Time-Reversed Water Waves Generated from an Instantaneous Time Mirror

TL;DR

This paper explores the behavior of water waves generated by an instantaneous time mirror, demonstrating experimentally and theoretically that the reversed wave pattern relates to the Laplacian of the initial wave, with implications for wave manipulation.

Contribution

It provides a novel theoretical and experimental analysis of time-reversed water waves, revealing their relation to the Laplacian of the initial wave pattern and exploring effects in inhomogeneous media.

Findings

Reversed wave pattern is related to the Laplacian of the initial wave.

Experimental verification of the theoretical prediction.

Discussion of energy change phenomena in inhomogeneous media.

Abstract

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.