On the radiation from a short current-carrying straight wire oriented perpendicular to a stratified medium

In a previous work, improved full-wave analytical expressions have been derived for the Sommerfeld Integrals (SIs) describing electromagnetic radiation from a short vertical straight wire located in close proximity to a conductive soil. Such formulas ensure high accuracy of the result of the computation, as well as time savings with respect to conventional techniques used to evaluate the SIs, but unfortunately may be used only when both source and field points are located at the air-medium interface. The scope of this paper is to overcome the limitations implied by the previous approach, and provide series-form expressions for the generated field components that are valid for an arbitrarily stratified medium and for any position of the vertical wire antenna and observation point in the air space above it. The expressions follow from the analytical evaluation of the integral representation for the magnetic vector potential, performed through contour integration after substituting an equivalent pole set for each branch cut of the integrand. Validity, efficiency and accuracy of the developed formulas are illustrated through numerical examples.