Communication With a Magnetic Dipole: Near-Field Propagation From Air to Undersea

In this article, the famous Sommerfeld integrals (SIs) have been revisited by assuming that the approximation of γ
₀
≈ iλ is valid for the near-field propagation of low frequencies over a plane conducting ground. A deduction from that is proposed and adopted in the present study, which is defined by |γ
₀
γ
₁
| ≫ k
₀
²
, extending to cover a magnetic dipole source in air-to-undersea communications. The focus is on deriving complete and effective solutions in air and seawater regions under the cylindrical coordinates for the electromagnetic nearfield, which is generated by a vertical magnetic dipole above sea surface. The resulting formulas can be given by a few summands in closed form as the well-known Fourier-Bessel integrals. It is believed to go a step further by relaxing the reliance on various distance conditions and replacing the integrands by simple, exact integrated terms which are usable at the frequencies of interest for any distance from the source. Computations and discussions are carried out by comparing with related works and late experiments, including the field components and Poynting vectors. It is verified that the derived formulas can be degenerated into some simplified forms which are in accord with those obtained by a “quasi-static” treatment.