Temporal boundaries in electromagnetic materials

Temporally modulated optical media are important in both abstract and applied applications, such as spacetime transformation optics, relativistic laser-plasma interactions, dynamic metamaterials. Here we investigate the behaviour of temporal boundaries, show that traditional approaches assume constant dielectric properties, with loss incorporated an imaginary part, necessarily lead to unphysical solutions. Further, although physically reasonable predictions can be recovered a narrowband approximation, appropriate models should use materials response dispersive behaviour.