Compact expression of dyadic Green's function for homogeneous dielectric half‐space and its efficient double integral representation

Abstract

The dyadic Green's function can be represented via spatial derivatives of two Sommerfeld integrals when an infinitesimal electric dipole and an observation point are located above an infinite planar dielectric interface. The two dielectric spaces are assumed to be homogeneous. Recently, new representations have been proposed for two Sommerfeld integrals and their complete uniform asymptotic expansions. The new formulation for the dyadic Green's function contains fourth-order spatial derivatives, so its explicit expression is lengthy and not compact. Thus, a compact form of the dyadic Green's function was formulated by converting the fourth-order spatial derivatives into second-order ones. Based on the new representation, a numerically efficient double integral expression of Green's function was obtained and numerically verified. In addition, five components among nine total electric field components were analytically evaluated in terms of the incomplete Hankel function when the source and observation point both are on the interface.