Iterative time reversal with tunable convergence

Introduction: Spatiotemporal focusing of waves has applications in fields such as imaging and communication. Time reversal (TR) mirrors have been used to focus waves in both space and time [1]. An ideal TR mirror consists of a wave source located inside a lossless medium that is completely enclosed by a surface of transceivers, which record and absorb the signal initially broadcast by the source. Later, the transceivers rebroadcast a time reversed version of the recorded waves and, because of the TR invariance of the lossless wave equation, the waves focus on the location of the source and reconstruct a time reversed version of the original signal. In practice, TR mirrors have several limitations that result in loss of information about the waves broadcast by the source; these include (i) limited coverage by the transceivers, and (ii) dissipation during the wave propagation (which breaks TR invariance) [2, 3]. The first limitation of TR mirrors can be overcome by the use of a reflecting wave chaotic cavity with partial spatial coverage of the transceivers, along with a long recording time [3]. However, the limitation due to dissipation persists, and leads to increasing loss of information as the recording time increases. The loss of information during the reconstruction results in temporal and spatial sidelobes of the reconstructed pulse. In previous work, we used the compensating technique of exponential-in-time amplification of the rebroadcasted time-reversed signal to partially undo the adverse effects of dissipation, and to enhance the range of sensors which utilise TR mirrors [2, 4]. However, this technique does not improve the temporal focusing of the reconstructed pulse. On the other hand, [5] has introduced an iterative TR technique which has been shown to be effective in eliminating the spatiotemporal sidelobes of the reconstructed pulse. The iterative technique can be useful in applications in which TR mirrors could benefit from enhanced focusing [6]. In this Letter, we introduce into the iteration method an amplification parameter to compensate for dissipation. By tuning this parameter, we can substantially improve the accuracy and convergence of the iterative focusing technique. This is demonstrated both experimentally and numerically.