Transmission of electromagnetic waves through thin metal films with randomly rough surfaces

By means of perturbation theory and a computer simulation approach we study the transmission of p-polarized electromagnetic waves through a thin, free-standing metal film. The illuminated (upper) surface is a one-dimensional, randomly rough surface: the back surface is planar. The plane of incidence is perpendicular to the generators of the rough surface. The film is sufficiently thin that the two surface plasmon polaritons it supports in the absence of the roughness have distinct wave numbers ${\mathit{q}}_1$(ω) and ${\mathit{q}}_2$(ω) at the frequency ω of the incident wave. As a consequence, the angular dependence of the intensity of the incoherent component of the transmitted field displays satellite peaks at angles of transmission ${\mathrm{\theta }}_{\mathit{t}}$ that are related to the angle of incidence ${\mathrm{\theta }}_0$ by sin${\mathrm{\theta }}_{\mathit{t}}$=-sin${\mathrm{\theta }}_0$±(c/ω)[${\mathit{q}}_2$(ω)-${\mathit{q}}_1$(ω)], in addition to the enhanced transmission peak. Analogous satellite peaks are also present in the angular dependence of the intensity of the incoherent component of the reflected field, in addition to the enhanced backscattering peak.