A vector solution for electromagnetic wave scattering from a rough surface of arbitrary dielectric constant

A vector solution for electromagnetic wave scattering from a rough surface of arbitrary dielectric constant is developed through the use of the Stratton-Chu integral under the assumption that the horizontal extent of the surface irregularities (and possibly the vertical extent also) is large compared with the incident wavelength. Other assumptions implicit in this solution are that the incident wave is a plane wave of arbitrary polarization, that the observation point is at any arbitrary direction in the far field zone of the scattering surface, and that the rough surface can be represented by a stationary random process with normal height distribution and Gaussian correlation function, the mean value of the surface being a plane. For a rough surface of lossless dielectric, plots showing the effects of dielectric constant, angles of incidence and scattering, and the statistical parameters of the rough surface are presented for the special cases of backscattering and bistatic scattering in the plane of incidence. For bistatic scattering the scattering behavior near the Brewster angle is clearly shown; the results for backscattering indicate the need for a more general rough surface model incorporating surface structure both large and small with respect to the incident wavelength.