Eigenvalues of a dielectric-coated conducting cone

The general problem of radiation/scattering from a dielectric coated semi-infinite conical structure excited by an arbitrary surface current distribution on the dielectric layer is formulated. Since the angular eigenfunction expansion is not suitable for this problem, the radial eigenfunction expansion is employed. The boundary value method is applied to obtain the fields in the form of infinite double series over the appropriate eigenfunctions in terms of spherical Hankel and associated Legendre functions. The conical dielectric shell may be lossy or lossless and the series solution generally involves complex eigenvalues which are calculated numerically. Using a small conducting sphere at the tip of the cone, the singularity of the Hankel functions at the origin is overcome, thus permitting the use of the orthogonality relations of Sommerfeld's complex-order wave functions to solve the problem and construct sets of infinite simultaneous linear equations which are presented in matrix form.