Backscattering from Wide-Angle and Narrow-Angle Cones

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.