Suppression of Anderson localization in disordered metamaterials

We study wave propagation in mixed, 1D disordered stacks of alternating right- and left-handed layers and reveal that the introduction of metamaterials substantially suppresses Anderson localization. At long wavelengths, the localization length in mixed stacks is orders of magnitude larger than for normal structures, proportional to the sixth power of the wavelength, in contrast to the usual quadratic wavelength dependence of normal systems. Suppression of localization is also exemplified in long-wavelength resonances which largely disappear when left-handed materials are introduced. © 2007 The American Physical Society

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

We review some recent (mostly ours) results on the 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 the vicinity of the 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 the polarization. At resonant frequencies or realizations, such nonreciprocity results in effectively unidirectional transport of light. Third, we discuss the analogy between the wave propagation through multilayered samples with metamaterials and the charge transport in graphene, which enables a simple physical explanation of unusual conductive properties of disordered graphene superlatices. We predict disorder-induced resonances of the transmission coefficient at oblique incidence of the 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 the wave transmission and unidirectional transport of light. © S.A. Gredeskul, Y.S. Kivshar, A.A. Asatryan, K.Y. Bliokh, Y.P. Bliokh, V.D. Freilikher, and I.V. Shadrivov, 2012

Anderson delocalization in one dimensional μ or ε-near-zero metamaterial stacks and other dispersion effects on localization

We have carried out a comprehensive study of dispersion and absorption effects on Anderson localization in one-dimensional metamaterial stacks and have shown that the field is delocalized in μ or ε-near-zero media at normal incidence. © 2011 OSA

Transmission and Anderson localization in dispersive metamaterials

Comprehensive theoretical and numerical studies of the effects of dispersion and absorption on the Anderson localization of classical waves in weakly disordered, one-dimensional stacks composed of dispersive metamaterials and normal materials are presented. An asymptotic analysis for studying the effects of dispersion and absorption is developed. It is shown that the localization of waves in random stacks composed entirely of either metamaterial or normal dielectric layers is completely suppressed at frequencies where the magnetic permeability or the dielectric permittivity is zero. In mixed stacks of alternating layers of normal and metamaterials with disorder present in either the dielectric permittivity or the magnetic permeability, localization is substantially suppressed not only at these frequencies but in essentially wider frequency ranges. When both the permittivity and the permeability are random, the localization behavior is similar to that in monotype stacks. At the transition from a double negative metamaterial to a single negative metamaterial, the transmission length drops dramatically in a manner that might be useful in optical switching. Polarization effects are also considered and it is shown that localization is suppressed at the Brewster angle, in a manner dependent on both the polarization and the nature of the disorder. Theoretical predictions are in excellent agreement with numerical calculations. © 2012 American Physical Society

The effect of metamaterials on Anderson localisation

We study ID stacks comprising alternating layers of normal and metamaterials, with disorder in both refractive index and layer thickness, and show strong suppression of localisation with only index disorder. © 2008 Optical Society of America

Dispersion effects on the Anderson localization in disordered one dimensional metamaterial stacks

We have carried out a comprehensive study of dispersion and absorption effects on Anderson localization in one-dimensional metamaterial stacks and have shown that the field is delocalized in μ or ε-near-zero media at normal incidence. © 2011 IEEE

Some Mathematical Remarks Concerning the Localisation of Planetary Waves in a Stochastic Background Flow

In this article we develop some mathematically rigorous ideas to explain the phenomenon of localisation of planetary waves in a stochastic background flow as presented in the physical companion paper. For this purpose the barotropic vorticity equation linearised around a zonal background wind and driven by a local source is transformed into a Sturm-Liouville problem with random potential function. We distinguish between two types of localising mechanisms. The first type is a background effect of localisation symmetrical with respect to the equator which is due to the nodes of the potential function (critical lines). The second is a more subtle effect and forces localisation around the source. It comes from the superposition of the source term with the Green's kernel expressed in terms of the eigenfunctions of the spectral resolution of the random Sturm-Liouville operators involved. On average, this effect is moderate for zero damping, and stronger for small non-zero damping

The Spectrum Of Periodic Point Perturbations And The Krein Resolvent Formula

this paper that under certain natural conditions the Krein formula works for the case of point perturbations of elliptic operators on a manifold, too. With the help of this formula we prove that the gaps of a periodic point perturbation of such an operator are labelled by the elements of the K 0 -group of an appropriate