Diffraction of plane waves on a parabolic cylinder

We prove that the diffraction of a harmonic plane wave on a perfectly conducting cylinder has an exact analytical solution in terms of the Weber functions. The asymptotic approximation of these functions gives a simple physical interpretation of the solution far from the diffracting obstacle and we discuss how quantitative results could be obtained from these asymptotic approximations. The generalization to an imperfectly conducting parabolic cylinder is also discussed.