Role of polarization mode dispersion on modulational instability in optical fibers - art. no. 066616

We introduce the theory of modulational instability (MI) of electromagnetic waves in fibers with random polarization mode dispersion. Applying a linea r stability analysis and stochastic calculus, we show that the MI gain spec trum reads as the maximal eigenvalue of a constant effective matrix. In the limiting cases of small or large fluctuations, we give explicit expression s for the MI gain spectra. in the general configurations, we give the expli cit form of the effective matrix and numerically compute the maximal eigenv alue. In the anomalous dispersion regime, polarization dispersion widens th e unstable bandwidth. Depending on the type of variations of the birefringe nce parameters, polarization dispersion reduces of enhances the MI gain pea k. In the normal dispersion regime, random effects may extend the instabili ty domain to the whole spectrum of modulations. The linear stability analys is is confirmed by numerical simulation of the full stochastic coupled nonl inear Schrodinger equations.