Diffraction by an isorefractive cone: Two-interval formulation and numerical evaluation

The radiation of a radially oriented dipole in the presence of a semi-infinite isorefractive cone of circular cross-section is calculated analytically via the two-interval Sturm-Liouville formulation, which was previously used by the authors to treat the electrostatic problem of the dielectric cone. This method presents an alternative to the Kontorovich-Lebedev transform method, which was used by other researchers to treat the isorefractive problem. Furthermore, numerical results, based on the eigenfunction expansion of the field, are presented for the first time.