On the Sommerfeld half-space problem: appraisal of approximate solutions with extensions to plasmonics

Abstract

The classical Sommerfeld problem of a vertical electric dipole radiating over an imperfectly conducting half-space is revisited. Two variants of the modified saddle-point integration method are employed to derive new, closed-form, second-order approximations of the far-zone electromagnetic fields. The new formulas are applied to compute radiation patterns and surface fields for sample problems including both ordinary and plasmonic media, and their accuracy is assessed by comparison with the results of rigorous numerical evaluation of the Sommerfeld integrals.