresponding to a standard step index fiber) and 1 ps/nm/km (corresponding to a DS fiber). The dependence of the efficiency from the input field spacing and on the dispersion is clear and similar plots can be used to understand the impact of FWM in WDM systems. 4.2.8 Raman Scattering Raman scattering is the photon scattering caused by local optical phonons of the glass and in Equation 4.39 it is taken into account via the imaginary part of the third-order nonlinear susceptibility [6,7]. When a monochromatic light beam propagates in an optical fiber, spontaneous Raman scattering occurs. It transfers some of the photons to new frequencies. The scattered pho- tons may lose energy (Stokes shift) or gain energy (anti-Stokes shift). If photons at other frequencies are already present then the probability of scattering to those frequencies is D=1 ps/nm/km D = 16 ps/nm/km Aw/2n (GHz) FIGURE 4.7 FWM efficiency in the higher-efficiency case (w1 the spacing between adjacent fre- quencies All parameters are evaluated at 1.55 um and two values of D are considered: 16ps/ nm/km (corresponding to a standard step index fiber) and 1 ps/nm/km (corresponding to a DS fiber). Telecommunication Networks Frequency shift (THz) FIGURE 4.8 Raman gain spectrum in an SSMF versus the frequency shift from the pump wavelength. (After Shibate, N. et al., J. Non Cryst. Solids, 45, 115, 1981.) enhanced. This process is known as stimulated Raman scattering and rely on stimulate