s We have seen that SPM, XPM, and FWM all depend on the effective length of the transmis- sion fiber, as given by equation 6.36. However, equation 6.35 applies when one or more signals are launched into a single span of length L. In the section on the Friis cascade formula (and with reference to Figure 6.10) we addressed the question of whether the noise figure of a point-to-point system is better with a large number of low-gain amplifiers or a small number of high-gain amplifiers. By using the effective length, we can do the same for accu- mulated nonlinear crosstalk. We assume that there are no interactions between the amplifier noise and the nonlinear effects in the fiber. (In particular, we ignore a process called "modu- lation instability" [Agrawal, 2001]). Equation 6.36 can then be adapted for a chain of N amplified fiber spans, in which the objective is to obtain net end-to-end power transparency, as shown in Figure 6.10. Leff becomes Leff exp(-aL/N)] (6.40) Equation 6.40 assumes for simplicity that all of the system's fiber has the same loss coefficient, a. It is plotted in Figure 6.31, in which we use the same values of L and a as in Fig. 6.31 Effective length for nonlinear optical effects as a function of the number of amplified segments. System physical length = 500 km; fiber loss = 0.2 dB/km. Each point represents a system that conforms to the requirements illustrated in Figure 6.10. Number of Amplifiers (N) Chapter 6 Optical Fiber Transmission Figure 6.11. We see that Leff (and hence the crosstalk) increases with the number of amplified spans. The straightforward reason is that the amplifiers maintain the signal power at a rela- tively high value throughout the system. Therefore, best performance requires a relatively small number of high-gain amplifiers spaced far apart. The messages from Figures 6.11 and 6.31 are in conflict. The largest optical SNR is pro- vided by using an amplifier strategy that maintains the signal power at a high level. In contrast, the lowest nonlinear crosstalk is achieved b