A Direct Spectral Domain Method for Near-Ground Microwave Radiation by a Vertical Dipole Above Earth in the Presence of Atmospheric Refractivity

A spectral domain method is presented to calculate the potential of a vertical dipole in a multilayered medium as a model of long-range radio propagation. The spectral domain Green’s function (SDGF) for structures with up to hundreds of thousands of layers is calculated using an efficient matrix formulation, thus enabling simulation of continuously stratified media. The SDGF is sampled to perform pole/residue-extraction using contour quadratures and to perform a novel asymptotic Filon-Clenshaw-Curtis (FCC) quadrature to calculate the far-field Green’s functions. The near-fields are directly calculated using an adaptive Clenshaw-Curtis quadrature without pole-extraction. Results of numerical simulations are presented in the case of a graded-index waveguide and an atmospheric gradient-layer above a realistic lossy ground.