Abstract
Time reversal mirrors work perfectly only for lossless wave propagation; dissipation destroys time-reversal invariance and limits the performance of time-reversal mirrors. Here, a new measure of time-reversal mirror performance is introduced and the adverse effect of dissipation on this performance measure is investigated. The technique of exponential amplification is employed to partially overcome the effect of non-uniform loss distributions, and its success is tested quantitatively using the new performance measure. A numerical model of a star graph is employed to test the applicability of this technique on realizations with various random spatial distributions of loss. A subset of the numerical results are also verified by experimental results from an electromagnetic time-reversal mirror. The exponential amplification technique is a simple way to improve the performance of emerging technologies based on time-reversed wave propagation such as directed communication and wireless power transfer.
Highlights
Time reversal (TR) mirrors can, under ideal circumstances, precisely reconstruct a wave disturbance which happened at an earlier time, at any given later time
This paper quantitatively demonstrates that the exponential amplification technique partially mitigates the adverse effects of dissipation on the performance of TR mirrors, for different spatial loss distributions
Exponential amplification improves the performance of time reversal mirrors best if the loss is uniformly distributed in space
Summary
Time reversal (TR) mirrors can, under ideal circumstances, precisely reconstruct a wave disturbance which happened at an earlier time, at any given later time. The waves broadcast in step two eventually focus on the location of the source and reconstruct a time reversed version of the original signal, which was broadcast in step one This is possible because of the TR invariance property of the lossless wave equation. Practical TR mirrors have several limitations, which result in an imperfect reconstruction of the original signal These limitations include i) limited spatial coverage by the transceivers, and ii) dissipation during the wave propagation (which breaks TR invariance of the wave equation).[14,18]. This paper quantitatively demonstrates that the exponential amplification technique partially mitigates the adverse effects of dissipation on the performance of TR mirrors, for different spatial loss distributions.
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