Iterative time reversal with tunable convergence

Abstract

An iterative technique for improving the temporal focusing of a time reversal mirror is proposed and tested. A single amplification parameter is introduced to tune the convergence of the iteration. The tunable iterative technique has been validated by tests on an experimental electromagnetic time reversal mirror, as well as on a novel numerical model.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.

The effects of non-uniform loss on time reversal mirrors

“…Noise, which is not considered in the theory, also affects the performance of TR mirrors as seen, for example, in Ref. 23. As shown in Fig.…”

“…This compares with η ≈ 78% which is achieved by the tunable iterative technique on the same experimental set up. 23 Therefore, the iterative technique performs better than the exponential amplification technique when both of them use their respective optimum parameters. Nonetheless, the exponential amplification has an advantage because of its speed, and computational simplicity.…”

“…6,7,23,29 We use the star graph because it is a type of quantum graph that has generic properties of wave chaotic systems, 29 but it is relatively simple to understand and simulate. The star graph is a quasi-1D chaotic system.…”

“…21,22 However, the iterative technique may not converge fast enough, despite a recent result showing the tunability of its convergence. 23 A faster alternative to the iterative technique is the inverse filter technique. 21,24 But, the inverse filter requires detailed measurements at multiple locations in the medium, and is computationally costly unless it is replaced with an iterative technique, 21,22 which can also be time-consuming.…”

Focusing waves at arbitrary locations in a ray-chaotic enclosure using time-reversed synthetic sonas

“…For our microwave time reversal experiments [25,38], the billiard is a quasi-2D, ray-chaotic cavity. That is, it is thin in one dimension (z) so that, at the frequencies of interest, the modes of the cavity have electric fields E = E z (x, y)ẑ [39].…”