Dispersion Relation of a Surface Wave at a Rough Metal-Air Interface

We derived a dispersion relation of a surface wave at a rough metal-air interface. In contrast to previous publications, we assumed that an intrinsic surface impedance due to a finite electric conductivity of the metal can be of the same order as the roughness-induced impedance. We then applied our results to the analysis of a long-standing problem of the discrepancy between the experimental data on the propagation of surface waves in the terahertz range of frequencies and the classical Drude theory.