An exact solution for diffraction of a line-source field by a half-plane

This paper deals with the exact solution of a special electromagnetic diffraction problem namely, diffraction of a line-source field by a half-plane. The line source is located on the surface of the half-plane, and radiates an E-polarized wave described by uin=H(1)n (kr1) sinnφ1, where n=1,2,3,⋅⋅⋅, and (r1,φ1) are polar coordinates with the origin at the source point. A new, closed-form, exact solution for the total field on the shadow boundary is presented. This exact solution consists of n terms of order k−p, where p=1,2,...,n. Its first two terms, which are of orders k−1/2 and k−3/2 relative to the incident field, agree with the asymptotic solution derived in a companion paper by the uniform asymptotic theory of edge diffraction.