Focusing with plane time-reversal mirrors: An efficient alternative to closed cavities

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Abstract
In this paper, a theoretical foundation is proposed and numerical results are provided for focusing by plane, time-reversal mirrors of finite dimensions in a homogeneous fluid. The basic ideas are the same as those used in the closed time-reversal cavity (CTRC) system [Cassereau et al., Proc. IEEE Ultrason. Symp., 1613–1618 (1990); D. Cassereau and M. Fink, IEEE Trans. Ultrason. Ferroelec. Freq. Control 39, 579–592 (1992)], except that the most unrealistic assumptions made in this theoretical approach are dropped. Plane mirrors are considered that do not surround the object source, and different kinds of radiation conditions are introduced on the surface of these mirrors, in order to obtain more realistic situations from an experimental point of view. The results are compared with those of the CTRC system and it is shown how the focal pattern is changed in comparison with the pattern of the theoretical (and ideal) model. The differences between several radiation conditions on the surface of the mirror are also analyzed. The theory is based on a time domain formulation of diffraction, but a frequency analysis provides closed form solutions in some particular cases. Numerical results show that plane time-reversal mirrors of finite dimensions represent an efficient and realistic alternative to the CTRC system.

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