tical fiber, an amplified fiber-optic link is intrinsically linear.15 A simple justification comes as follows. At the end of the link, the optical signal is converted by the receiver into a photocurrent. It can be shown that the dominant noise component in the receiver photocurrent output is of the form: o2=2PN, (14.27) where P is the optical power input to the (transparent) link and, hence, to the end receiver, and N is the optical amplifier noise accumulated along the link, which is power-independent. 16 The electrical signal power is of the form Pe=P2. (14.28) The electrical signal-to-noise ratio (SNR) is, thus, (14.29) whose noise denominator is now seen to be independent of the signal power. Thus, the SNR scales linearly with the input (optical) power, which is the linearity condition for the communication channel. But the transmission medium, the optical fiber, is intrinsically nonlinear. It is beyond the scope of this book to detail the different types and causes of fiber nonlinearities. The introduction of channel nonlinearity in the field of information theory is relatively recent (2001). 17 As we shall see, this new hypothesis is rich in implications in the analysis of channel capacity, in particular for optical transmission systems. We shall, thus, assume that the nonlinear channel noise, N*, has the power-dependent form N*(P)=N+sP, (14.30) where N is the linear channel noise (P=0) = and P is the power-dependent contribution to the channel noise, which is attributed to optical fiber nonlinearities. The nonlinearity parameter S can be written as (14.31) As in any amplifiers, the amplification factor (gain) of optical amplifiers saturates with increasing signal power. However, optical amplifiers deployed in transmission systems are designed to yield constant gain regardless of signal power changes. 16 See, for instance: E. Desurvire, Erbium-Doped Fiber Amplifiers, Devices and System Developments (New York: J. Wiley & Sons, 2002), Ch. 3. P.P. Mitra and J.B. Stark, Nonlinear limits to the information capac