Surface Phonon Modes of a Microcrystal Slab

The frequencies of long-wavelength normal modes of a stab consisting of small spheres are calculated by using a dipole-dipole interaction Hamiltonian proposed by Clippe, Evrard and Lucas. Two optically active modes are found, one with a frequency lower than the Fröhlich mode frequency ω F and the other with a frequency higher than ω F . It is shown that for a thick enough slab the frequencies of the active modes coincide with those derived from the Maxwell-Garnett theory. This result indicates that the Maxwell-Garnett theory is reliable, even though it takes into account only approximately the dipole-dipole interaction.