Time reversal methods are widely used to achieve wave focusing in acousticsand electromagnetics. A typical time reversal experiment requires that atransmitter be initially present at the target focusing point, which limits theapplication of this technique. In this paper, we propose a method to focuswaves at an arbitary location inside a complex enclosure using a numericallycalculated wave excitation signal. We use a semi-classical ray algorithm tocalculate the signal that would be received at a transceiver port resultingfrom the injection of a short pulse at the desired target location. Thetime-reversed version of this signal is then injected into the transceiver portand an approximate reconstruction of the short pulse is created at the target.The quaility of the pulse reconstruction is quantified in three different waysand the values of these metrics are predicted by the statistics of thescattering-parameter $|S_{21}|^2$ between the transceiver and target points inthe enclosure. We experimentally demonstrate the method using a flat microwavebilliard and quantify the reconstruction quality as a function of enclosureloss, port coupling and other considerations.
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