 [17] (compare Chapter 9, Ultra Long Haul 100 Gbit/s systems). If nonlinear polarization evolution can be neglected, the third term can be simplified introducing a scalar third-order susceptibility, SO that (4.33) rewrites (4.34) x(3) is a complex term, whose real part XL causes the Kerr effect and whose imaginary part x(3) causes the Raman effect. A typical value of the real part of is reported in Table 4.1. The presence of a nonlinear part of the susceptibility implies the dependence of the refraction index on the propagating field intensity I. In particular, from the definition of the diffraction index, the following equation is derived: (4.35) From what we have seen up to now, it is evident that nonlinear effect is a distributed cause of modification of the input pulses and it is more and more effective increasing the trans- mission fiber length. However, by increasing the transmission length, attenuation tends to decrease the non- linear contribution to the index, which is proportional to the local field intensity. On the other hand, increasing the dimension of the mode, the peak intensity decreases and the nonlinear effect should be less effective. It is thus intuitive that some characteristic length has to exist, depending on fiber attenuation, mode area, and launched power, such that when the transmitted signal goes beyond this characteristic length, it is SO attenuated that the nonlinear effect is no more effective. Telecommunication Networks Let us define an effective length Le such that the overall optical power present along the link is equal to the injected power multiplied by the characteristic length. The definition can be converted in a simple equation for L that reads P = whose solu- tion is (4.36) where L is the fiber link length. If the fiber length is much greater than 1/a, Le results to be of the order of 1/a, that is about 20 km in standard transmission fibers. Equation 4.36 is a pure empirical definition, but provides a useful idea of what is the fiber length causing relevant nonlinear effe