Tuz V. Polarization and nonlinear effects enhancement in periodical structures and systems with strong field localization

The object of study: the physical process of the interaction of electromagnetic fields with artificial media and structures which are defined by a complex composition and consist of optically active (anisotropic, gyrotropic, chiral) and non-linear inclusions. The aim of the thesis: the identification of new physical effects and peculiarities of electromagnetic field interaction with artificial layered structures and metamaterials, which provide a strong localization of the electromagnetic field inside the system. Methods: The method of differential Berreman matrices, transfer matrix method and operator method of generalized scattering matrix, mathematical methods of the theory of matrix functions, linear differential equations with periodic coefficients and stability theory, the method of equivalent boundary conditions, the effective medium theory, the method of moments. Theoretical and practical results, the novelty: the scientific novelty of this work is in identification of a number of new physical effects and peculiarities in the propagation of electromagnetic waves in complex artificial media that are defined by the spatial dispersion, optical activity, non-linear properties and provide a significant localization of the electromagnetic field, which was achieved due to the development of methods of analysis of spatially heterogeneous composite media. A number of physical models of periodic and non-periodic structures containing gratings, anisotropic, gyrotropic, chiral layers and nonlinear materials are studied. The properties of the scattered fields for structures consisting of magnetic or chiral layers in which the value of the real part of permittivity and permeability are close to zero while the gyrotropy or chirality parameters are not equal to zero are studied. The parameters of the structure, allowing for a significant increase in the angle of rotation of the polarization ellipse in the Faraday effect, backward wave propagation and wave matching of such a medium with free space are studied. The conditions which are necessary to achieve nonreciprocal bistable and multistable operation regimes and nonlinear polarization switching in magnetic and chiral periodic structures are found out. The dependence of the polarization transformation, the formation of the resonant modes and the degree of the field concentration in the fractal and quasi-periodic layered structures versus the chirality parameter are studied. The ability of a planar metamaterial, which provides a strong field concentration due to the excitation of the trapped mode to control bistability or multistability operation is shown. The degree of implementation: The implementation is planned to be in future. Applications: Radio Physics and Electronics.