Tunable modulation instability in metamaterials with pseudo-quintic nonlinearity, self-steepening effect and delayed Raman response

Abstract

Modulation instability (MI) in metamaterials induced by pseudo-quintic nonlinearity, self-steepening effect along with delayed Raman response (DRR) is investigated and expression for MI gain is presented by linear stability method. Compared to the previous results with saturable nonlinearity, it is found that the MI without DRR may occur in four primary cases with different threshold behaviors depending on the combination of dispersion and nonlinearity and the competition of pseudo-quintic nonlinearity and self-steepening effect. This implies that we may manipulate or tune the MI by adjusting the power and frequency of incident waves at will. In addition, we consider the influence of DRR on MI and find that the DRR leads to additional regions where it entirely governs the MI gain, besides the primary ones where the self-steepening and the pseudo-quintic nonlinearity dominate the MI gain. Moreover, the DRR makes MI happen in three new cases exhibiting monotonous growth with perturbation frequency, which means that it is possible to observe MI at arbitrary high frequency. Finally, we confirm the analytical results by numerical simulations. The obtained results may be useful for manipulating or tuning the MI in metamaterials and provide more ways to generate ultrashort pulses with ultrahigh repetition rate.