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Time-reversal inside a granular suspension to probe ultrasound diffusion

Yamil Abraham1,2, Bart A. van Tiggelen3, Nicolas Benech2, Carlos Negreira2, Xiaoping Jia1, and Arnaud Tourin1,*

  • *Contact author: arnaud.tourin@espci.psl.eu
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Phys. Rev. Research 7, 023291 – Published 23 June, 2025

DOI: https://doi.org/10.1103/47wj-s8lj

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/Dt, 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.

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Phys. Rev. Research 7, 023291– Published 23 June, 2025
  • Received 4 March 2025
  • Accepted 3 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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