Electromagnetic diffraction and scattering of a complex-source beam by a semi-infinite circular cone

A complex-source beam (CSB) is used to investigate the electromagnetic scattering and diffraction by the tip of a perfectly conducting semi-infinite circular cone. The boundary value problem is defined by assigning a complex valued source coordinate in the spherical-multipole expansion of the field due to a Hertzian dipole in the presence of the PEC circular cone. Since the incident CSB field can be interpreted as a localized plane wave illuminating the tip, the classical exact tip scattering problem can be analysed by an eigenfunction expansion without having the convergence problems in case of a full plane wave incident field. The numerical evaluation includes corresponding near- and far-fields.