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Journal Articles Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal Year : 2023

Speckle Memory Effect in the Frequency Domain and Stability in Time-Reversal Experiments

Abstract

When waves propagate through a complex medium like the turbulent atmosphere the wave field becomes incoherent and the wave intensity forms a complex speckle pattern. In this paper we study a speckle memory effect in the frequency domain and some of its consequences. This effect means that certain properties of the speckle pattern produced by wave transmission through a randomly scattering medium is preserved when shifting the frequency of the illumination. The speckle memory effect is characterized via a detailed novel analysis of the fourth-order moment of the random paraxial Green’s function at four different frequencies. We arrive at a precise characterization of the frequency memory effect and what governs the strength of the memory. As an application we quantify the statistical stability of time-reversal wave refocusing through a randomly scattering medium in the paraxial or beam regime. Time reversal refers to the situation when a transmitted wave field is recorded on a time-reversal mirror then time reversed and sent back into the complex medium. The re-emitted wave field then refocuses at the original source point. We compute the mean of the refocused wave and identify a novel quantitative description of its variance in terms of the radius of the time-reversal mirror, the size of its elements, the source bandwidth, and the statistics of the random medium fluctuations.

Dates and versions

hal-04219492 , version 1 (27-09-2023)

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Josselin Garnier, Knut Sølna. Speckle Memory Effect in the Frequency Domain and Stability in Time-Reversal Experiments. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2023, 21 (1), pp.80-118. ⟨10.1137/22M1470414⟩. ⟨hal-04219492⟩
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