Miza O. Modeling and optimization of spectral coefficients of layered optical systems with inhomogeneous boundaries

The dissertation is devoted to the development of mathematical, algorithmic and software for computer design of optical systems taking into account the inhomogeneities at the interface, refractive index variance, mass transport, nanodefects, oxidation and the analysis of stability layered structures to technological errors. Methods of mathematical modeling of layered optical systems, being widely used in such areas of high technology as laser technology, optoelectronics, telecommunications, have been considered in the thesis. The spectral coefficients of layered optical systems have been determined using the Abele matrix method. The primary task in the design of such systems is to ensure the maximum selectivity and operational reliability while using a minimum number of thin-film layers. The influence of inhomogeneities at the interface and film nanodefects on the spectral characteristics of different optical filters has been modeled. The dynamics of changes in the spatial-polarization parameters of narrowband, cut-off and broadband optical filters with the light falling at the angle has been studied. A model most effectively approximating the variance of the refractive index has been proposed as well as the one of the structure of the defective layer. The influence of nanodefects depending on their nature, size and position on the spectral coefficients of the studied multilayer optical system was also in the focus of the attention. Smooth and non-smooth optimization methods (Shore r-algorithm) are used for the synthesis of optical filters. A two-steps method has been proposed. It allows to take into account partial inhomogeneity, refractive index variance, mass transport, nanodefects, oxidation and stability to technological errors. The Monte Carlo method is used to study the stability of spectral characteristics. Approaches allowing to accelerate the finding of solutions in the problems of synthesis of optical coatings (SOC) are considered in the thesis as well. This is the usage of an analytical derivative (accelerated version), tabulation of values, rapid multiplication of matrices and the usage of an efficient method for one-dimensional optimization. The choice of initial approximations for the effective solution of the problem of synthesis of optical filters has been offered. The proposed methods improve the spectral characteristics of existing broadband interference filters. The solution of the problem of reconstruction of the refractive index profile of the chalcogenide film As2S3 after irradiation is proposed. It is based on the developed models of layered structures and the methods for solving the problems of synthesis of optical coatings. Models of the refractive index profile along the film thickness before and after irradiation of the chalcogenide film GeS2 are proposed and an estimate of the growth of its thickness after irradiation has been obtained. With the help of the developed methods of solving SOС problems, the parameters of inhomogeneous films deposited on highly refracting substrates of chalcogenide photonics were optimized to ensure maximum light transmission. The obtained results were introduced into the educational process of the Faculty of Information Technologies of Uzhhorod National University and the research process of the Institute of the Institute of Electronic Physics of the National Academy of Sciences of Ukraine, about which there are relevant acts of implementation.