A very simple model is found for phase insensitive laser amplification, Signal and noise along the active fiber are modeled as marked Poisson processes (corresponding to flows of photon bunches of random size) and are dealt with as independent processes, A probabilistic approach, founded on the theory of birth-and-death processes, enables us to give a simple characterization of the amplifier in terms of the statistics of the random gain, of the time intensity of the ASE (amplified spontaneous emission) noise bunches, and finally of the statistics of their sizes. The theory is limited to the linear amplification range, while is valid also for nonhomogeneous inversion along the active fiber. The model can be easily applied for the evaluation of the statistics of the global gain and of the accumulated ASE noise in optically amplified links.
