Backscattering from Wide-Angle and Narrow-Angle Cones

Abstract

Solutions are obtained for the diffraction of the waves radiated by scalar and vector point sources on the axis of a semi-infinite cone. The scalar problems are solved by the method of characteristic Green's functions to yield directly various alternative representations whose different convergence properties are discussed; the vector problem is solved by an application of spherical transmission line theory. To evaluate the plane wave scattering observed far from the cone tip, a highly convergent contour integral representation is selected and evaluated approximately for the special case of backscattering from cones having large and small apex angles. The results for the large-angle cone exhibit the transition from a backscattered spherical wave to a plane wave as the cone degenerates into an infinite plane.