Time reversal super resolution in randomly layered media

In this paper we extend previous work on time reversal in randomly layered media [J.-P. Fouque, J. Garnier, A. Nachbin, K. Sølna, Time reversal refocusing for point source in randomly layered media, Wave Motion 42 (2005) 238–260]. We consider first the case of an active source embedded below the surface in a finely layered random medium. We carry out time reversal with a time reversal mirror placed at the surface and we consider here the case where this mirror is larger than the carrier wavelength. In contrast with the situation addressed in our previous paper, where the size of the mirror was comparable to the wavelength, we show that multi-pathing dramatically enhances the effective aperture of the mirror so that super resolution at the location of the source can be obtained. In other words, the focal spot radius of the refocused field obtained in the case of a multiply scattering medium is much smaller than the spot size obtained in the case of a homogeneous medium. This super resolution effect is obtained by time-reversing the long incoherent waves generated by the multiple scattering due to the thin layers. We also give an application to the problem of focusing on a passive scatterer buried in the random medium and illuminated by a source at the surface.