Temporal boundaries in electromagnetic materials

TL;DR

This paper explores the behavior of temporal boundaries in electromagnetic materials, highlighting the limitations of traditional models and emphasizing the need for dispersive, temporally responsive material models for accurate predictions.

Contribution

It demonstrates that conventional constant-property models are unphysical and advocates for models incorporating material dispersion and temporal response.

Findings

Traditional models lead to unphysical solutions

Dispersive models provide physically reasonable predictions

Narrowband approximation can recover some predictions

Abstract

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