  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.
