A general spectral-domain formulation of the electromagnetic scattering bya perfectly conducting circular cylinder

A full-wave method for the two-dimensional scattering problem by a perfectl y conducting circular cylinder is presented, providing an exact solution fo r the Helmholtz equation in very general cases. The method is based on the Fourier series expression of the boundary conditions (Dirichlet and Neumann ) generated by an arbitrary, finite-power, incident beam, and the analysis is performed in the complex plane of the analytic continuation of a space s pectral variable. This approach allows us to define an analytic continuatio n for cylindrical wave expansions, working with lossy propagation media and with a full incident spectrum, including inhomogeneous waves, both in E an d in H polarization. Convergence of the modal expansion is investigated, to verify that very weak hypotheses are needed, and no geometrical or paraxia l approximation is required. Exact expressions for the expansion coefficien ts are given, in terms of complex integrations involving the Fourier spectr um of the incident beam.