Generalized Snell's law and Maxwell equations
Analysis of PDEs
2025-07-21 v2 Materials Science
Mathematical Physics
math.MP
Optics
Abstract
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.
Cite
@article{arxiv.2305.01081,
title = {Generalized Snell's law and Maxwell equations},
author = {Cristian E. Gutiérrez and Ahmad Sabra},
journal= {arXiv preprint arXiv:2305.01081},
year = {2025}
}
Comments
33 pages. This is a significantly expanded version containing major changes