ity of optical fiber communications. Nature, 411 (2001), 1027; for a tutorial introduction, see also E. Desurvire, Erbium-Doped Fiber Amplifiers, Devices and System Developments (New York: J. Wiley & Sons, 2002), Ch. 3. 14.2 Nonlinear channel where Pth is the power threshold at which nonlinearity comes into effect. The exact definition of Pth in relation to the various fiber-optics link parameters can be found in the aforementioned references. The above definition of the nonlinearity parameter S shows that nonlinearity is negligible, or the optical channel is linear, for P << Pth or S sP << N), which, according to Eq. (14.30) gives the power-independent, additive channel noise N*(P) 2 N. In the general case, we see from the relation N*(P) = N + S P that a fraction sP of signal power is effectively converted into nonlinear noise. Because of energy conservation, the received signal power at the end of the link is not P, but rather P* = - P(1 - s). The actual SNR is now SNR* = P*/N*, which reduces to SNR* = P/N in the linear limit P << Pth (s 0). We can now evaluate the nonlinear channel capacity. According to the Shannon-Hartley theorem (SHT), Eq. (14.18), the channel capacity ((bit/s)/Hz) is given by: (14.32) Replacing the definition of the nonlinearity parameter S in the above yields: (-()) (14.33) log exp P The result in Eq. (14.33) shows that in the high-power limit P Pth 8, the channel capacity reduces to C = log(1 + E) with E 0, or C 0. Nonlinearity, thus, asymptot- ically obliterates channel capacity. Since in the linear regime channel, capacity increases with signal power, we then expect that a maximum can be reached at some power value. It can be shown that such a maximum capacity is reached for the optimal signal power Popt as analytically defined: (14.34) Gaussian channel and Shannon-Hartley theorem Replacing this definition of Popt into Eq. (14.33) yields the maximum achievable channel capacity Cmax: (14.35) A different model that I developed, 18 which takes into account the quantum nature of amplifier 