Near-Field to Far-Field Approximation Formulas Based on the Asymptotic Expansion Method for Electromagnetic Wave Propagation Across Air–Sea Boundary Due to a Vertical Magnetic Dipole

Evaluation of the electromagnetic (EM) field propagation across the air-sea interface is important for wireless communication between aerial and underwater vehicles and undersea remote sensing. Existing approximation formulas of the EM field components are only suitable either for near-field region or for far-field region. In this paper, a set of new approximation formulas for evaluating the EM field components excited by a vertical magnetic dipole (VMD) are derived for the case of undersea-to-air propagation by applying the asymptotic expansion method, and for the case of air-to-undersea propagation by adopting the field reciprocity property. Computation analysis shows that the approximation formulas of both electric and magnetic field components are valid for both the near and far fields at any frequency up to 10 MHz for underwater applications.