Interplay of XPM and nonlinear response time in the modulational instability of copropagating optical pulses

Abstract

We investigate the modulational instability induced by cross-phase modulation (XPM) of two incoherently coupled optical pulses copropagating in a lossless fiber with a finite nonlinear response time. The non-instantaneous character of the nonlinear response is introduced through a Debye relaxation process. We analytically obtain the exact dispersion relation for weak harmonic perturbations over the stationary solution. We show that the instability spectrum, present in both normal and anomalous dispersive regimes in instantaneously responding Kerr media, develops a double peak structure whose relative strength and typical frequency range depend on the response time. Further, we reveal that there are two unstable modes in the entire frequency spectrum. We report the dependence of the maximum gain and central frequency within each unstable mode as a function of the group velocity mismatch and response time, showing the crossover between the regimes of fast and slow nonlinear responses.