Anderson Localization of Electromagnetic Waves in a Dielectric Medium of Randomly Distributed Metal Particles

Arya, K.; Su, Zhao-Bin; Birman, Joseph L.

doi:10.1103/physrevlett.57.2725

Cited by 100 publications

(27 citation statements)

References 15 publications

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“…dimensional samples of metal spheres at various concentrations [4,5,29,30]. We find that in samples of 0.47-cm-diameter aluminum spheres of length L = 8. the search for and characterization of photon localization.…”

mentioning

confidence: 92%

Statistical signatures of photon localization

Chabanov

Stoytchev

Genack

2000

Nature

587

539

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The realization that electron localization in disordered systems (Anderson localization) [1] is ultimately a wave phenomenon [2,3] has led to the suggestion that photons could be similarly localized by disorder [3]. This conjecture attracted wide interest because the differences between photons and electrons -in their interactions, spin statistics, and methods of injection and detection -may open a new realm of optical and microwave phenomena, and allow a detailed study of the Anderson localization transition undisturbed by the Coulomb interaction. To date, claims of threedimensional photon localization have been based on observations of the exponential decay of the electromagnetic wave [4,5,6,7,8] as it propagates through the disordered medium. But these reports have come under close scrutiny because of the possibility that the decay observed may be due to residual absorption [9,10,11], and because absorption itself may suppress localization [3]. Here we show that the extent of photon localization can be determined by a different approach -measurement of the relative size of fluctuations of certain transmission quantities. The variance of relative fluctuations accurately reflects the extent of localization, even in the presence of absorption. Using this approach, we demonstrate photon localization in both weakly and strongly scattering quasi-one-dimensional dielectric samples and in periodic metallic wire meshes containing metallic scatterers, while ruling it out in three-dimensional mixtures of aluminum spheres.In the absence of inelastic and phase-breaking processes, the ensemble average of the dimensionless conductance g ≡ G /(e 2 /h) is the universal scaling parameter [12] of the electron localization transition [1]. Here ... represents the average over an ensemble of random sample configurations, G is the electronic conductance, e is the electron charge, and h is Planck's constant. The dimensionless conductance g can be defined for classical waves as the transmittance, that is, the sum over transmission coefficients connecting all input modes a and output modes b, g ≡ Σ ab T ab (Ref. 13). In the absence of absorption, g not only determines the scaling of transmission quantities, such as T ab and T a = Σ b T ab that we will refer to as the intensity and total transmission, respectively, but it also determines their full distributions [14,15,16]. In electronically conducting samples or in white paints, g ≫ 1 and Ohm's law holds, g = N ℓ/L, where N is the number of transverse modes at a given frequency, ℓ is the transport mean free path, and L is the sample length. But beyond the localization threshold, at g ≈ 1 (Refs. 12,17), the wavefunction or classical field is exponentially small at the boundary and g falls exponentially with L. Localization can be achieved in a strongly scattering three-dimensional sample with a sufficiently small value of ℓ (Ref. 2), or even in weakly scattering samples in a quasi-one-dimensional geometry of fixed N , once L becomes greater than the localization length, ξ = N ℓ (Ref. 1...

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confidence: 92%

Statistical signatures of photon localization

Chabanov

Stoytchev

Genack

2000

Nature

587

539

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“…In this case, the interference of the waves that have undergone multiple scattering, caused by the heterogeneities of the medium, may cause their localization. Unlike electrons, however, the classical waves do not interact with one another and, therefore, propagation of such waves in heterogeneous media (such as porous rock) provides [7] an ideal model for studying the classical Anderson localization [8][9][10][11][12] in strongly disordered media. This is the focus of this 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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“…By using the (-matrix and the diagrammatic Green's function method 4,7,[27][28][29] we also derive the criterion for Anderson localization of an em wave which is similar to that for an electron in a random potential. We then discuss various possibilities where this condition of localization can be satisfied.…”

Section: Discussion Of Anderson Localization Have Mostly Been Relatedmentioning

confidence: 98%

Anderson Localization of the Classical Electromagnetic Waves in a Disordered Dielectric Medium

Arya

Birman

1990

Scattering and Localization of Classical Waves in Random Media

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Anderson Localization of Electromagnetic Waves in a Dielectric Medium of Randomly Distributed Metal Particles

Cited by 100 publications

References 15 publications

Statistical signatures of photon localization

Statistical signatures of photon localization

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

Anderson Localization of the Classical Electromagnetic Waves in a Disordered Dielectric Medium

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