Theory of surface polaritons and image potentials in polar crystals

A quantum-mechanical derivation is presented for the dispersion of surface polaritons on polar materials. We do not assume a local dielectric function exists at the surface of the solid. We introduce quantum operators for the phonons (or excitons) and photons, and couple them in the Coulomb gauge. We derive and solve the equations of motion of these coupled oscillators. We find two solutions. One is the surface polariton that agrees with the classical result of Fuchs and Kliewer. The other is a new surface polariton that exists at the frequency of the bulk longitudinal phonon. We also prove that these are the only two solutions. We also find exactly the polarization in the solid from a static external charge, and show that it is not given by surface polaritons.