Modulation instability scenario in negative index materials

We present an investigation of the critical frequency windows permitting modulation instability in negative index materials. The principal motivation for our analysis stems from the impact of the inevitable presence of the effective dispersive magnetic permeability in addition to the effective dielectric permittivity determining the propagation model for ultrashort pulses in negative index materials. We emphasize the influence of nonlinear dispersion terms, arising out of the combinatorial effect of the dispersive permeability with the nonlinear polarization, over the MI phenomena, the outcome of its development achieved by using linear stability analysis. Gain spectrum investigation has been carried out for both anomalous and normal dispersion regime in the focusing and defocusing cases of nonlinearity and near zero dispersion regime where higher order linear dispersive effects emerge. The results of linear stability analysis have been validated by direct numerical simulation of the governing equation using the split-step Fourier transform method. We show that second-order nonlinear dispersion opens up distinct MI windows with their appropriate conditions and unlike the first-order nonlinear dispersion term, the sign of it has got deep consequences in the modulation instability scenario.