Phase factors representation for electromagnetic scattering from arough-surface perfect conductor

Abstract

The surface magnetic field (current) integral equation for a plane in an average rough interface between a vacuum and a perfect conductor is considered. This equation is presented in a form that contains the random elevations only as exponential functions with purely imaginary exponents. Iterations of this equation lead to a solution in powers of multiplicity of the Kirchhoff scattering, and each iterative term contains the random elevations only in exponents. Because the modulus of such functions is equal to unity, we may expect that convergence of such series is independent of the Rayleigh parameter. All mean values can be expressed directly in terms of joint characteristic functions of elevations in different points of a rough surface. To develop this representation of the scattering problem we use the three-dimensional Green function in terms of the one-dimensional Fourier integral with respect to z.