The VLF field generated by a loop antenna in the ionosphere

Very Low Frequency (VLF: 3-30 kHz) electromagnetic waves are widely used in submarine communications. By so far, the complete expressions of the electromagnetic field generated by a magnetic dipole in arbitrary direction in the F2-layer of the ionosphere have not been given. In this paper, with the dipole source placed in the ionosphere, we will attempt to derive the formulas of the VLF/ELF electromagnetic field on the sea surface. Finally, some new numerical results are obtained and some discussions are also carried out.