Electrodynamics of photonic temporal interfaces

Exotic forms of wave control have been emerging by engineering matter in space and time. In this framework, temporal photonic interfaces, i.e., abrupt changes in the electromagnetic properties of a material, have been shown to induce temporal scattering phenomena dual to spatial reflection and refraction, at the basis of photonic time crystals and space-time metamaterials. Despite decades-old theoretical studies on these topics, and recent experimental demonstrations, the careful modeling of these phenomena has been lagging behind. Here, we develop from first principles a rigorous model of the electrodynamics of temporal photonic interfaces, highlighting the crucial role of the mechanisms driving time variations. We demonstrate that the boundary conditions and conservation laws associated with temporal scattering may substantially deviate from those commonly employed in the literature, based on their microscopic implementation. Our results open new vistas for both fundamental investigations over light-matter interactions in time-varying structures and for the prospect of their future implementations and applications in optics and photonics.