Scattering and absorption of the H‐polarized plane wave by the infinite grating of flat graphene strips are considered in the environment met most frequently—on or at the surface of a dielectric‐slab substrate. The full‐wave meshless code is based on the analytical semi‐inversion using the Riemann–Hilbert problem solution. This leads to a Fredholm second‐kind matrix equation for the Floquet harmonic amplitudes that guarantees code convergence and provides easy control of computational error, which can be reduced to machine precision. The matrix elements are combinations of elementary functions, and therefore, the code is accurate and quite economical. This enables computation of the reflectance, transmittance, and absorbance as a function of the frequency in the wide band from static case to 10 THz. Numerical results show that such a metasurface with micrometre‐sized strips is a composite periodic open resonator. It is highly frequency‐selective thanks to the interplay of three types of natural modes—low‐Q slab, moderate‐Q plasmon strip, and ultra‐high‐Q lattice—that do not exist in the absence of the substrate. Varying the chemical potential of graphene, one can manipulate the electromagnetic characteristics of the metasurface at a fixed frequency from almost total transmission to almost total reflection.

We report a loss of tunability of the scattering from the dielectric substrate-backed graphene-strip grating in a narrow-band all-optical electromagnetically induced transparency regime, appearing due to the excitation of the high-Q lattice mode.

The modeling of very low-frequency (VLF) electromagnetic (EM) beam propagation in the Earth–ionosphere waveguide (WGEI) is considered. A new tensor impedance method for modeling the propagation of electromagnetic beams in a multi-layered and inhomogeneous waveguide is presented. The waveguide is assumed to possess the gyrotropy and inhomogeneity with a thick cover layer placed above the waveguide. The influence of geomagnetic field inclination and carrier beam frequency on the characteristics of the polarization transformation in the Earth–ionosphere waveguide is determined. The new method for modeling the propagation of electromagnetic beams allows us to study the (i) propagation of the very low-frequency modes in the Earth–ionosphere waveguide and, in perspective, their excitation by the typical Earth–ionosphere waveguide sources, such as radio wave transmitters and lightning discharges, and (ii) leakage of Earth–ionosphere waveguide waves into the upper ionosphere and magnetosphere. The proposed approach can be applied to the variety of problems related to the analysis of the propagation of electromagnetic waves in layered gyrotropic and anisotropic active media in a wide frequency range, e.g., from the Earth–ionosphere waveguide to the optical waveband, for artificial signal propagation such as metamaterial microwave or optical waveguides.