High-frequency asymptotic expansions of a backscattering cross-section and an HH/VV polarization ratio for smooth two-dimensional surfaces

High-frequency asymptotic expansions of electrical and magnetic fields are obtained at a perfectly conducting smooth 2D surface illuminated by a plane incident wave in two cases of TE and TM polarization. Corrections to the geometrical optics backscattering HH and VV cross-sections are derived and the polarization ratio HH/VV is estimated for the specular points of a general form. It is shown that the coefficient of the first term in this series ∼ 1/k2 depends not only on the local surface curvature radius at the specular reflecting points,but also on higher derivatives up to the sixth order. For backscattering from a statistically rough surface, averaging over surface random derivatives at the specular points was performed. It was shown that for statistically uniform (stationary on space variables) random surfaces, the polarization ratio HH/VV (dB) is positive on average and proportional to ∼ 1/k2