Theoretical and numerical study of conical diffraction by cylindrical objects

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Abstract
Thanks to a Fourier transform with respect to the spatial coordinate describing the direction of the cylinder axis, we are led to a two-dimensional problem. A set of four integral equations is then established from a rigorous integral theory, where the Fourier transform of the field on the surface of the cylinder is unknown. With the help of a boundary finite elements method, the integral system is converted into a linear system of equations. This system is not uniquely solvable for a discrete set of irregular frequencies. However, it is possible to overcome this difficulty by adding constraints out of the boundary. To ensure the accuracy of the numerical implementation, the singular parts of the kernels are isolated and their integration is performed analytically. In this paper, results are given when the excitation is a plane wave with arbitrary polarization and oblique incidence (conical diffraction), but only the knowledge of the Fourier transform of the incident field is required.