Extinction theorem for a temporal gas-plasma boundary

Abstract

Abstract Temporal discontinuity in a medium’s dielectric properties (temporal boundary) is a useful model for considering electromagnetic phenomena in dynamic materials and metamaterials. Here a counterpart of the Ewald–Oseen extinction theorem of classical optics is derived for light scattering at a temporal boundary. In particular, it is shown that the extinction of the initial electromagnetic wave and its replacement by the frequency shifted waves at a temporal gas-plasma boundary can be understood as a result of a superposition of the elementary waves scattered by the suddenly appeared individual free electrons. In contrast to the classical extinction theorem, the extinction at a temporal boundary is closely related to causality and transient effects; the electromagnetic field at any observation point is formed by the elementary waves arriving from a sphere expanding with the speed of light.