Scattering and diffraction of a uniform complex-source beam by a slit in a perfectly conducting plane screen

A new multipole solution in plane-polar coordinates for the scattering of an arbitrary TE- or TM-polarized incident field by an infinitely extended slit in a plane screen is derived. To this end a classical three-domain problem with a complete multipole expansion in each of the domains is formulated. The unknown multipole amplitudes are found from the continuity conditions of the tangential electric and magnetic field components. Finally an infinite system of linear equations is derived which can be approximated by a numerically tractable finite one leading to a solution with an arbitrary accuracy. The results are numerically successfully compared to those ones obtained by classically solving the strip problem using Mathieu functions and by a subsequent application of the rigorous form of the Babinet principle. Numerical results include the comparison of the scattered fields obtained for an incident uniform complex-source beam and for an incident plane wave.