Statistical analysis of nonlinear optical amplifier in high saturation

In the work, analytic expressions describing the behaviour of a strongly saturated nonlinear optical amplifier are deduced. These expressions make possible the calculation of the mean and variance of the amplified light photon number. Results are compared with those obtained by the numerical resolution of the photon density matrix equation, and good accordance is observed in the strong saturation regime. The results numerically obtained enable us to make conclusions about the statistical fluctuations of the optical power at the nonlinear optical amplifer output.