, Volume 56, Issue 12, pp 1-14
Date: 03 Dec 2013

Metamaterial band theory: fundamentals & applications

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Remarkable progress has been made over the past decade in controlling light propagation and absorption in compact devices using nanophotonic structures and metamaterials. From sensing and modulation, to on-chip communication and light trapping for solar cells, new device applications and opportunities motivate the need for a rigorous understanding of the modal properties of metamaterials over a broad range of frequencies. In this review, we provide an overview of a metamaterial band theory we have developed that rigorously models the behavior of metamaterials made of dispersive materials such as metals. The theory extends traditional photonic band theory for periodic dielectric structures by coupling the mechanical motion of electrons in the metal directly to Maxwell’s equations. The solution for the band structures of metamaterials is then reduced to a standard matrix eigenvalue problem that nevertheless fully takes into account the dispersive properties of the constituent materials. As an application of the metamaterial band theory, we show that one can develop a perturbation formalism based on this theory to physically explain and predict the effect of dielectric refractive index modulation or metallic plasma frequency variation in metamaterials. Furthermore, the metamaterial band theory also provides an intuitive physical picture of the source of modal material loss, as well as a rigorous upper bound on the modal material loss rate of any plasmonic, metamaterial structure. This in turn places fundamental limits on the broadband operation of such devices for applications such as photodetection and absorption.