Localized plasmons on a metal surface

This paper considers collective oscillations of electron density localized near a metal surface. Its description involves the wave equation of plasma oscillations. Assuming the axial symmetry of the problem, separation of variables in the equation is carried out and a set of analytical functions providing the variety of solutions is obtained. The solutions provide natural multipole quantization of surface plasmon states. Expressions are obtained for local potential fields formed by multipole plasmon modes at the interface. Their role in physical implementation of mechanisms of localization of excess electrons on the metal surface is discussed.