Electromagnetic Boundary Conditions for Space--time Interfaces

Gratus, Jonathan and Horsley, Simon A. R. and McCall, Martin W. (2025) Electromagnetic Boundary Conditions for Space--time Interfaces. Other. Arxiv.

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Abstract

We give a general family of electromagnetic boundary conditions applicable to arbitrary space--time interfaces between electromagnetic media, which include the known space--only and time--only boundary conditions as special cases. These boundary conditions describe a broad class of electromagnetic interfaces, including surfaces in arbitrary motion, ultra-thin (metasurface) media, and cases where the media on one or both sides of the boundary can be both spatially and temporally dispersive. Our approach utilizes 4-dimensional spacetime and addresses the question of how, and in what ways, an electromagnetic field may be connected across a 3-dimensional hypersurface. We show that our proposed boundary conditions are the most general conditions consistent with causality and linearity.