Theory of the time-reversal process in solids

Abstract

In this paper, a theoretical formulation is proposed to describe a time-reversal process in a solid medium with two propagation modes, longitudinal and transverse waves. A plane time-reversal mirror (TRM) is used, installed in a fluid which is in contact with the solid through a plane interface parallel to the TRM. The basic approach is similar to the case of a plane fluid–fluid interface [D. Cassereau and M. Fink, J. Acoust. Soc. Am. 96, 3145–3154 (1994)]; it is extended to take into account the different wave types. It is shown that the TRM is able to recreate properly in time and space the reversed fields of the longitudinal wave and the vertical polarization SV of the transverse waves, but not the horizontal polarization SH. The focusing quality of the backpropagating waves is limited by their respective wavelengths, so the slower SV wave can be better focused. Additional, unwanted wavefronts are created in the solid, too, but they are of weak amplitude and they are not focused. Numerical simulations illustrate the dependence of the focal pattern on parameters like distance–source interface, size, and eccentricity of the mirror.