Optical lattice vibrations in finite ionic crystals: II

Abstract

A theory for the polariton modes (long-wave optical phonons coupled to photons) in finite ionic crystals of arbitrary shape is given. The theory is exemplified by detailed calculations for the case of a spherical specimen. Stationary polariton states of three types are obtained, which, for small enough crystals, are characterized by (i) large amplitudes inside the solid (bulk modes), (ii) large amplitudes near the surface of the solid (surface modes) and (iii) small amplitudes inside the solid (vacuum modes). The absorption spectrum of spherical diatomic samples is calculated and it is found that the polariton modes cause absorption in regions which are forbidden for infinite crystals. The generalization of the theory to the case of complex cubic crystals is given and applied to interpret the absorption spectrum of small SrTiO₃ spheres.