Nonlinear and short-orbit time-reversal in a wave chaotic system

Abstract

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 [S. M. Anlage, J. Rodgers, S. Hemmady, J. Hart, T. M. Antonsen, E. Ott, Acta Physica Polonica A 112, 569 (2007).]. In previous work, we extended the concepts of Loschmidt Echo and Fidelity to classical waves, such as acoustic and electromagnetic waves, to realize a new sensor paradigm [B. T. Taddese, J. Hart, T. M. Antonsen, E. Ott, and S. M. Anlage, Appl. Phys. Lett. 95, 114103 (2009); B. T. Taddese, T. M. Antonsen, E. Ott, and S. M. Anlage, J. Appl. Phys. 108, 114911 (2010) ; B. T. Taddese, G. Gradoni, F. Moglie, T. M Antonsen, E. Ott, S. M. Anlage, New J. Phys. 15, 023025 (2013)]. Here we demonstrate the implementation of an electromagnetic time-reversal mirror in a wave chaotic system containing a discrete nonlinearity [M. Frazier, B. Taddese, T. Antonsen, S. M. Anlage, Phys. Rev. Lett. 110, 063902 (2013). See “Alice and Bob Go Nonlinear” Synopsis on Physics.APS.org]. We demonstrate that the time-reversed 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.