Abstract
The general theory outlined in previous papers for the vibrational properties of finite specimens is applied to ionic crystals of cylindrical shape. Unlike the previously studied cases, the polariton modes are mixtures of magnetic- and electric-type oscillations, except for normal incidence. Our calculated absorption curves agree well with those observed on small fibres. An alternative formulation of the polariton absorption process in finite crystals is given in terms of the quantal Green function theory in the spirit of Hopfield's treatment for infinite crystals.