Scattering of electromagnetic waves from a slightly random surface—reciprocal theorem, cross-polarization and backscattering enhancement

The present paper deals with the electromagnetic (EM) scattering from a perfectly conductive, random surface by means of the stochastic functional approach and aims to study the backscattering enhancement associated with co-polarized and cross-polarized scattering. The treatment is based on the stochastic functional theory where the random EM field is represented in terms of a Wiener-Hermite functional of the homogeneous Gaussian random surface. To obtain more precise solutions than the previous works (Nakayama J et al 1981 Radio Sci. 16 831-53), we first establish the reciprocal theorem for vector Wiener kernels which describe the stochastic functional representation of the EM field and, using this, we derive the reciprocal relations for the co-polarized and cross-polarized scattering distribution relative to TE and TM polarizations of incident wave. Solutions for the vector Wiener kernels up to the second are obtained so precisely as to satisfy the reciprocal relations and are expressed in terms of generating matrices, so that complex EM scattering processes described by the vector Wiener kernels are given dear physical interpretations. Compact operator representations are introduced to reformulate the hierarchical kernel equations, the mass operator equation and higher-order kernel solutions. It is shown that the second vector Wiener kernel physically describes a 'dressed double-scattering' process, similar to the scalar theory (Ogura H and Takahashi N 1995 Waves Random Media 5 223-42), and that the 'dressed double scattering', which involves anomalous scattering in the intermediate scattering processes, creates the backscattering enhancement in both co- and cross-polarized scattering for both TE and TM wave incidence.