Abstract
We analyze modulation instability (MI) in metamaterials with saturable and focusing nonlinearity according to the propagation model, including the self-steepening (SS) parameter and the second-order nonlinear dispersion (SOND). A detailed discussion on the common role of saturable nonlinearity, SS, and SOND terms on the MI is presented. It is found that MI is irrespective of the sign of the SS parameter and dependent on the sign of SOND. Generally, SS and saturable nonlinearity suppress the MI generation, and SOND promotes the MI in the anomalous group-velocity dispersion (GVD) region. Moreover, linear stability analysis predicts that MI may occur in both the abnormal GVD and normal GVD regime, even at the zero-GVD point, which is to say that some interesting MI phenomena appear involving the additional excited SOND term induced by the dispersive magnetic permeability. In particular, the saturable nonlinearity changes the generation condition of MI seriously. Finally, the numerical simulation is performed to confirm the theoretical predictions.
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