Alexander M. Lerer

Two-sided approximate boundary conditions are obtained for an absolutely absorbing (“black”) layer lying on a multilayer dielectric. Paired summation equations (PSEs) are obtained for the tangent components of the electric and magnetic field strengths at the slots. These equations are solved by the Galerkin method with basis functions in the form of Chebyshev and Legendre polynomials. The resulting system of linear algebraic equations has fast internal convergence. To control the accuracy of the obtained solution, a dual problem is solved – a lattice of “black stripes.” In this case, the unknowns in the PSU are the current density on the strips. The properties of lattices are analyzed.

The paper presents the results of a study of the microwave absorption properties of ceramic materials based on bismuth ferrite containing rare earth elements, as well as systems of solid solutions ([ ])BiFeO₃–xPbFe[ ]Nb[ ]O₃ in a wide range of component concentrations. The methodology for measuring and calculating the parameters of samples of the materials under study is described. The influence of structural and microstructural factors on the average and maximum level of microwave absorption of the materials under study in a wide frequency range is analyzed. A comparison of the microwave absorbing properties of these materials with industrial absorbers has been carried out, and prospects for application in microwave technology have been shown.

Ceramic samples of Bi_1−xHo_xFeO₃, where x = 0.00–0.50, with a modifier concentration variation step ∆x = 0.05–0.10, were prepared by a two-step solid-phase synthesis followed by sintering using conventional ceramic technology. X-ray phase analysis showed that all the solid solutions studied were formed in the presence of impurities. With increasing Ho concentration, a non-monotonic shift in all loss maxima towards the low-frequency region is observed, as well as an increase in their half-width. An increase in the external temperature leads to a monotonic shift in the absorption maxima towards the low-frequency region, which enables the necessary control of the microwave parameters in the X band. A conclusion has been drawn on the feasibility of using the data obtained in the design of new functional materials based on BiFeO₃, as well as devices with thermally controlled frequency.

A fast and rigorous method is developed for the electrodynamic analysis of an infinite cylindrical lens made of an artificial material, which is an array of hollow conducting cylinders of finite length and finite wall thickness, identically oriented along the lens axis. It is shown that the method makes it possible to calculate the characteristics of lenses consisting of multiple elements using a personal computer. The focusing properties of the lens are studied. The method is an alternative to and a technique to verify the approach based on the analysis of a lens made of a homogenized material with a refractive index of an infinite 3D photonic crystal.

A fast and rigorous method is developed for the electrodynamic analysis of an infinite cylindrical lens made of an artificial material, which is an array of hollow conducting cylinders of finite length and finite wall thickness, identically oriented along the lens axis. It is shown that the method makes it possible to calculate the characteristics of lenses consisting of multiple elements using a personal computer. The focusing properties of the lens are studied. The method is an alternative to and a technique to verify the approach based on the analysis of a lens made of a homogenized material with a refractive index of an infinite 3D photonic crystal.

A method for solving the problem of nonlinear diffraction on two-dimensional periodic gratings of graphene ribbons has been developed. The third-order nonlinear conductivity of graphene under the action of two waves is taken into account, which is determined by the field of the pump wave, for which we use the field on graphene ribbons obtained by solving the linear diffraction problem. Numerical analysis shows the efficiency of nonlinear frequency conversion in the terahertz and infrared ranges when the frequencies of the incident pump and signal waves coincide with the resonant frequencies of the fundamental and higher order modes of surface plasmon polaritons in graphene ribbons.