Scattering and Diffraction of a Uniform Complex-Source Beam by a Slit

The two-dimensional problem of the scattering and diffraction of a TMz-polarized uniform complex-source beam by a slit is solved directly and analytically by using plane-polar coordinates. Suitable orthogonality relations finally yield a finite system of linear equations. Its numerical solution is successfully compared to the classical one obtained via the solution of the strip problem in elliptic coordinates using Mathieu functions and then applying Babinet's principle. The evaluation of the numerical results reveals that a suitably chosen uniform complex-source beam can replace an incident plane wave if the scattering features of a small part of the object are needed.