Simple approximate formulas for evaluating Sommerfeld type integrals

The analysis of antennas and scatterers, located in a close proximity to the air/ground interface is concerned with calculation of Sommerfeld improper integrals. This problem has no rigorous solution in a closed form, therefore it is solved either by numerical integration or with the use of approximation. The purpose of the paper is development of more accurate expressions for evaluating the near fields of an infinitesimal electric dipole located over the lossy half-space. Comparative analysis of the numerical results shows that the derived formulas ensure rather high accuracy of the Hertzian potential calculations for the vertical or horizontal electric dipoles over the lossy half-space. The simplicity of the formulas and the absence of numerical integrations makes them convenient for many electromagnetic applications