Additional Boundary Conditions: An Historical Mistake

Abstract

Since their introduction by Pekar in 1956, additional boundary conditions (ABC's) have been used in innumerable papers and in different ways to calculate the reflectivity for frequencies where more than one wave can propagate in a dielectric medium, particularly in connection with the polariton problem. Regarding the surface as a source of radiation into the medium this long lasting problem is removed demonstrating a unique solution to exist if, as usually assumed, the thickness of the surface layer is small compared with the wavelength. The analysis applies to any medium described by a dielectric function $\varepsilon (q,\omega )$. Half-space and slab geometry are studied in general, and simple analytical results are provided for the polariton problem. The method is then further utilized to consider exactly spatial dispersion in the retarded photon Green's function.