The authors present a simple model of a travelling wave semiconductor optical amplifier with an appreciable degree of saturation. The model uses a particular way of linearising the total carrier recombination R(N) to find useful expressions for the saturation parameter and/or the carrier lifetime. By combining these expressions and the gain measurements realised, it is possible to establish the dependence between the mentioned parameters and the input optical power.
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 the authors to make conclusions about the statistical fluctuations of the optical power at the nonlinear optical amplifier output.