With a semiclassical model of the optical amplifier, we calculate the evolution of noise along optically amplified lines in presence of nonlinear interaction between signal and amplified spontaneous emission, amplifiers saturation, fiber dispersion and vacuum field fluctuations associated with attenuation of the fiber. The noise figure (NF) is calculated for two representative cases of long and short-distance links with different numbers of optical amplifiers and for several fiber dispersions. Results indicate that the optimum number of optical amplifiers is limited by the increase of nonlinear effects with signal power.
Michele Norgia, Guido Giuliani, and Silvano Donati, "Noise Evolution Along Optically Amplified Links in Presence of Nonlinear Parametric Gain," J. Lightwave Technol. 17, 1750- (1999)