Infrared absorption by surface phonons and surface plasmons in small crystals

A continuum model is developed which describes the infrared absorption of interacting spheres very much smaller than the wavelength of light. A mode with uniform polarization inside the sphere is assumed responsible for the absorption. The frequency of this mode in a small isolated sphere can be greatly shifted from the bulk value due to the surface polarization charge. If the particles are not isolated, this frequency is also influenced by the dipolar interaction of neighboring particles. We find that it is possible to define an average dielectric function for a layer of small interacting, absorbing spheres which has the Lorentz form for either phonon or plasmon excitations. If both plasmon and phonon excitations are possible in the same particle, the absorption coefficient of the coupled system displays two resonances and an antiresonance.