Spherical wave representation of the dyadic Green's function for a spherical impedance boss at the edge of a perfectly conducting wedge
In this work, canonical problem of a scatterer at the edge of a wedge is considered and eigenfunction solution is developed. Initially, a dyadic Green's function for a spherical impedance boss at the edge of a perfect electrically conducting (PEC) wedge is obtained. Since scattering from objects at the edge is of interest, a three-dimensional Green's function is formulated in terms of spherical vector wave functions. First, an incomplete dyadic Green's function is expanded in terms of solenoidal vector wave functions with unknown coefficients, which is not valid in the source region. Unknown coefficients are calculated by utilizing the Green's second identity and orthogonality of the vector wave functions. Then, the solution is completed by adding general source correction term. Resulting Green's function is decomposed into two parts. First part is the dyadic Green's function of the wedge in the absence of the sphere and the second part represents the effects of the spherical boss and the interaction between the wedge and the scatterer. In contrast to cylindrical vector wave function expansions and asymptotic solutions which fail to converge in the paraxial region, proposed solution exhibits good convergence everywhere in space. Using the developed Green's function scattered field patterns are obtained for several impedance values and results are compared with those of a PEC spherical boss. Effects of the incident angle and surface impedance of the boss on the scattering pattern are also examined.