" frequencies slower. For 2 > 20 the situ- ation changes substantially. Now, the "red" frequencies in the rising edge of the pulse are delayed and the "blue" frequencies at the falling edge are speeded up; consequently, the pulse width contracts. However, as the blue frequencies catch up with the red ones and overtake them, the pulse starts broadening again. This feature of the interaction of SPM with anomalous dispersion is used in soliton transmission. Figure 5.24 summarizes the interaction of SPM with fiber dispersion. [1b] Stimulated Brillouin Scattering The physical origin of Stimulated Brillouin Scattering (SBS) is the interaction between an incident optical wave and the elastic acoustic wave induced by the radiation. A threshold can be established for the onset of SBS, and it is given by (5.62) where PPol takes the value 1.5 if the polarization is completely scrambled and 1.0 otherwise; Aeff is the effective area of the mode; gB is the Brillouin (Br) gain, which is around x 10-11 m/W at 1550 nm; Leff is the effective fiber length; Afsource is the bandwidth of the incident radiation; and AfBr is the bandwidth of the SBS effect, which is approximately 20 MHz. In the worst case for source << Af Br and PPol = 1 with Aeff = 50 um2 and Leff = 20 km the threshold power is 1.3 mW. This is very low and care must be taken to enhance the thresh- old. For high-speed modulation this is not a problem. In SBS the scattered wave propagates backward and the effect appears in the receiver as a reduction of the power of the wave carrying the information. Figure 5.25 illustrates the basic features of SBS. The SBS is a narrowband effect and consequently does not interact with other waves unless they fall within its bandwidth. For this reason SBS once suppressed in individual channels is not an issue in WDM systems. Nonlinear Optical Effects in Fibers Forward-Propagating Wave with Information SBS Wave Fig. 5.25 Stimulated Brillouin scattering (SBS) effect. Fiber Length [2a] Cross-Phase Modulation The SPM discussed earlier opera