A probabilistic model for traveling wave optical amplifiers is presented. Optical signal and noise are assumed to be bunches of photons traveling along the active region with size varying accordingly to simple random rules. The theory leads to the complete statistical characterization of signal and noise as marked Poisson processes. In spite of the fact that its validity is confined to small-signal regimes, the result may be very useful for a more accurate performance evaluation and design criteria of optical transmission systems using recently developed erbium-doped fiber amplifiers.
