Abstract
In this paper, the dispersion relation and modulation instability (MI) have been studied in one-dimensional bi-periodic optical lattice of negative index metamaterials waveguide arrays. It is found that the plateaus will be appeared on the dispersion curve when the coupling coefficient is around 0.25. The plateau will become wider with the increase of the nonlinear and longitudinal modulation depth. The phase shift has little effect on MI the gain spectrum when the values of coupling coefficient, nonlinear coefficient and longitudinal modulation depth coefficient are in the range that is conducive to the generation of plateaus. However, if the values of these coefficients are in the range that is not conducive to the generation of plateaus, the effect of phase shift on the MI gain spectrum will become significant. In addition, it is found that the inverse periodic modulation between waveguides causes the light intensity to change periodically during transmission.
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