Time reversal and holography with spacetime transformations


Wave control is usually performed by spatially engineering the properties of a medium. Because time and space play similar roles in wave propagation, manipulating time boundaries provides a complementary approach. Here, we experimentally demonstrate the relevance of this concept by introducing instantaneous time mirrors. We show with water waves that a sudden change of the effective gravity generates time-reversed waves that refocus at the source. We generalize this concept for all kinds of waves, introducing a universal framework which explains the effect of any time disruption on wave propagation. We show that sudden changes of the medium properties generate instant wave sources that emerge instantaneously from the entire space at the time disruption. The time-reversed waves originate from these ‘Cauchy sources’, which are the counterpart of Huygens virtual sources on a time boundary. It allows us to revisit the holographic method and introduce a new approach for wave control.

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Figure 1: Schematic of the instantaneous time mirror.
Figure 2: ITM experimental implementation.
Figure 3: ITM on a wavepacket.
Figure 4: Image sequence of the instantaneous time reversal of a complex wave field.
Figure 5: The time equivalent of a mirror.


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We are grateful to Y. Couder and S. Perrard for fruitful and stimulating discussions. We thank A. Souilah and X. Benoit-Gonin for their help in building the experimental set-up. The authors acknowledge the support of the AXA research fund and LABEX WIFI (Laboratory of Excellence ANR-10-LABX-24) within the French Program ‘Investments for the Future’ under reference ANR-10-IDEX-0001-02 PSL.

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All the authors discussed, interpreted the results and conceived the theoretical framework. M.F. and E.F. conceived the initial concept. V.B., A.E., M.F. and E.F. designed the experiment. V.B. and A.E. performed the experiments. M.L. extended the model to water waves and designed the simulations. V.B., M.F. and E.F. wrote the paper. All authors reviewed the manuscript.

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Correspondence to Mathias Fink or Emmanuel Fort.

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The authors declare no competing financial interests.

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Bacot, V., Labousse, M., Eddi, A. et al. Time reversal and holography with spacetime transformations. Nature Phys 12, 972–977 (2016). https://doi.org/10.1038/nphys3810

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