Generalized Snell's law and Maxwell equations

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.

31 pages, 2 figures. This is an updated version containing major changes, to appear in the SIAM Journal of Applied Mathematics