Abstract
A rigorous solution to the Neumann boundary value problem (BVP) for semicircular trough in a perfectly electrically conducting (PEC) ground plane is presented. The known Rayleigh's method expansion of a solution by eigensolutions of the Helmholtz equation in cylindrical coordinates coupled with partial orthogonality of trigonometric functions is used. In contrast to previous works on this theme, a Fredholm 2nd kind matrix equation for modal coefficients is obtained, which permits one to derive very fast convergent approximate solution for any incidence angle and trough dimension. The method solution permits one to consider a dielectric loading as well. A strong broadband fall-off of backscattering from apertures loaded with lossy dielectric is theoretically revealed.
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