Semiclassical Theory of Time-Reversal Focusing

TL;DR

This paper develops a semiclassical theory to quantitatively describe time-reversal focusing of waves in chaotic media, explaining the robustness and linear growth of the refocusing signal observed in experiments.

Contribution

It introduces a semiclassical framework that accurately models the refocusing process and highlights the importance of chaotic dynamics for signal stability.

Findings

Refocusing signal grows linearly with injection time.

Refocused wave reaches the same spatial extent as the original.

Chaotic dynamics are crucial for signal reconstruction and stability.

Abstract

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.