Modulation instability in nonlinear oppositely directed coupler with a negative-index metamaterial channel

The nonlinear optical coupler with a negative-index metamaterial (NIM) channel is different from a conventional one, mainly in that the former has an effective feedback mechanism due to the opposite directionality of the phase velocities in the two channels. In this paper, we study modulation instability (MI) in this new kind of couplers, trying to identify the different MI properties from those in conventional couplers. It is found that MI in the nonlinear optical coupler with a NIM channel is significantly influenced by the ratio of the forward- to backward-propagating wave’s power and the nonlinear parameters. And the threshold condition for the ratio and input power can exist only in the normal dispersion regime where the ratio is positive. In addition, it is shown that MI occurs only for finite values of input power when the NIM channel is self-defocusing nonlinear material and another channel is self-focusing nonlinear material in the anomalous dispersion regime. Further, increasing input power may suppress the MI, quite different from the MI in the conventional couplers. For the conventional one, the increase of input power generally promotes the occurrence of MI. These findings suggest that the controllability of NIMs provides more ways to manipulate MI and soliton in couplers with NIM channels.