The Microscopical Theory of Reflection and Transmission of Light by a Spatial Dispersive Dielectric Slab and the Ewald Dynamical Theory of Diffraction

TLDR: In this article, the dielectric slab is considered as a system of classical dipoles fixed on the lattice points of N + 1 parallel planes of a general primitive crystal lattice.

Abstract: The dielectric slab is considered as a system of classical dipoles fixed on the lattice points of N + 1 parallel planes of a general primitive crystal lattice. The dipoles interact with retarded electromagnetic and non-retarded mechanical forces. Thus media with spatial dispersion are also taken into account. Formulae are deduced for the intensity of the electromagnetic wave, reflected or transmitted by the dielectric slab. The resulting formulae are valid for all wavelengths where the dipole approximation is appropriate. Thus they include both the effects known in the dynamical theory of X-ray diffraction as well as Snell's law and Fresnel's formulae for visible light and the effects caused by spatial dispersion.