High-frequency asymptotic solutions for backscattering by cylinders with conic section directrixes

High-frequency asymptotic expansions are derived for electric and magnetic fields backscattered from a perfectly conducting smooth two-dimensional surface illuminated by a plane incident wave in two cases of TE and TM linear polarizations. Diffraction corrections up to the second order of the inverse large parameter p=ak (where a is a curvature radius at the specularly reflecting point, and k is a field wave number) to the geometrical optics fields, and specifically to their phases, backscattering cross sections (HH and VV for TE and TM polarizations, correspondingly), as well as the polarization ratio HH/VV, are derived for the specular points of a general form. These general results are applied to backscattering from cylinders with conical section directrixes (circle, parabola, ellipse, and hyperbola), and a number of new compact explicit equations are derived, especially for elliptic and hyperbolic cylinders illuminated at an arbitrary incidence angle relative to their axes of symmetry.