The dispersion relation of surface plasmons on rough surfaces; A comment on roughness data

Abstract

Surface plasmons (SP) having the maximum of their intensity in the surface, are sensitive to geometric perturbations as roughness or gratings. This influence can be measured by the change of the dispersion relation of the SP. Whereas the results on sinusoidal gratings of Ag and Au can be calculated and agree with the observed results, the situation of statistically rough surfaces is less clear. An attempt is made to display the present situation. The experimental roughness data of “smooth” (natural roughness) surfaces of silver films and of surfaces with enhanced roughness are collected and their consistency is discussed. There is agreement between the values of the rms height, δ ∼5 , of “smooth” vaporised silver films (about 500thick) measured by different authors. The first-order theory describes the results in a satisfactory way. The situation of surfaces of Ag films of 500thickness with enhanced roughness (underlayer of CaF 2 ), however, is not satisfying since the calculated data of the displacement of the dispersion curve and of the increase of the damping using second-order approximations of the field above the rough metal surface are smaller than the observed data. The theoretical explanation is not yet settled, probably the approximation is not sufficient. The observed values of δ at thick films of silver (some 1000 ) are discussed in section 5.