Efficient Evaluation of Green's Functions for Lossy Half-Space Problems

In this paper, a new technique is developed to evaluate efficiently the Sommerfeld integrals arising from the problem of a current element radiating over a lossy half-space. The annihilation of the asymptote and the branch-point singular behavior of the spectral Green's function is used in this technique. The contributions of the subtracted asymptotic and singularity terms are calculated analytically. The annihilation results in a remaining integral that is very smooth and can be calculated adaptively by using Gaussian quadratures and extrapolation methods to accelerate the convergence of the oscillating integrand. The accuracy and efficiency of the new technique has been confirmed by comparison with literature, and the commercial software NEC. The application of the proposed technique provides a robust and rapid procedure to calculate spatial Green's functions which can be used in ground-wave propagation, and lightning return stroke channel modeling.