Reflection of light by a semi-infinite dielectric

A microscopic theory of the reflection of S-polarized light by a perfect semi-infinite molecular crystal is developed. The interactions between molecules are assumed to be of the dipole-dipole type. When excited state van der Waals interactions are neglected, so that molecular polarizability tensors are independent of distance from the surface, the reflection power factorizes into separate normal mode contributions. Each mode is characterized by a complex amplitude and refractive index. For normal incidence, the theory of Mahan and Obermair is recovered. If interactions between crystal planes are negligible there is only one polariton mode and the reflection formula of classical optics is obtained. If the molecules in the surface plane have excitation energies different from those in other planes, then the reflectivity formula contains an additional frequency dependent factor. When the coupling between planes is weak this surface factor causes the appearance of either a deep narrow minimum within the stopping band or a sharp spike outside the band. Model calculations exploring this effect are described.