s at the input, which is difficult to reduce. For this reason (and not because of the internal gain processes [Zimmerman & Spiekman, 2004]), SOAs usually have higher noise figures than fiber-based amplifiers. The Noise Figure of Optical Amplifier Chains An additional useful insight provided by equation 6.5 relates to amplifier chains, such as in transoceanic systems. We could use a small number of high-gain amplifiers spaced far apart or a large number of low-gain amplifiers. This choice is of great economic importance because of the high cost of remote amplifiers and their electrical power supplies. Figure illustrates the choice when the objective is to provide net end-to-end power transparency. The total system length, L, consists of N equal segments of fiber with loss a, each followed by an amplifier of gain exp(+aL/N). We assume for simplicity that all amplifiers have a noise figure, F, regardless of how they are used in the system. (This is an approximation because amplifier noise figures nor- mally vary with gain, but it becomes increasingly acceptable as the number of amplifiers in the chain increases.) Substitution in equation 6.5 allows us to predict that the composite noise figure of the entire system is p=1+N[Fexp(+aL/N)-1] (6.8) Fcomp is plotted as a function of N for a 500-km network in Figure 6.11 for four different amplifier noise figures, F. In accordance with intuition, it is beneficial to use amplifiers with a low noise figure, but Figure 6.11 also shows that overall performance improves with the number of amplifiers, which might at first appear surprising because each one produces noise. A Few High- Gain Amplifiers System Length Fig. 6.10 In a transmission system the choice is a small number of high-gain amplifiers or a large number of low-gain Many Low- amplifiers. The objective in either Gain Amplifiers case is to ensure that the input and output powers are the same. System Length Amplifier Noise in Optical Systems Noise Figure (dB): Fig. 6.11 500-km system with a loss of 0.2 dB/km and equall