Robustness of time reversal for waves in time-dependent random media

This paper addresses the impact of time fluctuations of a random medium on refocusing during a time-reversal experiment. Even in the presence of moderate time perturbations a coherent refocused pulse is observed. The theory predicts the level of recompression observed as well as the conditions for the loss of statistical stabilization. It is shown that the statistical properties of the refocused pulse depend on a simple set of parameters that describe the correlation degree of the medium. The refocused pulse has in general a random shape that can be described in terms of a system of stochastic transport equations driven by a single Brownian motion. Pulse stabilization is also demonstrated for some particular configurations, and the convolution kernel that describes the pulse reshaping is explicitly computed. Numerical simulations are presented and show a very good agreement with the theoretical predictions, thus providing a clear illustration of the robustness of time reversal.