Modulation instability in positive refractive-index metamaterials with saturable nonlinearity

The dispersion relation, instable condition, and the dimensionless critical perturbation frequency and gain spectra of modulation instability(MI) are deduced in metamaterials by directly starting from the extended nonlinear propagation equation including saturable nonlinearity, self-steepening and the second-order nonlinear effects and by adopting the linear stability analysis. Variations of the dimensionless gain spectra with the normalized angular frequencies and incident power densities are calculated in the positive refractive-index region of metamaterials. The results show that, in the positive refractive-index region of metamaterials, depending on different normalized angular frequencies and incident power densities, the gain spectra will take on three kinds of forms. Namely, the per