Bandwidth constraints for passive superluminal propagation through metamaterials

Superluminal transmission of electromagnetic waves is usually observed in a narrow bandwidth range and the velocity outside this range is subluminal. In this paper, it is shown that the transmission coefficient for superluminal propagation through a periodic metamaterial structure satisfies a sum rule. The sum rule and its corresponding physical bound relate frequency regions with a phase velocity above an arbitrary threshold with the thickness of the slab. The theoretical results are illustrated with numerical examples