 the following coupled equations are obtained for the two opti- cal waves intensities: (4.52) In the condition of very small nonlinear effect, the Stokes intensity can be neglected in the equation for the pump and the system (4.52) can be solved exactly. Technology for Telecommunications: Optical Fibers, Amplifiers, and Passive Devices Input signal power (dBm) FIGURE 4.10 Power exiting from the far end (continuous line) and the near end (dotted line) of 13 km of DS fiber versus the input power at the near end of the fiber. Since the optical power is proportional to the optical intensity via the simple relation- ship JA = P, where the proportionality coefficient is the effective area defined in (4.37), and since the Stokes is counter-propagating with respect to the pump, the solution for the Stokes power exiting from the fiber input facet is (4.53) From Equation 4.53, it is possible to evaluate the Brillouin threshold as the pump power at which the Stokes power at the input facet is equal to the pump power at the output facet. Assuming PS(L) equal to the average spontaneous emission noise at the wavelength of 1.55 um, thus representing the case of the absence of a coherent Stokes signal at the far end fiber facet and describing the pump evolution in the nondepleted pump approximation, the Brillouin threshold can be expressed as [27] (4.54) The value of polarization factor 8 lies between 1 and 2 depending on relative polarization of pump and Stokes waves. Typically, A 22 50 um ², Le 2 20km, and gB=4x10-11 m/W for a fiber system at 1550 nm. With these values and taking 8 = 1, Pth 2 1.3mW. The threshold power becomes just dou- ble if polarization factor is taken equal to 2. When threshold is reached, the effect of stimu- lated Brillouin scattering (SBS) on the signal power is described by the Figure 4.10, where the power exiting from the far and the near end of 3km of DS fiber is plotted versus the input power at the near end of the fiber. Up to the threshold power, the transmitted power increases linearly. When scat