The Ewald Dynamical Theory of Reflection and Transmission of Light by a Dielectric Slab. The Extinction Theorem in Spatially Dispersive Media

Abstract

Abstract The dielectric slab is considered as a system of classical dipoles fixed on the lattice points of N + 1 parallel planes of a simple cubic lattice. The dipoles interact with retarded electromagnetic and non-retarded mechanical forces. Thus the media with spatial dispersion are taken into account, too. The problem of reflection and transmission of light by this system is solved in two steps. First, the amplitudes of the dipole moments are evaluated as a function of the incident electromagnetic wave. Then the electromagnetic field generated by the vibrating dipoles of the entire slab is calculated. The resulting formulae for the angle of refraction and for the intensity of the reflected and transmitted waves coincide with the classical Snell law and Fresnel formulae, if the wavelength of the incident light is much greater than the lattice constant of the slab. A generalized proof of the Ewald extinction theorem valid for all wavelengths and for spatially dispersive media is given.