Anderson localization in metamaterials and other complex media (Review Article)

Abstract

This is a review of some recent (mostly ours) results on Anderson localization of light and electron waves in complex disordered systems, including: (i) left-handed metamaterials, (ii) magnetoactive optical structures, (iii) graphene superlattices, and (iv) nonlinear dielectric media. First, we demonstrate that left-handed metamaterials can significantly suppress localization of light and lead to an anomalously enhanced transmission. This suppression is essential at the long-wavelength limit in the case of normal incidence, at specific angles of oblique incidence (Brewster anomaly), and in vicinity of zero-ε or zero-μ frequencies for dispersive metamaterials. Remarkably, in disordered samples comprised of alternating normal and left-handed metamaterials, the reciprocal Lyapunov exponent and reciprocal transmittance increment can differ from each other. Second, we study magnetoactive multilayered structures, which exhibit nonreciprocal localization of light depending on the direction of propagation and on polarization. At resonant frequencies or realizations such nonreciprocity results in effectively unidirectional transport of light. Third, we discuss the analogy between wave propagation through multilayered samples with metamaterials and charge transport in graphene, which provides a simple physical explanation of unusual conductive properties of disordered graphene superlatices. We predict disorder-induced resonance of the transmission coefficient at oblique incidence of Dirac quasiparticles. Finally, we demonstrate that an interplay of nonlinearity and disorder in dielectric media can lead to bistability of individual localized states excited inside the medium at resonant frequencies. This results in nonreciprocity of wave transmission and unidirectional transport of light.