Time-reversal waves and super resolution

Time-reversal mirrors (TRMs) refocus an incident acoustic field to the position of the original source regardless of the complexity of the propagation medium. TRM's have now been implemented in a variety of physical scenarios from MHz ultrasonics with order centimeter aperture size to hundreds/thousands of Hz in ocean acoustics with order hundred meter aperture size. Common to this broad range of scales is a remarkable robustness exemplified by observations at all scales that the more complex the medium between the probe source and the TRM, the sharper the focus. The relation between the medium complexity and the size of the focal spot is studied in this paper. It is certainly the most exciting property of TRM compared to standard focusing devices. A TRM acts as an antenna that uses complex environments to appears wider than it is, resulting for a broadband pulse in a refocusing quality that does not depend of the TRM aperture. In this paper, we investigate the time-reversal approach in various media of increasing complexity We will also demonstrated that time-reversal focusing opens completely new approaches to super-resolution. We will show that in medium made of random distribution of sub-wavelength scatterers, a time-reversed wave field interacts with the random medium to regenerate not only the propagating but also the evanescent waves required to refocus below the diffraction limit. Finally, we will discuss the link existing between time-reversal approaches and new imaging methods recently developed where Green's functions of complex media can be extracted from diffusive noise by cross-correlating the recordings of a diffuse random wave field