Output moments and photon statistics in fiber raman amplification

The problem of output moments, photon statistics, and signal-to-noise ratio in fiber Raman amplification is considered using a master equation approach, including absorption in the signal and pump modes. In the parametric approximation for the pump, results are obtained for the output moments which can be cast in a general form derived by Loudon and Shepherd [23] for phase-insensitive quantum amplifiers and attenuators. Beyond the parametric approximation, it is shown that the output moments of the signal may be obtained through iteration from lower order moments in an approximation where signal-pump correlation is ignored. Comparison with other work is discussed.