Thus, if we have to evaluate the pulse broadening for a certain fiber length L, we have to multiply and divide for the square of the length of the single piece lj of fiber and make the limit N 0 in such a way that N1; L. By calculating the limit the following relation is obtained OAT = DPMDVL (4.31) where the DPMD is the PMD parameter and it is evident that, due to its statistical nature the pulse broadening due to PMD increases with the square root of the fiber length. The same result can be derived from a statistical approach on the Jones matrix (or on the equivalent representation in the Stokes space). A statistical polarization dispersion theory has been carried out both in the Jones and in the Stokes space [13,14] and a very elegant relationship has been developed between the two approaches based on the use of the o spin matrixes [15]. The rigorous statistical theory arrives at the conclusion that, considering a very large ensemble of macroscopically identical fibers, the PSPs of every fiber piece are different. A statistical average of the delay can be done considering the link as a cascade of a large number of identical pieces and studying polarization evolution in this case. The propagation along one piece of fiber generates a dispersion given by Equation 4.29, while the overall propagation, can be viewed as a random walk [14,15]. Due to the properties of the random walk, the standard deviation of the propagation time depends on the square root of the number of jumps. Since the jumps are equally probable in every fiber piece, depending on the probability on the fiber length L, the aver- age pulse broadening 'Ave evaluated as time delay standard deviation, is given exactly by Equation 4.31. Telecommunication Networks 4.2.6 Nonlinear Propagation in Optical Fibers Even if the optical power launched in a fiber transmission system is not huge, the core radius is SO small that it is not difficult to generate SO high fields that they change the equi- librium of the dielectric composing the fiber [6,7]. In this c