Modulational instability in lossless fibers with saturable delayed nonlinear response

Abstract

We investigate the modulational instability of optical pulses propagating in a lossless fiber where both effects of relaxation and saturation of the nonlinearity are taken simultaneously into account. The saturation of the nonlinearity is incorporated in the relaxation dynamics of the Kerr response. We calculate the exact dispersion relation for harmonic perturbations over the stationary solution. In the anomalous dispersive regime, the gain spectrum exhibits two bands in the fast relaxation regime. The low energy band is reduced by the saturation of the nonlinearity but is roughly insensitive to the nonlinearity response time. The high energy band is mainly due to the Raman response. These frequency bands superpose for fast relaxation responses and a new behavior sets up. In the normal dispersive regime, a single instability band sets up associated with the finite response time of the nonlinearity with distinct features for fast and slow nonlinear relaxation.