Time reversal through a solid–liquid interface and super-resolution

Abstract

Time-reversal can be used to refocus optimally a signal back onto the source that emitted it. An active array antenna is used to record the wave as a function of time and then, the recorded field is time reversed and retransmitted. The time reversed wave backpropagates through the medium and refocuses approximately on the initial source position. From the experimental point of view, time-reversal devices are designed to work primarily in a fluid environment. However, time reversal refocusing can be realized also in solids. To do so, the solid is surrounded by a fluid in which the active antenna is located. We propose a numerical formulation describing the time reversal phenomenon through a fluid–solid interface and we analyze with numerical simulations the refocusing resolution obtained in homogeneous media. We also show numerically that multipathing caused by random inhomogeneities improves the focusing of the back-propagated elastic waves beyond the diffraction limit. This phenomenon is called super-resolution and was seen previously in acoustic wave propagation.