Effects of fourth-order dispersion on modulational instability in metamaterials with exponential saturable nonlinearity and self-steepening coefficients

We studied the modulational instability in negative index materials with higher-order effects. An expression for the instability gain is derived through the linear stability analysis. We identify and discuss the salient features of the effect, like fourth-order dispersion, self-steepening and saturable nonlinearity on the modulational instability. The results show that the instability gain depends on the sign of the higher-order dispersion and, for anomalous dispersion, the instability regime is constituted of two parts: the conventional gain spectrum and the secondary gain spectrum induced by the fourth-order dispersion. For large values of the fourth-order dispersion, the secondary instability region spectrum vanishes and merges with the ordinary gain. In the normal dispersion regime, an efficient control of the modulation instability is successfully demonstrated by adjusting the fourth-order dispersion, depending on the presence of the self-steepening parameter or the normalized input power.