Diffraction of a tm-polarized electromagnetic wave by two-dimensional thin screens and obstacles with edges

The solution to the scattering of an E-polarized plane wave from perfectly conducting infinite cylinders having arbitrary cross-sections and a finite number of edges is constructed by the polynomial expansions-Fourier transforms (PE-FT) method. The proposed method is based on the idea of reformulation of the integral equation in terms of the dual series equations with the trigonometrical kernel and the use of the properties of the orthogonal Gegenbauer polynomials. The initial problem is reduced to the problem of scattering from N bodies. As the result, the integral equation of the first kind with logarithmic singularity is reduced to N coupled systems of linear algebraic equations of the second kind. Particular cases of the circular cylindrical strip and the bodies with circular cylindrical facets are considered and analysis of scattering from the obstacles is presented.