One-channel inverse filter: Spatio-temporal control of a complex wave-field from a single point

Abstract

Can we make good use of the degrees of freedom of a wave-field trapped in a cavity to perform complete spatio-temporal inversion from a single emitter? To answer these questions, we used experiments conducted in the ultrasonic regime to investigate the wave-field in a water cavity where the energy was not homogeneously distributed over all of the degrees of freedom. While the time reversal from a single emitter gives poor results, we show the possibility to recover optimal spatio-temporal focusing by converting the multi-channel focusing technique of the spatio-temporal inverse filter into a single-channel method that we call the one-channel inverse filter. In particular, this method has the advantage of leaving the choice open for the duration of the time window for the inversion of the wave-field. We, thus, demonstrate that the shorter the time window, the better optimized the inversion. We believe that in addition to demonstrating the possibility of controlling the waves in a cavity, this method might have an interesting role in the improvement of solid imaging devices that are based on the exploitation of reverberations in cavities.