Efficient calculation of spatial Green´s functions by singularity subtraction for a half-space medium

A new technique is presented to evaluate efficiently the Sommerfeld integrals arising from the problem of a current element radiating over a half-space. The annihilation of the asymptote and the branch-point singular behavior of a 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. The numerical results show that the new method can accurately and efficiently calculate spatial Green´s functions.