Ultrasonic investigation of phonon localization in a disordered three-dimensional "mesoglass"

Abstract

One of the long standing questions in phonon physics has been whether or not the Anderson localization of acoustic phonons can be demonstrated unambiguously in disordered materials. In this paper, this question is addressed by reporting signatures of the localization of ultrasonic waves in a "mesoglass" made from a disordered three-dimensional network of aluminum beads. In the upper part of the intermediate frequency regime, which extends over the range of frequencies where the acoustic phonon wavelength is comparable with the sizes of the pores and beads, the intensity distributions of the speckle patterns due to strong multiple scattering show clear departures from Rayleigh statistics, with a variance that increases with frequency. This intensity distribution can be fitted with a stretched exponential, consistent with recent predictions for localization. In this frequency range, the time-of-flight profile of the transmitted intensity exhibits a non-exponential decay, which may be construed as a slowing down of the phonon diffusion coefficient with propagation time. These results are interpreted using recent theoretical predictions based on the self-consistent theory of the dynamics of localization, showing that our experimental data are consistent with the localization of acoustic waves in this mesoglass, and further elucidating their behaviour.