The spatial focusing of a leaky time reversal chaotic cavity

Elastic waves propagating inside a solid chaotic cavity create a diffusive random field that contains both longitudinal and shear waves. In the current paper, we are interested in the field radiated in a fluid in contact with such cavity. The goal of this paper is to predict the spatial focusing properties that can be obtained in the fluid using a time-reversal piezoelectric transducer in contact with the cavity. We present a statistical approach that supposes a fully diffused wavefield inside the cavity with an equipartition of energy between longitudinal and shear waves. We show that the critical angles of transmission in the solid-fluid interface generate a cut-off of the spatial frequencies and then a degradation in the spatial focusing. This limitation can be overcome using a rough surface. A set of experiments conducted in the MHz range confirm the theoretical model.