Influence of the functional form of nonlinearity in the Modulational Instability spectra of relaxing saturable nonlinear system

Abstract

We investigate the modulational instability (MI) of the optical beam propagating in the relaxing saturable nonlinear system. We identify and discuss the salient features of various functional forms of saturable nonlinear responses such as exponential, conventional and coupled type on the MI spectrum. Using Debye relaxation model, the relaxation of nonlinear response is effectively included along with the saturable nonlinear response (SNL). Using linear stability analysis, an explicit dispersion relation is determined for considering different functional forms of SNL. Firstly, we analyze the impact of SNL on the MI spectrum and found that the MI gain and bandwidth is maximum for exponential nonlinearity in comparison to other types of SNL's. Latter the relaxation of the nonlinearity is included, the inclusion of the finite value of the response time extends the range of the unstable frequencies literally down to infinite frequencies. In the regime of slow response, the MI inevitably suppressed regardless of the sign of the dispersion coefficient. To give insight into the MI phenomena, the maximum MI gain and the optimum modulation frequency is drawn as a function of the delay. Thus the MI dynamics in the system of relaxing saturable nonlinear media is emphasized and the significance of various functional forms of SNL are highlighted.