Gain statistics of a fiber optical parametric amplifier with a temporally incoherent pump

We present an investigation of the statistics of the gain fluctuations of a fiber optical parametric amplifier pumped with a temporally incoherent pump. We derive a simple expression for the probability distribution of the gain of the amplified optical signal. The gain statistics are shown to be a strong function of the signal detuning and allow the possibility of generating optical gain distributions with controllable long-tails. Very good agreement is found between this theory and the experimentally measured gain distributions of an incoherently pumped amplifier.