 to remember the convention we have already introduced in Chapter 5 to evaluate the noise power of amplified systems. We define a unilateral power spectral density as S(@) = hw GNF where W is the carrier angular frequency. Since the noise factor is involved in the expression of the noise power spectral density instead of the population inversion, the noise power is obtained by multi- plying it by the unilateral optical bandwidth Bo If the signal spectrum is mainly contained in the angular frequency interval (@c - and in the symmetric on the negative W axis, Bo is defined as Bo=wm/2r. The signal at the end of the chain can be written as (6.49) where ON and sup represent casual polarization vectors N is the in-line amplifiers' number SO that the overall number of amplifiers is N+2 The transmitted field intensity Ek(t) contains the information. The indexes j and V run over the number N of amplifiers and the index k over the number No of WDM channels. Due to the hypothesis that every amplifier compensates exactly the loss of the previous span, we can set (6.50) thus greatly simplifying expression (6.49). Moreover, from the consideration that all the ASE processes are independent since they come from different amplifiers, it results that the noise power is simply the sum of the ASE noise powers generated by each amplifier of the chain and the same holds for the overall noise figure, SO that (6.51) Starting from Equation 6.51, it is possible to optimize the amplifiers span, that is, to set the optimum value of N once given the amplifier noise characteristics and the link length L. To do that, it is necessary to fix the bonds under which the optimization has to be per- formed. If amplifiers are used, periodically the signal returns to a high power level; thus, different from the case of unamplified systems, nonlinear effects happen over a long part of the link. Telecommunication Networks If the link has to work it is needed to limit the average power below a threshold, SO to be sure that nonlinear effects remain under c