Time mirror in a lumped transmission line

Abstract

Refraction and reflection of wave motion are fundamental phenomena studied across various physics domains. These effects occur when waves encounter spatial changes in the medium, such as obstacles or variations in refractive index. Traditionally, these boundaries are spatially localized but persist over time. The linear wave equation, symmetric in space and time, suggests the possibility of a temporal counterpart to spatial mirrors. A temporal mirror, unlike a spatial one, is spatially extended but temporally confined to brief instances. This can be realized by abruptly altering the medium's properties within a timescale shorter than the wave's dynamics. This study presents a temporal mirror implemented in a one-dimensional electrical transmission line. Numerical simulations were conducted to understand the system's behavior and study system dynamics in more details. Numerical and experimental results confirmed that the temporal mirror effectively converges the wave towards its original shape, validating theoretical predictions.