QUANTUM-STATISTICAL PROPERTIES OF PULSE AMPLIFICATION IN OPTICAL FIBERS WITH GAIN SATURATION

We studied the quantum-statistical properties of pulse amplification i n erbium-doped fiber amplifiers (OFAs), including saturation of the at omic population inversion and pump depletion, We use a fully quantum t heory to describe the atom-field interaction as well as the light prop agation, The generating function of the output photon number distribut ion (PND) is determined as a function of time during the course of the pulse, with an arbitrary input PND assumed. For input light with Pois son PND, the output PND is shown to be the Laguerre distribution with parameter 1 at all times smaller than the coherence time tau(c), even in the presence of nonlinear effects. An expression for the photon cou nt moment generating function is found for counting times T >> tau(c). The mean pulse shape is shown to be altered by the nonlinear amplific ation, The variance is similarly altered, and the excess amplifier noi se is greater at the leading side of the pulse.