  An instantaneous time mirror (ITM) is an interesting approach to manipulate
wave propagation from the time boundaries. In the time domain, the reversed
wave 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.

Classical Physics