Air to undersea communication with magnetic dipoles

Simplified expressions are derived for the electromagnetic fields produced by a vertical or horizontal magnetic dipole (loop antenna) located in air above the sea. The expressions hold over the quasi-near range in both media subject to certain mild restrictions. The solutions are obtained by first applying the boundary conditions to determine the magnetic Hertz potential
\bar{\pi}^{\ast}
in the form of Sommerfeld integrals, and then relating these to two auxiliary integrals
U, V
and their derivatives, asymptotic series for which are obtained by extending the work of Baños and Wesley. The horizontal magnetic dipole (loop in the vertical plane) is found to be superior to the vertically-oriented dipole of the same size and excitation from the point of view of field strength induced in the sea at large distances from the source. A comparison with previously published results for the electric dipole shows the magnetic dipole to be better, provided the number of turns in the loop exceeds a certain minimum. An approximate analysis on the basis of equal powers also shows the magnetic dipole to be better except for points near the outer rim of the quasi-near range, where the two types of dipoles are equivalent.