nly other possible direction in guided propagation is I = IT that represents backward direction and gives the maximum shift. The backward Stokes shift can be evalu- ated from Equation 4.48 obtaining (4.50) where n is the effective mode index, that is, the ratio between the light speed in vacuum and the mode group velocity. Telecommunication Networks Frequency shift (GHz) FIGURE 4.9 Brillouin gain spectra at pump wavelength 1.5251 mm for a silica-core fiber (a), a depressed-cladding fiber (b), and a DS fiber (c). (After Nikles, M. et al., J. Lightwave Technol., 15, 1842, 1997.) The dependence of gain on frequency can be described evaluating the Brillouin gain spectrum. The finite life time TB of acoustic phonons is the cause of the frequency depen- dence of the gain and of the small spectral width of the gain spectrum. Solving the coupled wave equations of the input optical wave, the Stokes wave, and the acoustic wave, the following expression can be obtained for the Brillouin gain gB (4.51) The peak value of the Brillouin gain occurs at W=WB. The gain 8B0 depends on many param- eters like concentration of dopants in the fiber, inhomogeneous distribution of dopants, and the electrostrictive coefficient. Figure 4.9 describes the Brillouin gain spectra at pump wavelength 1.525 mm for a silica-core fiber, a depressed-cladding fiber, and a DS fiber. The inhomogeneous distribution of germania within the core of the depressed-cladding fiber used for the experiment is responsible for the double peak in the Brillouin gain spec- trum of the figure, while difference in Brillouin shift among various fibers is due to the different percentage of germania in the core. Exploiting the expression of the Brillouin gain, it is possible to develop a simple model of the evolution of the pump and Stokes wave intensities during propagation. As a matter of fact, separating the equation for the pump and the equation for the Stokes from the general wave equation and applying the rotating wave and the slowly varying envelope approximations,