Impact of higher-order effects on modulation instability in negative index materials

Abstract

In this article, we present a systematic investigation of modulation instability (MI) in negative index materials (NIMs) with higher-order dispersion and nonlinearity. We adopt the method of linear stability analysis and obtain an expression for the instability gain. Special attention is paid to studying the effect of fourth-order dispersion, quintic nonlinearity, first-order nonlinear dispersion, and second-order nonlinear dispersion on the instability gain. It is found that the fourth-order dispersion forms new instability regions and gives new ways to generate solitons or ultrashort pulse trains. Our study also shows that in the presence of higher-order dispersion a switching of the sign of cubic nonlinearity can generate two distinct MI regions. This result may provide a better way to generate different frequency ultra-short pulses as a result of switching of the sign of cubic nonlinearity by tuning the parameters of constituent elements of the metamaterials. Further, we observed that the cooperating cubic and quintic nonlinearities widen the MI by enhancing maximum gain and bandwidth, on the other hand, the competing cubic and quintic nonlinearities suppress the MI considerably.