Diffraction at a plane angular sector

Abstract

A closed form solution is presented for the scattering in the far zone by a vertex at the interconnection between the two edges of a plane angular sector, when it is illuminated by a plane wave. The solution is obtained as a superposition of simple interaction mechanisms between the two adjacent edges. The spectral representation of the field diffracted by the first edge is used to illuminate the second edge. The response of the latter is evaluated by applying the induction principle at the plane angular sector. In spite of the simplicity of this basic assumption, the resulting expressions recover in the pertinent directions the dominant edge ray field contributions, including second order diffraction mechanisms. The solution is cast in a very simple, compact matrix form, which explicitly satisfies reciprocity.