Preprint A248/2003
Robustness of Time Reversal for Waves in Time-dependent Random Media

Andre Nachbin | Alfaro Vigo, Daniel | Fouque, Jean-Pierre | Garnier, Josselin

**Keywords: **
inhomogeneous media | asymptotic theory | time reversal

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.