o be equal to zero. Let us consider the slowly varying envelope of the field in Equation 4.8. To simplify the notation, it is useful to eliminate on both sides of Equation 4.8 the transversal field shape and to write k(a)) (4.20) ax(0,00x (4.21) ay(0,w)y where p is the polarization vector. Technology for Telecommunications: Optical Fibers, Amplifiers, and Passive Devices If the input field is a PSP, by definition the first-order derivative of the output field has to be zero. Deriving Equation 4.8 and equaling the result to zero, the following equation is obtained: (4.22) where (4.23) Taking into account that the Jones matrix is unitary, it is easy to recognize that Equation 4.22 always has two solutions, which are the fiber PSPs and whose coordinate expression is easy to evaluate solving Equation 4.22. This procedure demonstrates that, for a given fiber piece, there exist two orthogonal input polarization states, called PSPs that characterize the polarization behavior of the fiber. In particular, if a field is launched into the fiber along one of the PSPs, the output polarization does not change, at least at first order, changing W. This means that a finite duration pulse injected in the fiber along a PSPs does not experiment widening due to Since a higher-order dependence of the PSP output polarization on the angular fre- quency exists, if the bandwidth of the input signal rises above a certain value, the PSP output polarization is no more W independent and the concept of PSPs becomes quite useless. The PSPs bandwidth is generally on the order of 100 GHz [10]; thus, it is quite larger than the bandwidth of normal modulated signals, but for modulation at 100 Gbit/s. In this case, if pure on-off modulation is used, PSPs probably cannot be used and some other means have to be adopted to describe polarization evolution. Even if the PSP approximation can be used, the expression of the PSPs depends on the elements of the Jones matrix and thus slowly changes with time due to the change of the random birefringence [11].