Localization of Classical Waves in Weakly Scattering Two-Dimensional Media with Anisotropic Disorder

We study the localization of classical waves in weakly scattering 2D systems with anisotropic disorder. The analysis is based on a perturbative path-integral technique combined with a spectral filtering that accounts for the first-order Bragg scattering only. It is shown that in the long-wavelength limit the radiation is always localized, and the localization length is independent of the direction of propagation, the latter in contrast to the predictions based on an anisotropic tight-binding model. For shorter wavelengths that are comparable to the correlation scales of the disorder, the transport properties of disordered media are essentially different in the directions along and across the correlation ellipse. There exists a frequency-dependent critical value of the anisotropy parameter, below which waves are localized at all angles of propagation. Above this critical value, the radiation is localized only within some angular sectors centered at the short axis of the correlation ellipse and is extended in other directions.Comment: 10 pages, 5 figure

Bistability of Anderson localized states in nonlinear random media

We study wave transmission through one-dimensional random nonlinear structures and predict a novel effect resulting from an interplay of nonlinearity and disorder. We reveal that, while weak nonlinearity does not change the typical exponentially small transmission in the regime of the Anderson localization, it affects dramatically the disorder-induced localized states excited inside the medium leading to bistable and nonreciprocal resonant transmission. Our numerical modeling shows an excellent agreement with theoretical predictions based on the concept of a high-Q resonator associated with each localized state. This offers a new way for all-optical light control employing statistically homogeneous random media without regular cavities

Effects of polarization on the transmission and localization of classical waves in weakly scattering metamaterials

We summarize the results of our comprehensive analytical and numerical studies of the effects of polarization on the Anderson localization of classical waves in one-dimensional random stacks. We consider homogeneous stacks composed entirely of normal materials or metamaterials, and also mixed stacks composed of alternating layers of a normal material and metamaterial. We extend the theoretical study developed earlier for the case of normal incidence [A. A. Asatryan et al, Phys. Rev. B 81, 075124 (2010)] to the case of off-axis incidence. For the general case where both the refractive indices and layer thicknesses are random, we obtain the long-wave and short-wave asymptotics of the localization length over a wide range of incidence angles (including the Brewster ``anomaly'' angle). At the Brewster angle, we show that the long-wave localization length is proportional to the square of the wavelength, as for the case of normal incidence, but with a proportionality coefficient substantially larger than that for normal incidence. In mixed stacks with only refractive-index disorder, we demonstrate that p-polarized waves are strongly localized, while for s-polarization the localization is substantially suppressed, as in the case of normal incidence. In the case of only thickness disorder, we study also the transition from localization to delocalization at the Brewster angle.Comment: 15 pages, 11 figures, accepted for publication in PR

Anderson Localization of Classical Waves in Weakly Scattering Metamaterials

We study the propagation and localization of classical waves in one-dimensional disordered structures composed of alternating layers of left- and right-handed materials (mixed stacks) and compare them to the structures composed of different layers of the same material (homogeneous stacks). For weakly scattering layers, we have developed an effective analytical approach and have calculated the transmission length within a wide region of the input parameters. When both refractive index and layer thickness of a mixed stack are random, the transmission length in the long-wave range of the localized regime exhibits a quadratic power wavelength dependence with the coefficients different for mixed and homogeneous stacks. Moreover, the transmission length of a mixed stack differs from reciprocal of the Lyapunov exponent of the corresponding infinite stack. In both the ballistic regime of a mixed stack and in the near long-wave region of a homogeneous stack, the transmission length of a realization is a strongly fluctuating quantity. In the far long-wave part of the ballistic region, the homogeneous stack becomes effectively uniform and the transmission length fluctuations are weaker. The crossover region from the localization to the ballistic regime is relatively narrow for both mixed and homogeneous stacks. In mixed stacks with only refractive-index disorder, Anderson localization at long wavelengths is substantially suppressed, with the localization length growing with the wavelength much faster than for homogeneous stacks. The crossover region becomes essentially wider and transmission resonances appear only in much longer stacks. All theoretical predictions are in an excellent agreement with the results of numerical simulations.Comment: 19 pages, 16 figures, submitted to PR

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

Transport and localization in periodic and disordered graphene superlattices

We study charge transport in one-dimensional graphene superlattices created by applying layered periodic and disordered potentials. It is shown that the transport and spectral properties of such structures are strongly anisotropic. In the direction perpendicular to the layers, the eigenstates in a disordered sample are delocalized for all energies and provide a minimal non-zero conductivity, which cannot be destroyed by disorder, no matter how strong this is. However, along with extended states, there exist discrete sets of angles and energies with exponentially localized eigenfunctions (disorder-induced resonances). It is shown that, depending on the type of the unperturbed system, the disorder could either suppress or enhance the transmission. Most remarkable properties of the transmission have been found in graphene systems built of alternating p-n and n-p junctions. This transmission has anomalously narrow angular spectrum and, surprisingly, in some range of directions it is practically independent of the amplitude of fluctuations of the potential. Owing to these features, such samples could be used as building blocks in tunable electronic circuits. To better understand the physical implications of the results presented here, most of our results have been contrasted with those for analogous wave systems. Along with similarities, a number of quite surprising differences have been found.Comment: 10 page

Anderson localization in metamaterials and other complex media

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) magneto-active 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-epsilon or zero-mu 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 magneto-active 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.Comment: 37 pages, 30 figures, Review pape

Bistability and nonreciprocity in nonlinear disordered media

We study wave transmission through a nonlinear random medium and predict a novel effect resulting from an interplay of nonlinearity and disorder. We reveal that nonlinearity leads to bistable and nonreciprocal transmission properties of the localized modes

Bistability and nonreciprocity in nonlinear disordered media

We study wave transmission through a nonlinear random medium and predict a novel effect resulting from an interplay of nonlinearity and disorder. We reveal that nonlinearity leads to bistable and nonreciprocal transmission properties of the localized modes

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