Modulational instability in randomly dispersion-managed optical fiber links

We study modulational instability in a dispersion-managed optical fiber system where the sign of the group-velocity dispersion is changed at uniformly distributed random distances around a reference length. We find an instability gain of stochastic origin comparable to the conventional values found in a homogeneous anomalous dispersion fiber. We develop an accurate analytical technique based on transfer matrices to estimate the instability gain from the linearized nonlinear Schrödinger equation, which is also solved numerically. The comparison of numerical and analytical results confirms the validity of our approach. Modulational instability sidebands of purely stochastic origin appear and the competition between sidebands of periodic and stochastic origin is also discussed. These results may be of interest in tailoring and controlling modulational instability sidebands for telecommunications and parametric sources. Our method can also be applied to general linear stochastic differential equations with multiplicative noise, which broadly occur in Physics.