Analytical Formulas for Wave Propagation at Low Frequencies in Half-Spaces Due to a Horizontal Magnetic Dipole

The Sommerfeld Integrals (SIs) are re-visited in the presence of half-spaces under the assumption of γ
₀
≈ iλ being valid for low-frequency propagation in order to investigate the near-field due to a Horizontal Magnetic Dipole (HMD). Analytical expressions are derived for the excited waves over a planar homogeneous conducting ground or sea surface, and a numerical Finite Element Method (FEM) approach is also exploited to validate its correctness and effectiveness. The proposed method is additionally verified by late released experimental data, and it is shown that the results for various simplified expressions qualitatively corroborate the conclusions found in published papers. The proposed formulas can be used as a valuable tool for the study of the properties of near-field propagations from a loop antenna.