TIME-REVERSAL FOCUSING THROUGH A PLANE INTERFACE SEPARATING 2 FLUIDS

In this paper, a theoretical formulation is proposed and numerical results are provided for focusing with a plane time-reversal mirror (TRM) through a plane interface separating two homogeneous fluids. The basic approach is the same as in the case of a single homogeneous fluid [D. Cassereau and M. Fink, J. Acoust. Sec. Am. 94, 2373-2386 (1993)], but the analysis is carried out in the frequency domain in order to include the boundary conditions at the interface. Nevertheless, the numerical computations are performed in the time domain with TRMs of finite size, and the numerical results are compared to those obtained in the single unbounded homogeneous fluid configuration, The differences between two TRMs working on the reflected and transmitted components of the acoustic field generated by the initial source are also analyzed. It is shown that the mainlobe size of the focal pattern created by a TRM in transmission is mainly related to the greatest value of the sound speed in fluids 1 and 2, while the size of the mainlobe resulting from a TRM in reflection only depends on the sound speed of the fluid that contains the initial source. Furthermore, it is shown how the superposition of two TRMs, synchronized in time, improves the focus on the initial source position.