Electromagnetic-wave propagation in a half-space bounded by a surface with 1D stochastic irregularities of the height and impedance

Propagation of electromagnetic waves in a half-space is investigated. The half-space is bounded by a surface whose height and impedance are characterized by 1D stochastically nonuniform perturbations. The analysis is performed taking into account multiple scattering from irregularities of the boundary. It is assumed that the slope angles of surface irregularities are small, the surface impedance and height exhibit smooth fluctuations over a wavelength, and the variance of impedance perturbations is large. Under these assumptions, the expression for the effective surface impedance is obtained.