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-ɛ 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.
We also thank our co-authors, especially L. C. Botten, M. A. Byrne, R. C. McPhedran, F. Nori, P. Rajan, and S. Savel’ev for the fruitful collaboration and discussions of many original results summarized in this review paper. S.G. is grateful to N. M. Makarov, P. Markos, and L. A. Pastur for useful comments and helpful discussions.
This work was partially supported by the European Commission (Marie Curie Action). V.F. acknowledges partial support from the Israeli Science Foundation (Grant No. 894/10).
II. Random multilayered structures
. Transmission length and the Lyapunov exponent
. Transfer matrices and weak scattering approximation
III. Suppression of localization in metamaterials
. Mixed stack
. Homogeneous stack
. Transmission resonances
. Polarization effects
. Dispersive metamaterials
. Anomalous suppression of localization
IV. Localization in complex media
. Nonreciprocal transmission in magnetoactive optical structures
. Charge transport in disordered graphene
. Bistability of Anderson localized states in nonlinear media
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