Transmission of acoustic waves in a random layered medium

Baluni, Varouzhan; Willemsen, Jorge F.

doi:10.1103/physreva.31.3358

Cited by 81 publications

(93 citation statements)

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“…We calculate the one-loop beta functions [8,14] for both spatially delta-correlated and power-law correlated disorder in the elastic constants, and show that in any case there is a disorder-induced transition from delocalized to localized states for any d. In addition to be interesting on its own, our study is motivated in part by the recent discovery [15] that the distribution of the elastic moduli of heterogeneous rock contains long-range correlations characterized by a nondecaying power-law correlation function. Baluni and Willemsen [16] studied propagation of acoustic waves in a 1D layered system, which can be thought of as a simple model of rock (although their goal was not to study acoustic wave propagation in rock), and showed that the waves are localized. However, they did not consider higher-dimensional systems, nor did they study the type of disorder that we consider in the present Letter.…”

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confidence: 99%

Localization of Elastic Waves in Heterogeneous Media with Off-Diagonal Disorder and Long-Range Correlations

et al. 2005

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Using the Martin-Siggia-Rose method, we study propagation of acoustic waves in strongly heterogeneous media which are characterized by a broad distribution of the elastic constants. Gaussian-white distributed elastic constants, as well as those with long-range correlations with non-decaying powerlaw correlation functions, are considered. The study is motivated in part by a recent discovery that the elastic moduli of rock at large length scales may be characterized by long-range power-law correlation functions. Depending on the disorder, the renormalization group (RG) flows exhibit a transition to localized regime in any dimension. We have numerically checked the RG results using the transfer-matrix method and direct numerical simulations for one-and two-dimensional systems, respectively.Understanding how waves propagate in heterogeneous media is fundamental to such important problems as earthquakes, underground nuclear explosions, the morphology of oil and gas reservoirs, oceanography, and medical and materials sciences [1]. For example, seismic wave propagation and reflection are used to not only estimate the hydrocarbon content of a potential oil or gas field, but also to image structures located over a wide area, ranging from the Earth's near surface to the deeper crust and upper mantle. The same essential concepts and techniques are used in such diverse fields as materials science and medicine.In condensed matter physics, a related problem, namely, the nature of electronic states in disordered materials, has been studied for several decades and shown to depend strongly on the spatial dimensionality d of the materials [2]. It was rigorously shown that, for onedimensional (1D) systems, even infinitesimally small disorder is sufficient for localizing the wave function, irrespective of the energy [3], and that the envelop of the wave function ψ(r) decays exponentially at large distances r from the domain's center, ψ(r) ∼ exp(−r/ξ), with ξ being the localization length. The most important results for d > 1 follow from the scaling theory of localization [4] which predicts that, for d ≤ 2, all electronic states are localized for any degree of disorder, while a transition to extended states -the metal-insulator transition -occurs for d > 2 if disorder is sufficiently strong. The transition between the two states is characterized by divergence of the localization length, ξ ∝ |W − W c | −ν , where W c is the critical value of the disorder intensity.Wegner [5] derived a field-theoretic formulation for the localization problem which, together with the scaling theory [4], predict a lower critical dimension, d c = 2, for the localization problem. These predictions have been confirmed by numerical simulations [6].Wave characteristics of electrons suggest that the localization phenomenon may occur in other wave propagation processes. For example, consider propagation of seismic waves in heterogeneous rock. In this case, the interference of the waves that have undergone multiple scattering, caused by the heterogeneities of t...

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confidence: 99%

Localization of Elastic Waves in Heterogeneous Media with Off-Diagonal Disorder and Long-Range Correlations

et al. 2005

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“…Therefore albeit localization in disordered H-stacks with right-handed layers has been studied by many authors 6,26,49,66,74 , we also consider this problem here in its most general formulation. This consideration enables us to compare localization properties of M-and H-stacks.…”

Section: A Modelmentioning

confidence: 99%

“…It was known that, in normal multilayered systems comprising right-handed media, the localization length is proportional to the square of wavelength λ in the long-wavelength limit, tends to a constant in a shortwavelength regime, and oscillates irregularly in the intermediate region 4,6,49,66,67 . Natural question arises: how inclusion of metamaterial layers influences the localization and transmission effects.…”

Section: Suppression Of Localization In Metamaterialsmentioning

confidence: 99%

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

Gredeskul

Kivshar

Asatryan

et al. 2012

Low Temperature Physics

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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-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 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.

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“…The effort in searching for localization of classical waves such as acoustic and electro-magnetic waves is tremendous. It has drawn intensive attentions from both theorists [2][3][4][5][6][7][8] and experimentalists [9,10]. Snice the pioneering work of Anderson et.al.…”

Section: Introductionmentioning

confidence: 99%

Statistics of the Lyapunov exponent in one-dimensional layered systems

Luan

2001

Phys. Rev. E

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Localization of acoustic waves in a one dimensional water duct containing many randomly distributed air filled blocks is studied. Both the Lyapunov exponent and its variance are computed. Their statistical properties are also explored extensively. The results reveal that in this system the single parameter scaling is generally inadequate no matter whether the frequency we consider is located in a pass band or in a band gap. This contradicts the earlier observations in an optical case. We compare the results with two optical cases and give a possible explanation of the origin of the different behaviors.

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Transmission of acoustic waves in a random layered medium

Cited by 81 publications

References 13 publications

Localization of Elastic Waves in Heterogeneous Media with Off-Diagonal Disorder and Long-Range Correlations

Localization of Elastic Waves in Heterogeneous Media with Off-Diagonal Disorder and Long-Range Correlations

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

Statistics of the Lyapunov exponent in one-dimensional layered systems

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