Local fields near the surface of a crystalline dielectric

We calculate the variation of the local electric field with depth near the surface of a crystalline dielectric, for the cases of induced atomic dipoles oriented perpendicular and parallel to the surface. The crystalline dielectric is modelled by a cubic lattice of polarizable atoms, with the surface in the (001) plane. Our calculations show that the departure of the local field from its bulk value is confined almost entirely to the outermost plane, and even there is small (at the most a few percent).