An instantaneous time mirror (ITM) is an interesting approach to manipulate wave propagation from the time boundaries. In the time domain, the reversed waveform is previously proven to be the temporal derivative of the original pattern. Here, we further investigate into the relationship between the wave patterns in the spatial domain both theoretically and experimentally. The refraction of a square array of laser beams is used to determine the three-dimensional (3D) shape of the water surface. The experimental results verify the theoretical prediction that the reversed pattern is related to the Laplacian of the initial wave field. Based on these findings, the behaviors of the ITM activated in an inhomogeneous medium are discussed, and the phenomenon of total energy change is explained.

中文翻译：

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瞬时时间镜产生的与时间相反的水波

瞬时时间镜（ITM）是一种有趣的方法，可以从时间边界操纵波传播。在时域中，反向波形先前被证明是原始模式的时间导数。在这里，我们将在理论上和实验上进一步研究空间​​域中波型之间的关系。方阵激光束的折射用于确定水面的三维（3D）形状。实验结果验证了理论预测，即反向波型与初始波场的拉普拉斯算子有关。基于这些发现，讨论了在不均匀介质中激活的ITM的行为，并解释了总能量变化的现象。