Full-wave method for the analysis of the radiation characteristics of a VLF source in the atmosphere

•This paper established the propagation model of ground, air and layered anisotropic ionospheric space. We use the full-wave method to calculate radiation in the Earth–ionosphere waveguide when an electric dipole is located in the air.•To facilitate the calculation of the vertical wavenumber integral, we consider the air as an isotropic medium with a micro-conductivity. A method for solving the vertical wavenumber integral with second-order singularities is given.•The dipole radiation in the half-space and in the Earth’s atmosphere is compared. The graphs of the tangential component of the electric field of a short dipole at different distances from it are given. The field of the horizontal electric dipole in the layer of the earth’s atmosphere with the ionosphere and in the half-space is shown and compared. The basis of the full-wave method is the propagation matrix method and a plane wave expansion, which is generally used for the analysis of radiation problems in layered media. The radiation field in the spatial domain is represented as an integral in the wavenumber domain. By integrating the vertical wavenumber, the radiation can be represented as a superposition of plane waves with different directions. If the atmosphere and ionosphere are regarded as layered media, the vertical wavenumber integral contains first-order singularities when the radiation source is located in the ionosphere, which are relatively easy to handle. When the radiation source is located in the air, the vertical wavenumber integral contains second-order singularities, which are more complicated. Therefore, there are few full-wave studies on radiation characteristics in the air and ionosphere when a very-low-frequency (VLF) source is located in the air. In this paper, air is considered as an isotropic medium with a micro-conductivity, the vertical wave number integral that has second-order singularities is solved, and the radiation fields in the air and the ionosphere are calculated. The numerical results show the correctness and effectiveness of the proposed algorithm.