Propagation of electromagnetic waves in anisotropic crystals: Origins of the angular dependence of the Davydov splittings

Publisher Website
Google Scholar
Abstract
The preceding discussion of the propagation of electromagnetic fields in anisotropic crystals is extended to include crystals having many molecules per unit cell. The susceptibility, which enters the equation of motion for the vector potential, is evaluated for a simple model of an anisotropic crystal and found to depend on the direction of propagation k̂ in the long wavelength limit k → 0. When the susceptibility is specialized to a description of Frenkel excitons, the resonant energies and the Davydov splittings are shown to exhibit a dependence on k̂ as predicted by Fox and Yatsiv. The dielectrictensor ε, identified by deriving the customary Maxwell equations from the equation of motion for the vector potential, is found to be independent of k̂. The angular dependence of the Davydov splittings is thus predicted by the Fresnel equations of classical optics and is not unique to excitons. If such angular dependence is not observed, the customary Maxwell equations are not valid. A brief discussion of the failure of the model to give a proper account of interband transitions is given.