Temporal boundaries in electromagnetic materials.

Temporally modulated optical media are important in both abstract and applied applications, including time crystals, spacetime transformation optics, and dynamically controllable metamaterials. Here we investigate the behaviour of temporal boundaries, an important component in time crystals, and which have a range of potentially exotic properties. We show that traditional approaches based on an assumption of constant dielectric properties, with loss incorporated as an imaginary part, lead necessarily to unphysical solutions. Further, although physically reasonable predictions can be recovered using a narrowband approximation, here we show that the most appropriate models use materials with a temporal response and dispersive behaviour.