Resonances and localization of classical waves in random systems with correlated disorder

Samelsohn, Gregory; Gredeskul, S. A.; Mazar, Reuven

doi:10.1103/physreve.60.6081

Cited by 18 publications

(12 citation statements)

References 29 publications

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“…As is known, in multidimensional systems the components of the power spectrum (vectors K of the reciprocal lattices) that participate in the Bragg scattering and, therefore, contribute to the localization length, are located within the limiting circle (2D) or sphere (3D) of radius 2k in the Ewald construction; see Fig. 1 (in 1D, this diagram degenerates into three points K =0, ±2k only) [8]. Hence, to estimate the value of −1 ͑k͒ in higher dimensions in the same way as was done in the 1D case, we should perform spectral filtering by reducing the integration domain in Eq.…”

Section: ͑6͒mentioning

confidence: 99%

“…The present study is based on a path-integral approach [8] that enables a perturbative analysis of the localization length in random media with continuous-type disorder described by an arbitrary correlation function. It is shown that in the longwavelength limit, a two-dimensional (2D) anisotropic system is characterized by a finite localization length, which is independent of the direction of propagation.…”

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Localization of classical waves in weakly scattering two-dimensional media with anisotropic disorder

Samelsohn

Freilikher

2004

Phys. Rev. E

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We study the localization of classical waves in weakly scattering two-dimensional 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. Anderson-type localization of classical waves in disordered systems is a topic of increasing current interest due to its fundamental role in wave-matter interactions, and also due to the significance of possible applications [1]. While the localization in one-dimensional (1D) random systems has been studied in considerable detail, a quantitative analytical description of the phenomenon in higher dimensions still presents a challenge. The question here concerns the relationship between the localization and its characteristics (say, localization length), on the one hand, and the correlation properties of the scattering potential, on the other. However, most of the existing results are related to a ␦-correlated potential or obtained numerically by using discrete schemes, such as the tight-binding model, and therefore are relevant mainly for low-frequency excitations. Moreover, the theories describing wave localization have been developed primarily for systems with isotropic disorder, and those considering anisotropy [2,3] are not directly applicable to classical waves. The only exception is the limiting case of an infinite correlation scale in one direction (randomly stratified media), which has been studied rather comprehensively [4]. In such media, the radiation is localized in the direction across the layers and is typically channeled along the layers, similar to that occurring in a regular waveguide. Although this model can be useful for understanding the basic mechanisms of wave localization in anisotropic systems, it is of little help when media with finite anisotropy are concerned. Experimental studies dealing with both electronic [5] and classical wave [6,7] transport in anisotropic systems have been initiated only recently and are far from being complete.The present study is based on a path-integral approach [8] that enables a perturbative analysis of the localization length in random media with continuous-type disorder described by an arbitrary correlation function. It is...

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Localization of classical waves in weakly scattering two-dimensional media with anisotropic disorder

Samelsohn

Freilikher

2004

Phys. Rev. E

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“…In turbulence they determine the non-Gaissian statistics of the tails of the probability distribution functions for the properties of random flow [1] and in the linear theory of random wave localization the momenta non-selfaveraging quantities, like e.g. wave transmissivity are determined by rare non-typical realizations rather than the typical (localized) ones [2,3].…”

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confidence: 99%

Nonlinear propagation of an optical speckle field

Derevyanko

Small²

2012

Phys. Rev. A

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We provide a theoretical explanation of the results on the intensity distributions and correlation functions obtained from a random beam speckle field in nonlinear bulk waveguides reported in the recent publication Y. Bromberg et.al., Nat. Photonics \textbf{4}, 721 (2010). We study both focusing and defocusing case and in the limit of small speckle size (short correlated disordered beam) provide analytical asymptotes for the intensity probability distributions at the output facet. Additionally we provide a simple relation between the speckle sizes at the input and output of a focusing nonlinear waveguide. The results are of practical significance for the nonlinear Hanbury Brown and Twiss interferometry both in optical waveguides and Bose-Einstein condensates.Comment: Submitted to PR

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“…1a) 1 . Hence, localization may be viewed as an ensemble of waves diffracting from a random superposition of gratings, each with its spatial wavenumber 42 . Therefore, it is instructive to examine a disordered system in momentum space.…”

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“…For a plane wave incident upon this potential with wavenumber k in ≈ −k 0 /2, there are many possible phase-matched first-order transitions to the spectral region around k 0 /2, obeying the paraxial dispersion relation (k in ) = β(k 0 /2 ), where β(k) = β 0 − k 2 /2β 0 (see first section of the SI 37 ). This plane wave undergoes many sequential first-order transitions, from positive to negative wavenumbers and back, leading to the buildup of Anderson localization 42 . In this process, the spectrum of the localized wave packet reshapes but remains confined around ±k 0 /2.…”

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Observation of Anderson localization beyond the spectrum of the disorder

Dikopoltsev

Weidermann

Kremer

et al. 2021

Preprint

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Anderson localization is a fundamental wave phenomenon predicting that transport in a 1D uncorrelated disordered system comes to a complete halt, experiencing no transport whatsoever. However, in reality, a disordered physical system is always correlated, because it must have a finite spectrum. Common wisdom in the field states that localization is dominant only for wavepackets whose spectral extent resides within the region of the wavenumber span of the disorder. Here, we experimentally observe that Anderson localization can occur and even be dominant for wavepackets residing entirely outside the spectral extent of the disorder. We study the evolution of waves in synthetic photonic lattices containing bandwidth-limited (correlated) disorder, and observe Anderson localization for wavepackets of high wavenumbers centered around twice the mean wavenumber of the disorder spectrum. Likewise, we predict and observe Anderson localization at low wavenumbers, also outside the spectral extent of the disorder, and find that localization there can be as strong as for first-order transitions. This feature is universal, common to all Hermitian wave systems, implying that low-wavenumber wavepackets localize with a short localization length even when the disorder is strictly at high wavenumbers. This understanding suggests that disordered media should be opaque for long-wavelengths even when the disorder is strictly at much shorter length scales. Our results shed light on fundamental aspects of physical disordered systems and offer avenues for employing spectrally-shaped disorder for controlling transport in systems containing disorder.

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Resonances and localization of classical waves in random systems with correlated disorder

Cited by 18 publications

References 29 publications

Localization of classical waves in weakly scattering two-dimensional media with anisotropic disorder

Localization of classical waves in weakly scattering two-dimensional media with anisotropic disorder

Nonlinear propagation of an optical speckle field

Observation of Anderson localization beyond the spectrum of the disorder

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