Exploiting the time-reversal invariance and reciprocal properties of the lossless wave equation enables elegantly simple solutions to complex wave-scattering problems, and is embodied in the time-reversal mirror. Here we demonstrate the implementation of an electromagnetic time-reversal mirror in a wave chaotic system containing a discrete nonlinearity. We demonstrate that the timereversed nonlinear excitations reconstruct exclusively upon the source of the nonlinearity. As an example of its utility, we demonstrate a new form of secure communication, and point out other applications.PACS numbers: 05.45. Mt, 05.45.Vx, 41.20.Jb, 42.25.Dd Wave chaos concerns the study of solutions to linear wave equations that display classical chaos in their short-wavelength limit. Such systems are endowed with many universal wave properties, such as eigenvalue and scattering-matrix statistics, by virtue of their classically chaotic counterparts.[1] Although wave chaotic systems are strongly scattering and have complex behavior, they can be elegantly studied by exploiting the time-reversal invariance and reciprocal properties of the linear wave equation. [2-9] Adding objects with complex nonlinear dynamics to linear wave chaotic systems has only recently been considered, [10] and represents an exciting new direction of research. Here we examine a wave chaotic system with a single discrete nonlinear element, and create a new nonlinear electromagnetic time-reversal mirror that shows promise for both fundamental studies and novel applications.A time-reversal mirror works by taking advantage of the invariance of the lossless wave equation under timereversal; for a time-forward solution of the wave equation representing a wave travelling in a given direction, there is a corresponding time-reversed solution representing a wave travelling in the same direction backwards in time, or in the opposite direction forward in time. This can be realized by transmitting a waveform at a particular source location and recording the reverberating waveforms (sona) with an array of receivers; the recorded waveforms are reversed in time and retransmitted back from the receivers, propagating to and reconstructing a time-reversed version of the original waveform at the source [3]. Time-reversal mirrors have been demonstrated for both acoustic [2-9, 11, 12] and electromagnetic waves [6,8,13], and exploited for applications such as lithotripsy [2,4], underwater communication [2, 14, 15], sensing perturbations [11,12], and achieving sub-wavelength imaging [6][7][8]16].An ideal time-reversal mirror in an open environment would collect the forward-propagating wave at every point on a closed surface enclosing the transmitter, requiring a very large number of receivers. The receiving array can be simplified, without significant loss of fidelity of the reconstruction, if there is a closed, ray-chaotic environment where a propagating wave (with wavelength much smaller than the size of the enclosure) will eventually reach every point in the environment, allowin...
We consider time reversal of electromagnetic waves in a closed, wave-chaotic system containing a discrete, passive, harmonic-generating nonlinearity. An experimental system is constructed as a time-reversal mirror, in which excitations generated by the nonlinearity are gathered, time-reversed, transmitted, and directed exclusively to the location of the nonlinearity. Here we show that such nonlinear objects can be purely passive (as opposed to the active nonlinearities used in previous work), and we develop a higher data rate exclusive communication system based on nonlinear time reversal. A model of the experimental system is developed, using a star-graph network of transmission lines, with one of the lines terminated by a model diode. The model simulates time reversal of linear and nonlinear signals, demonstrates features seen in the experimental system, and supports our interpretation of the experimental results.
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