Electromagnetic Scattering by a Sphere Intersected by Metal Planes

The scattering of a plane wave of arbitrary polarization that is obliquely incident on a hemisphere lying on the top of a metallic plane, a quarter sphere whose center is located on the intersection of two faces of a dihedral reflector and an octant of sphere inside a trihedral reflector are considered. Exact solutions are obtained for all the three cases, by employing coordinate rotation and image theory. The analysis is conducted for both E- and H- polarization, in phasor domain. Particular attention is paid to the exact expression of scattered far field and electric current densities on the spherical and metallic portions of the structure. Numerical results are provided to verify the surface current continuity across the intersection between spherical and planar portions of the metallic structure.