Transverse confinement of ultrasound through the Anderson transition in three-dimensional mesoglasses

Abstract

We report an in-depth investigation of the Anderson localization transition for classical waves in three dimensions (3D). Experimentally, we observe clear signatures of Anderson localization by measuring the transverse confinement of transmitted ultrasound through slab-shaped mesoglass samples. We compare our experimental data with predictions of the self-consistent theory of Anderson localization for an open medium with the same geometry as our samples. This model describes the transverse confinement of classical waves as a function of the localization (correlation) length, $\ensuremath{\xi}\phantom{\rule{4pt}{0ex}}(\ensuremath{\zeta})$, and is fitted to our experimental data to quantify the transverse spreading/confinement of ultrasound all of the way through the transition between diffusion and localization. Hence we are able to precisely identify the location of the mobility edges at which the Anderson transitions occur.