Structure of the focal region at a focusing with a time reversal of waves in an inhomogeneous medium

A focusing array with a time reversal of waves in an inhomogeneous medium is considered. It is shown that, at the focus of such an array, an oscillation trap can be formed. In a homogeneous medium, a wave first travels to the array focus, is focused, and then travels away from the focus, whereas, in an inhomogeneous medium, the wave does not travel at all. In the oscillation trap, an intense oscillation is formed, which arrives from nowhere and escapes to nowhere. The size of the oscillation trap is much smaller than that of the focal spot of the array in free space. The physical nature of this phenomenon and the possible areas of its practical application are discussed.