TM plane wave scattering and diffraction from a randomly rough half-plane: (part I) Derivation of the random wavefield representation.

This paper deals with a scattering and diffraction problem by a one-dimensionally random rough half-plane with perfect conductivity when a TM plane wave is incident. Since a divergence difficulty appears in a perturbation analysis for such a problem, a new formulation by a combination of the stochastic functional approach and the Wiener-Hopf technique is presented. By the Dα-Fourier transformation, an inhomogeneous scattered wavefield is transformed into an s-homogeneous random field, where s is a complex wavenumber parameter. Such an s-homogeneous random field is represented in terms of a Wiener-Hermite expansion with unknown coefficients called Wiener kernels. Hierarchical equations for the Wiener kernels are derived by the boundary condition. First, a Wiener-Hopf equation is derived from the hierarchical equations by approximate evaluations of scattering processes due to the surface roughness. Next, the Wiener-Hopf equation is solved by the Wiener-Hopf technique, and then the Wiener kernels are determined. By the inverse Dα-Fourier transformation, the inhomogeneous random wavefield is made up of three types of Fourier integrals representing effects of multiple scattering due to surface roughness, single edge diffraction by the edge and interactions between them. As a result, any statistical properties of the random wavefield may be calculated reasonably. [ABSTRACT FROM AUTHOR]