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Generalized Snell's law and Maxwell equations

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arxiv 2305.01081 v3 pith:XBM6EWXO submitted 2023-05-01 math.AP cond-mat.mtrl-scimath-phmath.MPphysics.optics

Cristian E. Gutiérrez , Ahmad Sabra This is my paper · ORCID
classification math.APcond-mat.mtrl-scimath-phmath.MPphysics.optics
keywords generalizedmaxwellsnellalongamplitudeamplitudesanalysisboundary
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This paper examines the Maxwell system of electrodynamics within the framework of distributions. A primary objective is to establish boundary conditions for fields at interfaces when the charge and current densities are measures localized on the interface. From this analysis, the paper presents a derivation of the generalized Snell's law, along with formulas for the amplitudes of the reflected and transmitted waves in terms of the incident amplitude.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Refraction laws in spatio-temporal media

    math.AP 2026-08 reject novelty 5.0 of 10

    The paper derives generalized Snell laws and an amplitude system for spatio-temporal interfaces, but the amplitude system conflates temporal and spatial scattering, invalidating the example.

  2. Refraction laws in temporal media

    math.AP 2025-07 conditional novelty 4.0 of 10

    A rigorous distribution-theory derivation shows that at a temporal interface the fields satisfy jump conditions that yield a generalized Snell's law and explicit reflection/transmission coefficients.

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