Doubly diffracted ray from a hard quarterplane

On Radlow's quarter‐plane diffraction solution

“…As a matter of fact it embeds the correct half plane Sommerfeld's solution relevant to the two edges of the quarter plane, that ensure the correctness of the solution to the asymptotic order ( kr ). Furthermore, as presented by Albertsen [2000], it also embeds doubly diffracted rays, despite their expression does not blend into the form prescribed by the Geometrical Theory of Diffraction (i.e., the cascading of two edge diffractions) far from the transition with the vertex ray, i.e., for diffraction points far from the vertex, as occurs in the work of Maci et al [1994] or Capolino and Maci [1996]. Hence the challenge of deriving a readily computable vertex diffraction coefficient from an exact solution is still open.…”

“…A researcher who gave him credit was Albertsen who extended the solution to the electromagnetic case [ Albertsen , 1997], also providing a closed form vertex diffraction coefficient by means of an explicit calculation of the Wiener‐Hopf factorization involved in Radlow's solution. From the same canonical problem, Albertsen [2000] also derived a uniform high‐frequency description for the doubly diffracted rays, i.e., rays which experience two successive diffractions at the two edges. Indeed, the plane wave spectral representation which is obtained by Radlow is very appealing to derive high‐frequency description of the scattering via asymptotic ray optics approximation, however, as we will demonstrate in this paper, it is not correct.…”