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Time mirrors and temporal cavities
Wave control is usually performed by engineering the spatial properties of the medium. Because space and time play similar roles, it is possible to perform time manipulations with a dual approach. In this talk, I will show how such manipulations enable one to obtain a “time reversal machine” for the waves. In particular, I will introduce the concept of instantaneous time mirror which make waves relive their previous “life” using time discontinuities. This approach is complementary to the standard time reversal mirror approach using sensors/emitters positioned at the surface boundary of a given volume and using digital memories to re-emit the time reversed wave within this volume. I will present an experimental implementation of these new concepts using water waves propagating at the surface of a water tank. The time discontinuity is induced by a vertical jolt which induces an abrupt change of the effective gravity. Different theoretical approaches will be discussed in particular Cauchy, Loschmidt and Huygens-Fresnel points of view. The concept of instantaneous time mirror will be generalized. This will allows us to revisit Faraday instability and to interpret it as a phase conjugation mirror for surface waves.