Effect of chaos in a one-channel time-reversal acoustic mirror

Time-reversal of propagating waves has been intensely studied during the last years and successfully implemented in different experimental contexts. It has been argued that ergodic or chaotic ray dynamics improve the refocusing resolution. In this work we consider this fundamental aspect by studying the reversion of sound waves in two-dimensional reflecting cavities numerically. The boundary of the enclosure is deformed from a rectangle with regular ray dynamics to a completely chaotic hyperbolic billiard. We observed that both the regular and chaotic cases display a prominent refocusing peak, and also that in the first scenario many secondary maxima appear. We developed measures of the spatial and temporal contrasts of the reconstructed signal in order to gain insight on these phenomena and to distinguish between cases. The results obtained point to the necessity for a reconsideration of what is usually understood by successful time-reversal processes.