Quantum-statistical properties of pulse amplification in optical fibers with gain saturation

We studied the quantum-statistical properties of pulse amplification in erbium-doped fiber amplifiers (OFAs), including saturation of the atomic population inversion and pump depletion. We use a fully quantum theory to describe the atom-field interaction as wed as the light propagation. The generating function of the output photon number distribution (PND) is determined as a function of time during the course of the pulse, with an arbitrary input PND assumed. For input light with Poisson PND, the output PND is shown to be the Laguerre distribution with parameter 1 at all times smaller than the coherence time τ_c, even in the presence of nonlinear effects. An expression for the photon count moment generating function is found for counting times T≫τ_c. The mean pulse shape is shown to be altered by the nonlinear amplification. The variance is similarly altered, and the excess amplifier noise is greater at the leading side of the pulse