Free optical vibrations of an infinite plate of homogeneous isotropic elastic matter

Abstract

We adapt the standard theory of the free acoustic vibrations of an infinite plate of homogeneous isotropic elastic matter to the corresponding case of optical vibrations. Treating nonpolar material first, we show that the effect of the free surface is to couple LO and TO modes, and we demonstrate the existence of the optical analog of Rayleigh waves. Interface and guided modes are both present, and their respective mode patterns are derived. In polar materials the coupling between LO and TO is different because of the frequency splitting due to the ionic fields, but surface modes are still present. This result contradicts the conclusion of the hydrodynamic model that surface modes do not exist. The polar character also allows the existence of surface polaritons. It is shown that the standard description of these modes, which neglects the elastic properties of the material, is physically invalid. The effect of the free surface is to couple surface polaritons and LO modes, and a description is given of the mode patterns that may occur. General expressions for energy flux are given, and boundary conditions for the general case are suggested. This treatment goes some way towards reconciling the various theoretical models of phonon confinement that have been advanced recently.