Nonlinear magnetic metamaterials and possible applications on all-optical comparers and bistabilities in Fabry-Perot cavities

Abstract: 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.