Scattering at Temporal Interfaces: An overview from an antennas and propagation engineering perspective

Abstract

Recent years have witnessed a surge of interest in exotic electromagnetic (EM) wave propagation in time-varying systems. An interesting concept is the one of a temporal interface, the time-analogue of a spatial interface, formed by an abrupt and uniform change of the EM properties of the host medium in time. A time interface scatters the incident wave in a dual fashion compared to its spatial counterpart, conserving momentum but transforming frequency and exchanging energy with the wave. This article provides an overview of the wave-scattering features induced by time interfaces from an antennas and propagation engineering perspective. We first discuss the dualities of wave propagation across spatial and temporal interfaces, by recasting the telegrapher equations in a linear time-variant (LTV) transmission line (TL). Then, we introduce the scattering matrix to describe temporal scattering processes, and derive the conditions for reciprocity and momentum conservation. Understanding temporal scattering through the lens of conventional microwave engineering theory may facilitate the analysis and implementation of next-generation metamaterials encompassing temporal degrees of freedom.