Abstract
The conditions of the onset of a modulation instability of the signal wave in a doped fiber due to nonlinear cross-modulation interaction with the pump wave are investigated. The analysis takes into consideration the pump depletion and the group-velocity mismatch of the interacting waves. A dispersion relation coupling perturbation parameters with those of pump, analytic expressions governing the integral growth rate of a harmonic perturbation, and other important characteristics determining the dynamics of the signal-wave cross-modulation instability are obtained. Based on computer simulation, the behavior of the above characteristics as a function of the initial signal-wave power, fiber length, and group-velocity mismatch of the pump and signal waves is investigated.
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