On The Scalar Diffraction Field Of The Quarter Plane

摘要

The diffraction problem of the quarter plane with a Dirichlet boundary has been analyzed. The proposed scheme of solution includes application of the Kontorovich-Lebedev transform in the spherical coordinate system. The field excited by an incident plane wave have been considered. The problem reduces to that of an integral equation for the discontinuity of the normal derivative of the field on the quarter plane. The integral equation is solved through reduction to an inhomogenious system of linear equations. Expressions for the diffracted field are obtained by transforming the Kontorovich-Lebedev spectra into those of Malyuzhinets and the further evaluation of these spectral integrals on the Sommerfeld contour.