Abstract:

Acoustic time-reversal experiments usually need large arrays of transducers. An element reduction normally decreases the aperture and thus degrades reversal or focusing quality. However, one can use reflections to increase artificially the transducer aperture. It is shown that in a reflecting cavity with negligible absorption, a time-reversal of a pointlike source can be performed using a single element. The wave field is measured by the transducer over a long period of time at a point inside the cavity, and then the time-reversed signal is reinjected at the same location. The wave field thus created forms wave fronts of the same shape as the initially emitted ones, but propagating in the opposite direction. They finally collapse at the location of the initial source, leading to excellent focusing which is not aperture limited. The difference between a perfect and a one-channel time-reversal can be quantified. A chaotic shape of the system guarantees a successful time-reversal; in some regular cavities, the procedure fails. One-channel time-reversal experiments have been successfully carried out using elastic waves in a silicon wafer. Finite-difference computations simulating a time-reversal of a two-dimensional scalar wave field complete this work.