Diffraction and Weber Functions

The diffraction of harmonic plane waves at a perfectly conducting half-plane leads to a Dirichlet or Neumann problem for the two-dimensional (2D) Helmholtz equation. As proved by Bateman the solution may be expressed in terms of Weber functions. We first prove that his result can be generalized to a perfectly conducting wedge. Then, assuming that the electromagnetic properties of a diffracting obstacle can be described by a surface impedance we analyze the diffraction at nonperfectly conducting planes and wedges; this corresponds to a mixed boundary value problem for the 2D Helmholtz equation.