Focusing Waves at Arbitrary Locations in a Ray-Chaotic Enclosure Using Time-Reversed Synthetic Sonas

Time reversal methods are widely used to achieve wave focusing in acoustics and electromagnetics. A typical time reversal experiment requires that a transmitter be initially present at the target focusing point, which limits the application of this technique. In this paper, we propose a method to focus waves at an arbitary location inside a complex enclosure using a numerically calculated wave excitation signal. We use a semi-classical ray algorithm to calculate the signal that would be received at a transceiver port resulting from the injection of a short pulse at the desired target location. The time-reversed version of this signal is then injected into the transceiver port and an approximate reconstruction of the short pulse is created at the target. The quaility of the pulse reconstruction is quantified in three different ways and the values of these metrics are predicted by the statistics of the scattering-parameter $|S_{21}|^2$ between the transceiver and target points in the enclosure. We experimentally demonstrate the method using a flat microwave billiard and quantify the reconstruction quality as a function of enclosure loss, port coupling and other considerations.