e <t> is the average half width at half maximum of the output pulse 02 is the variance of the half width at half maximum of the output pulse as defined in Equation 4.29 Looking at Figure 9.11, it results that there is quite a difference between launching the input pulse along the worst and along the best polarization state. Thus, a way to attenuate Normalized pulse broadening factor Worst Average FIGURE 9.11 Dependence of the variance of the pulse width at the output of a PMD affected fiber on the launch polarization state: best, average and worst cases are shown. (After Sunnerud, H. a=<T>/T0 et al., IEEE Photon. Technol. Lett., 12(1), 50, 2000.) Telecommunication Networks the penalty due to PMD via the elimination of the worst cases is simply to apply a fast random polarization scrambling. If the polarization scans almost all the possible states during a bit period, the pulse spreading will be, in a very first approximation, always the average one and the worst cases will be avoided. In order to evaluate the effectiveness of this method, let us image that the outage prob- ability is PO = 10-3 in the absence of fast polarization scrambling and that, in order to avoid mixing of the PMD effect with self-phase modulation (SPM), we will introduce periodic scrambling along a 300 km long line at 100 Gbit/s with a PMD of 0.1 ps/km ¹/2 (see Figure 9.11). The effect on the outage probability of periodic polarization scrambling via equally spaced scramblers placed along the line is shown in Figure 9.12 versus the number of scramblers [8]. Polarization scrambling technique is quite effective in reducing penalty fluctuations due to the random nature of the PMD, with the additional advantage of being able to process a whole WDM comb without demodulation, but while the bit rate increases, it is more and more difficult to perform a perfect scrambling, that is, scramble at a SO high speed that almost all the polarizations states are traversed during the bit time. Let us imagine that the scrambling speed is not sufficient, in par