Analysis of noise amplification by a CW pump signal due to fiber nonlinearity

The amplifier spontaneous emission noise can be changed significantly due to fiber nonlinearity during its propagation through the fiber with a strong pump signal. We present, in this letter, a new analysis on this effect based on perturbation theory. The new analysis gives the parametric gain transfer matrix in a simple format which gives clear insight on the effect from dispersion, fiber nonlinearity, and their interaction.