Pump depletion measurement under Modulation Instability conditions

Modulation Instability (MI) is a nonlinear instable phenomenon arising in dispersive fiber optics under proper conditions. When a strong pump CW is injected a perturbation, initially negligible, undergoes amplification. In this paper we derive the instable regime theoretical conditions focusing on the pump depletion. This step is neglected in most of literature. Thus, we analyze MI effect as the interplay between a pump signal and a small perturbation propagating in anomalous dispersion regime. The pump depletion will lead, eventually, to the exhaustion of the nonlinear conditions. The CW power depletion is important for defining the optical gain offered by the fibre. In passing, the gain induced on small perturbation is measured, as well.