Anomalous diffusion of multiply scattered ultrasound in a two-component disordered medium

Abstract

Measurements of multiply-scattered wave transport allow the characterization of heterogeneous media and may reveal anomalous wave properties. When a wave propagates through a sufficiently disordered medium, it will undergo many scattering events. This may lead to diffusive transport or even, in highly disordered media, to localized behavior in which transport comes to a halt. These two regimes can be distinguished by measuring the evolution of the transverse intensity profile when point-like ultrasonic pulse is incident on the opposite side of a slab-shaped sample. In the case of diffusive propagation, the profile width grows without limit as the square root of time, while for localized waves, the width reaches a saturation value at long times due to the trapping of the waves in the medium. In our experiment, the sample consists of aluminum beads randomly packed in silicone oil. Contrary to expectations, the width goes through a maximum as a function of time and varies slowly afterwards. This novel behavior may be due to the existence of two coupled modes of propagation: a fast component travelling through the liquid and a slower component traveling through the bead network. The resonances of the beads influence strongly the propagation inside the solid network.