ИСТИНА

The project is aimed at solving a fundamental scientific problem related to the establishment of general laws between the parameters of probing light beams and the features of the structure of fractal-like objects. Fractal-like multilayer systems with inserts of metamaterials and lattice aperiodic diffraction structures of various geometries, including self-organizing systems of dendritic clusters, were selected as the objects of investigation. Using the theoretical studies of spectral characteristics of fractal-like objects, the features of scaling (scale invariance) in light fields are determined, which are manifested in the form of stable local formations, the so called patterns. The developed algorithms based on the use of matrix methods, fast Fourier transform and wavelet transformations were implemented in the calculations of fractal-like structures characteristics. For the first time, regularities were find that determine the quantitative relationship between the structural features of lattice systems of dendritic type and their diffraction patterns using the fractal parameterization apparatus. The connection was found using the detailed analysis of the dependence of the mass fractal dimensions of the formed dendritic structures and their diffraction patterns on the number of particles that constitute the investigated system. A new method of multiparametric identification of dendritic formations with quasi-central symmetry is proposed. The new generalized identification method is based on determining the conditions for the formation of scaling structures in the form of stable local formations (patterns) in light waves diffracting on fractal-like objects and determining the scaling parameters. For the first time, the scaling features of optical characteristics of fractal-like multilayer systems with metamaterials taking into account their absorption are determined using pattern analysis. The influence of structural changes in fractal-like multilayer structures (and their approximants) with inserts of metamaterials on the shape stability of fractal patterns of their optical spectra taking into account the absorption in meta-layers is estimated. The stability of Fourier images of fractal structures as the physical basis of their aesthetic properties was evaluated for the first time. The obtained results of the study of fractality in the characteristics of dendrites indicate additional diagnostic possibilities of fractal properties of a wide class of stochastic structures, as well as open new prospects for their use in biomedicine. On the basis of the results included in the final report of the research the master's thesis and two bachelor's diploma thesis were made and the programs of two training courses ("Fundamentals of fractal optics" and "Methods of analysis of stochastic signals") at the Faculty of Physics of Lomonosov Moscow State University, were enhanced.