Time-reversal inside a granular suspension to probe ultrasound diffusion

Abstract

We demonstrate that ultrasound diffusion—typically associated with the transport of average wave energy and the breaking of time-reversal symmetry—can nonetheless be revealed through a time-reversal experiment. This is achieved using an unprecedented configuration: A single piezoelectric transducer, acting as a time-reversal mirror (TRM), is buried deep inside a strongly scattering medium (a dense granular suspension), while an array of transducers is positioned at a distance, outside the scattering region. A short pulse is emitted by a single array element and the TRM records the resulting ultrasonic field, composed of a coherent ballistic wave followed by a diffuse coda wave. When the entire coda is time-reversed and re-emitted from the TRM, the wave refocuses at the original source with a focal spot size that decreases with the inverse of the TRM depth, consistent with diffusive transport. By time-reversing short coda segments at increasing times 𝑡, we observe a focal spot size scaling as 1/√𝐷⁢𝑡, where 𝐷 is the ultrasound diffusion coefficient. Fitting this evolution with a microscopic diffusion model allows us to extract 𝐷. Remarkably, this measurement does not require ensemble averaging, because of the inherent stability of time-reversal against statistical fluctuations.