Generalized Sommerfeld integrals and field expansions in two-medium half-spaces

Time harmonic modal electromagnetic fields in two-medium half-spaces are investigated. For practical and numerical considerations, the primary sources of the modal fields are chosen to be the spherical multipoles, and the potential vectors are z-directed. It is shown that modal fields of such combination are not able to represent a conventional spherical modal field. The horizontal rotating potentials are added to ensure proper representation and fast convergence. The recurrence relations which transform the spherical Hankel-Legendre functions into the Fourier-Bessel integrals are derived. The secondary fields of the Sommerfeld type are obtained for all spherical multipole sources and the added horizontally rotating potentials. The combination of the modal fields are capable of representing arbitrary electromagnetic fields resulting from radiation and scattering problems.