PLASMONS ON A RANDOMLY ROUGH-SURFACE

The spectral density of plasmons on a randomly rough surface is calculated as a function of the rms amplitude of its departure from flatness and the extent of its lateral correlation. The spectral density is obtained from a surface self-energy-like function, which is in turn numerically calculated from an integral equation. Its kernel, containing effects of all orders in the rms amplitude, is given here explicitly. An earlier treatment of Farias and Maradudin is thus generalized, and results valid for an extended range of values of the statistical parameters are obtained. It is found that the predicted splitting of the surface-plasmon spectrum into two peaks appears only for values of the roughness amplitude larger than a certain critical size, and disappears for values of the lateral correlation length which are either too small or too large. © 1990 The American Physical Society.