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We report very low frequency (VLF) orbital angular momentum (OAM) vortex electromagnetic waves propagation in an anisotropic ionosphere by proposing a Hertizan dipole array antenna. The circular array with linear insulated antennas is designed and demonstrated to generate vortex waves carrying OAM modes. To match the impedance of the ionosphere with high refractive index in the VLF band, electromagnetic characteristics of single linear antenna in the ionosphere is adjusted by selecting proper radii and electrical length. Effects of high and anisotropic refractive index of the time-and space-varying ionosphere on the OAM spectra and phase profiles generated by the array antenna are analyzed. Numerical results show that the propagation features present obvious differences if OAM vortex electromagnetic waves change their topological charges. The VLF vortex waves can provide an efficient avenue to increase the spectrum efficiency, more information will be offered by the OAM VLF waves for wireless communications and information transmissions.

This paper presents an efficient approach to implement electromagnetic-thermal (EM-T) co-simulation of a planar monopole antenna based on hybrid implicit-explicit finite-difference time-domain method (HIE-FDTD-M). First, the EM simulation is carried out by solving Maxwell’s curl equation. Once the EM field reaches steady state, the EM power loss is computed according to the electric conductivity of the material. Finally, the thermal field is simulated by taking the EM power loss as the heat source in the heat transfer equation (HTE). For comparison, HIE-FDTD-M and FDTD-M are adopted respectively in the computation of the EM field. The simulated EM parameters of the planar monopole antenna, including S11 and radiation pattern, are consistent with those obtained by using CST software. The thermal field distribution on the surface of the antenna computed by the proposed method in this paper is approximately similar to that obtained using COMSOL software. However, the EM-T co-simulation of the antenna using HIE-FDTD-M takes only 1/11 of the time required using FDTD-M.