Kvitka N. Propagatіon of electromagnetіc excіtatіons іn layered superconductors controlled by a dc magnetіc field

The purpose of the work is to investigate analytically the transport of terahertz electromagnetic waves through a layered superconductor plate and determine the possibilities of its tuning using a static magnetic field. The object of research is the transport of terahertz plane waves and terahertz wave beams of Gaussian profile in a layered superconductor plate. Theoretical and practical results. It is shown that in the geometry when the layers of a layered superconductor are parallel to the interface between the vacuum (on both sides) and the plate, the breaking of charge neutrality can cause the appearance of anomalous dispersion of localized waves in the frequency region close to the Josephson plasma frequency. Other consequences of this effect are also revealed, such as the appearance of an additional forbidden zone near this frequency and the fact that for some parameters a degeneration of the spectrum is observed. It is shown that the dispersion law for localized waves in a plate of a layered superconductor in the case when the layers are perpendicular to the surfaces is sensitive to an external static magnetic field. It is shown that in the Otto geometry, when a sample of a layered superconductor is in a dielectric medium and separated from it by thin spatial vacuum gaps, a change in the static magnetic field allows to obtain different types of resonant dependencies of the transmittance on the angle of incidence, which differ in the number of peaks and their width. It is shown how the static field can be used to adjust the transparency of the sample and requires two orders of magnitude less relative accuracy in setting than in the case of control by changing the frequency. The expressions for the focal length and minimum radius of the Gaussian beam focused by a layered superconductor plate, which depend on the static magnetic field, are obtained. It is shown that changing the field magnitude allows to adjust these values in a wide range of values, as well as to switch the plate between focusing and defocusing modes. Novelty of scientific results. For the first time, the law of dispersion of localized waves in a plate of a layered superconductor of finite thickness in different geometries was found, taking into account the effect of violation of the charge neutrality of the superconductor layers and the presence of an external static magnetic field. For the first time, the transfer-matrix method was modified to describe the propagation of nonlinear electromagnetic waves in a layered superconductor plate under an external constant magnetic field, and for the first time, specific matrices responsible for the interaction of Josephson plasma waves with an external magnetic field were found. For the first time, the effect of a static magnetic field on the resonant transparency of a thin sample of a layered superconductor for THz waves is theoretically investigated when the sample is in a dielectric medium and separated from it by thin spatial vacuum gaps. The effect of a static magnetic field on the focusing of a Gaussian laser beam by a layered superconductor plate is investigated theoretically for the first time. Research methods. Well-tested and generally accepted methods of theoretical physics, methods of numerical calculations, and approximate methods of asymptotic analysis were used to obtain the results. The fields in a layered superconductor were analyzed by solving the coupled sinusoidal Gordon equations. Wave propagation through the multilayer system was studied using the transfer matrix method. Comparison of the results of the obtained analytical expressions with numerical calculations served as an additional verification of the applied approaches. Degree of implementation. The results of the thesis extend the existing fundamental theoretical understanding of the peculiarities of THz electromagnetic wave propagation in high-temperature superconductors of layered structure. Based on these results, it is possible to create new devices operating in the THz frequency range characteristic of layered high-temperature superconductors, including filters, mixers, and amplifiers. Scope of use. The scope of possible applications of such devices is very wide: from medical diagnostics to astronomical observations. The investigated possibility of using a static magnetic field to adjust the parameters of a layered superconductor allows us to propose this as an effective method of controlling the operation of such devices in experimental installations.