Energy Band Models for Spatially Dispersive Dielectric Media

Abstract

The effects of spatial dispersion on the optical properties of dielectric crystals, arising from the broadening of the molecular energy levels into energy bands by the intermolecular interaction, are discussed both in the microscopic and the macroscopic theory. The microscopic equations of motion for the internal degrees of freedom describing the molecular excitations are derived using semiclassical radiation theory, and the conditions are given under which a description in terms of only the dipole moment is possible. The corresponding macroscopic equations are derived and the nature of the boundary conditions and integral relations appearing in the theory are discussed. The characterization of spatially dispersive media as nonlocal is shown to be based on a misinterpretation of the meaning of the integral kernels relating to infinite media. The breakdown of the macroscopic theory due to the previously predicted onset of an antiresonant response is explicitly demonstrated for slab geometries for which rigorous solutions are given of both the macroscopic and the microscopic equations. Finally, we introduce a mechanical coupling varying exponentially with the intermolecular separation, which provides a two parameter model for the exciton bands and which prevents the proliferation of microscopic refractive indices occurring in other models. The exp model is shown to be useful to study the dependence of the optical properties for example on the effective mass and the width of an exciton band.