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arXiv · 2608.03995

Refraction laws in spatio-temporal media

Cristian E. Gutiérrez·Eric Stachura
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Abstract

We study the time-dependent Maxwell system, formulated in the sense of distributions, for electromagnetic waves propagating through media with temporal and spatial material interfaces. Under explicit trace and regularity assumptions on the permittivity and permeability, we derive the jump conditions produced by temporal discontinuities and by subsequent spatial interfaces. These conditions are used to obtain generalized Snell laws for the wave vectors generated by temporal splitting, reflection, and transmission. We also derive the associated amplitude equations and organize them as a finite-dimensional linear system for a space-time slab geometry. Finally, we provide an explicit oblique-incidence example. Our approach does not impose a smooth-field ansatz and allows material parameters that need not be constant away from the interfaces.

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Cristian E. Gutiérrez, Eric Stachura. 2026-08-04. Refraction laws in spatio-temporal media. https://arxiv.org/abs/2608.03995

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