On the dielectric theory of a crystalline slab of point molecules

We discuss the dielectric response of a crystalline slab of point molecules to an incident plane electromagnetic wave. The slab is assumed to be made up of non-polar, polarizable molecules (a) lying at points of a simple cubic lattice and (b) interacting only via the electromagnetic field. Expressions for the dispersion relations, polarisation and electric fields and the transmission coefficient are derived. Conditions under which a point dielectric equation of state holds are obtained. This simple system exhibits three resonances near the transverse optic frequency.