The Wiener--Hopf Technique for Impenetrable Wedges Having Arbitrary Aperture Angle

The diffraction by impenetrable wedges having arbitrary aperture angle is studied by means of the Wiener-Hopf (W-H) technique. A system of functional equations called generalized Wiener-Hopf equations (GWHE) is obtained. Only for certain values of the aperture angle these equations are recognizable as standard or classical Wiener-Hopf equations (CWHE). However, in all cases, a mapping to a suitable complex plane reduces the generalized Wiener-Hopf equations to classical Wiener-Hopf equations. It means that the diffraction by an impenetrable wedge always reduces to a standard Wiener-Hopf factorization. The explicit solution for the diffraction by a two-face impedance wedge having arbitrary aperture angle may be given by direct factorization methods.