Far-field calculation of an arbitrarily oriented electric dipole in horizontal layered confined space

Abstract

The far-field calculation of arbitrarily oriented electric dipole in a stratified confined space is of great significance in analyzing electromagnetic properties in the lightning return stroke, submarine communication, over-the-horizon ground-wave radar, etc. Based on the mirror image method and the far-field approximation of an electric dipole in free space, a three-layer horizontal confined space model with an arbitrarily oriented dipole is established in this work. Through novel vector operations, the expression of the far field generated by an arbitrarily oriented electric dipole in the confined space model is derived, where the direct wave from the source point to the observation point and the waves reflected by the upper boundary and the lower boundary are all comprehensively considered. On this basis, the radiation characteristics of the electric dipole with frequencies of 100 kHz, 6 MHz and 10 MHz at different positions in the Earth-ionosphere waveguide are compared and analyzed, which are taken for example. Three different orientations of electric dipoles,i.e. vertical direction, horizontal direction, and 45º tilt are taken into account and the corresponding radiation patterns are presented. The results show that the radiation characteristics of electric dipoles in the Earth-ionosphere waveguide will change greatly with their frequencies, orientations and positions. For the electric dipole source at the same location, the higher the frequency, the more the number of radiation lobes is. In addition, when the source frequency keeps unchanged, the farther the dipole source is from the bottom boundary, the more the radiated lobes are. The proposed expression can conveniently and accurately consider the direct wave of a dipole source and its primary reflection from the upper interface and the lower interface in a confined space, and can also be further extended to solving the contribution of multiple reflections from the interfaces.