One-channel time-reversal in chaotic cavities: Theoretical limits

One-channel time-reversal experiments in closed chaotic cavities produce excellent, but not perfect, time-reversed focusing. This paper investigates such experiments by a simple eigenmode analysis of the system. It shows that the process is, even for long reversed signals, subject to an information loss during recording and re-emission which prevents perfect time-reversal. This fact can be expressed by a simple equation,,called the cavity equation, which states that the signal of a one-channel time-reversal is equal to the signal of a perfect time-reversal after convolution with the backscattering impulse response of the reversal point (i.e., from this point to this point). The latter convolution describes the introduction of the loss of information. Furthermore, arguments are presented suggesting that one third of the total energy of the time-reversed wave field is actually contained in the refocusing wavefront. The predictions are verified by numerical finite-difference time-domain simulations. (C) 1999 Acoustical Society of America. [S0001-4966(99)04201-0].