  We investigate the modulational instability and time-domain dynamics of
nonlinear magnetic metamaterials composed of coupled split-ring resonators
loaded by Kerr nonlinearity. Our results indicate that the recently proposed
optical switching of local optical index based on uniform-response assumption
seems fragile. We conceive two alternative schemes to utilize the valuable
enhanced non- linearity, one is to focus on few-body systems and directly make
use of the modulational instability (e.g., an optical comparator design), the
other is to consider global switching arising from global feedbacks as in usual
cases (e.g., Fabry-Perot cavities) rather than local-resonances-based switching
of optical constants which may be destroyed by the discreteness and
interactions as we show in this paper. We also try to provide comprehensive
understanding of the relations between our results on discrete nonlinear
metamterials and those on continuous metamaterials and natural materials in the
literatures.
