Temporal negative refraction

Negative refraction is a peculiar wave propagation phenomenon that occurs when a wave crosses a boundary between a regular medium and a medium with both constitutive parameters negative at the given frequency. The phase and group velocities of the transmitted wave then turn anti-parallel. Here we propose a temporal analogue of the negative refraction phenomenon using time-dependent media. Instead of transmitting the wave through a spatial boundary we transmit it through an artificial temporal boundary, created by switching both parameters from constant to dispersive with frequency. We show that the resulting dynamics is sharply different from the spatial case, featuring both reflection and refraction in positive and negative regimes simultaneously. We demonstrate our results analytically and numerically using electromagnetic medium. In addition, we show that by a targeted dispersion tuning the temporal boundary can be made nonreflecting, while preserving both positive and negative refraction.