Spatiotemporal instability in a periodic structure consisting of negative-index and positive-index materials

In this paper, we apply the conventional method of linear stability to investigate the dynamical behaviors of spatiotemporal instability in a periodic structure consisting of negative-index materials and positive-index materials. It is found that the high-order diffraction (HOD) originating from spatial dispersion in such physical setting not only leads to the appearance of new instability regimes, but also may exert significant influence on the original instability, depending on the combined signs of both diffraction and dispersion. In the conventional positive diffraction regime, the most notable property is that HOD shrinks the regime of the original instability for the normal dispersion case through suppressing the higher frequency components growth while it leads to the appearance of new instability regimes in addition to deforming the original instability for the anomalous dispersion case. However, in the negative diffraction regime, HOD may lead to the occurrence of spatiotemporal instability even for the normal dispersion case while it mainly shrinks the regimes of the original instability for the anomalous dispersion case.