Characterization of time-reversed elastic waves in ergodic billiards

Abstract

One year ago, this laboratory showed experimentally and numerically that an elastic wave can be time reversed in a highly reflecting cavity with a single pointlike source [Draeger and Fink, J. Acoust. Soc. Am. 101, 3090(A) (1997)]. This is possible because the cavity is low dissipative and its shape is ergodic. Now the properties of this experiment are better understood. Clearly, two parameters are involved. The first one (T) is the beginning of the time reversal window; the second one is its duration ΔT. The lowest value of T which gives an isotropic focusing is the ‘‘angular mixing time;’’ it may be related to the ergodicity time. There is another characteristic time: beyond a certain limit, increasing ΔT does not improve the quality of focusing any longer. This ‘‘saturation time’’ is very dependent on the initial pulse length; it is analogous to the Heisenberg time. Also, the difference beteween the perfect theoretical time reversal and the experimental one is explained.