Semiclassical theory of time-reversal focusing

Time-reversal mirrors have been successfully implemented for various kinds of waves propagating in complex media. In particular, acoustic waves in chaotic cavities exhibit a refocalization that is extremely robust against external perturbations or the partial use of the available information. We develop a semiclassical approach in order to quantitatively describe the refocusing signal resulting from an initially localized wave packet. The time-dependent reconstructed signal grows linearly with the temporal window of injection, in agreement with the acoustic experiments, and reaches the same spatial extension of the original wave packet. We explain the crucial role played by the chaotic dynamics for the reconstruction of the signal and its stability against external perturbations.