Evaluation of Sommerfeld integrals arising in the ground stake antenna problem

Abstract
A novel approach is described to the numerical evaluation of Sommerfeld integrals, which offers a compromise between efficiency and simplicity. In this method, the real-axis path of integration is deformed to a contour, which is the steepest-descent path for the exponential function present in the integrand. This new contour also avoids the singularities of the integrand which occur near the original path. The proposed technique is applicable if the radial displacement of the source and field points is electrically small and is most efficient if this displacement is smaller than the vertical separation between these points. Such conditions prevail, for example, in the analysis by means of the integral equation technique of a thin, vertical wire antenna, which penetrates the interface between two media (the so-called ground stake antenna)

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