Surface roughness and the optical properties of a semi-infinite material; the effect of a dielectric overlayer

Abstract

We derive expressions for the rate at which radiation is scattered and absorbed because of surface roughness on a semi-infinite material, in the presence of a dielectric overlayer. We confine our attention to the case of normal incidence. A formalism developed in an earlier paper by the present authors is utilized in the discussion. We also present a series of numerical calculations which explore the roughness-induced scattering and absorption of electromagnetic radiation for aluminum overcoated by aluminum oxide, in the ultraviolet region of the spectrum. The position of the reflectivity dip produced by roughness-induced coupling to the surface plasmon is found to shift toward the visible as the thickness of the oxide layer increases. The size of the dip is controlled strongly by the degree of correlation between the roughness on the vacuum-oxide interface, and that on the oxide-substrate interface. Under conditions discussed in the text of the paper, the presence of the oxide layer can greatly enhance the coupling between the incident radiation and surface plasmons.