The dispersion relation and modulation instability (MI) of an array of alternating positive-index material (PIM) and negative-index material (NIM) waveguides are investigated. It is found that the transverse wave vector of the stability wave solution has modulation on the linear part of the dispersion relation, which leads to the dispersion relation being linear in the staggered case. The MI region for the staggered case is larger than the unstaggered case, which is the same as that of a conventional waveguide array. Whether in the staggered case or the unstaggered case, the self-focusing or self-defocusing nonlinear property of PIM and NIM channels affects the gain value of the array, and the gain structure of the array for the unstaggered case has an important dependence on the nonlinear property of PIM and NIM channels, but is not affected by the nonlinear property of the channels for the staggered case. It is also found that in addition to the nonlinear property of the channels, the interaction of the nonlinear effects of the channels also has great influence on the generation of the MI. These findings indicate that we can manipulate MI in an array of positive- and negative-index waveguides with the controllability of a NIM channel.
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