Anderson localization of ultrasound in disordered anisotropic media
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Date
2020-12-18
Authors
Goïcoechea, Antton
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Abstract
Wave transport in disordered anisotropic media is investigated experimentally and theoretically. Multiple scattering theory is reviewed, with a focus on the self-consistent theory of localization (SCT). To treat anisotropy, a new version of this theory is adapted to classical waves and extended to finite media. By obtaining analytical results, the two versions of the SCT have been compared in the infinite medium case and found to be in good agreement.
Experimentally, the transport is studied via ultrasonic techniques on samples made of brazed elongated aluminium particles oriented in a certain direction. In the diffusive regime, the effect of the anisotropy is to make directions of propagation inside the sample inequivalent. Instead of a single diffusion coefficient, components of a diffusion tensor can be measured in the anisotropic case. Experimental results show good agreement with diffusion theory for two different orientations of the particles. The frequency-independence of the transport anisotropy is demonstrated experimentally for the first time. Using a novel technique to increase the scattering inside the samples, transport regimes for which the diffusion approximation breaks down are reached. In particular, the effect of the anisotropy on the Anderson localization regime is studied. Using transverse confinement experiments, the first experimental observation of the reduction of the transport anisotropy close to the mobility edge is reported for both orientations of the anisotropy. The samples made of these irregular elongated particles also display a slow approach to the localization regime, motivating further experimental work.
A theoretical framework based on random matrix theory is used to study the effects of anisotropy on the transport of scalar waves. Introducing correlations such as grouping scatterers by pairs or surrounding scatterers by a spherical exclusion volume results in exotic behaviour compared to the independent scatterers case. The pair correlation is of special interest because by aligning the pairs along one direction, anisotropy is created, but it influences transport only over a narrow frequency range, precluding the study of its effect on Anderson localization. By considering instead an anisotropic random Green's matrix, it is shown that anisotropy can facilitate Anderson localization, and preliminary results on anisotropy reduction in this transport regime are reported.
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Keywords
Physics, Waves, Anderson localization, Scattering, Ultrasound