Electromagnetic diffraction by homogeneous cylinders of the field radiated by a dipole: a rigorous computation

Expanding the field radiated by a dipole as a superposition of cylindrical waves (Fourier transform with respect to the spatial coordinate describing the direction of the cylinder axis) permits us to solve the diffraction problem with the help of a rigorous integral method specialized for the diffraction of an obliquely incident wave by a homogeneous rod. A linear system is solved for each Fourier component, and the solution is obtained from the superposition of the elementary diffracted fields. In the complex plane of spatial frequencies, a discrete set of singular values lies along the real axis or close to it, describing the irregular frequencies, the branch points or the guided modes. In order to perform an accurate integration, special attention is given to the behavior of the transfer function in the neighborhood of such critical points.