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Abstract The finite‐difference time‐domain (FDTD) method was previously applied to high‐frequency electromagnetic wave propagation through 250 km of theFregion of the ionosphere. That modeling approach was limited to electromagnetic wave propagation above the critical frequency of the ionospheric plasma, and it did not include the lower ionosphere layers or the top of theF‐region. This paper extends the previous modeling methodology to frequencies below the critical frequency of the plasma and to altitudes encompassing the ionosphere. The following changes to the previous work were required to generate this model: (a) theD,Eand top of theFregions of the ionosphere were added; and (b) the perfectly matched layer absorbing boundary on the top side of the grid was replaced with a collisional plasma to prevent reflections. We apply this model to the study of extremely low frequency (ELF) and very low frequency (VLF) electric power line harmonic radiation (PLHR) through the ionosphere. The model is compared against analytical predictions and applied to PLHR propagation in polar, mid‐latitude and equatorial regions. Also, to further demonstrate the advantages of the grid‐based FDTD method, PLHR propagation through a polar cap patch with inhomogeneities is studied. The presented modeling methodology may be applied to additional scenarios in a straightforward manner and can serve as a useful tool for better tracking and studying electromagnetic wave propagation through the ionosphere at any latitude and in the presence of irregularities of any size and shape. 

The finite-difference time-domain (FDTD) method is a widespread numerical tool for full-wave analysis of electromagnetic fields in complex media and for detailed geometries. Applications of the FDTD method cover a range of time and spatial scales, extending from subatomic to galactic lengths and from classical to quantum physics. Technology areas that benefit from the FDTD method include biomedicine — bioimaging, biophotonics, bioelectronics and biosensors; geophysics — remote sensing, communications, space weather hazards and geolocation; metamaterials — sub-wavelength focusing lenses, electromagnetic cloaks and continuously scanning leaky-wave antennas; optics — diffractive optical elements, photonic bandgap structures, photonic crystal waveguides and ring-resonator devices; plasmonics — plasmonic waveguides and antennas; and quantum applications — quantum devices and quantum radar. This Primer summarizes the main features of the FDTD method, along with key extensions that enable accurate solutions to be obtained for different research questions. Additionally, hardware considerations are discussed, plus examples of how to extract magnitude and phase data, Brillouin diagrams and scattering parameters from the output of an FDTD model. The Primer ends with a discussion of ongoing challenges and opportunities to further enhance the FDTD method for current and future applications.