P.V. Korolenko - Dr.Sc.(Phys.-Math.), Professor, Department of OPTICS, SPECTROSCOPY and Nanosystems Physics, Physics Faculty, Lomonosov Moscow State University A.Yu. Mishin - Engineer, Department of Optics, Spectroscopy and Nanosystems Physics, Physics Faculty, Lomono-sov Moscow State University S.B. Ryzhikov - Ph.D.(Phys.-Math.), Associate Professor, Department of general physics, Physics Faculty, Lomo-nosov Moscow State University Yu.V. Ryzhikova - Ph.D.(Phys.-Math.), Senior Researcher, Department of Optics, Spectroscopy and Nanosystems Physics, Physics Faculty, Lomonosov Moscow State University

Efficient algorithms for constructing different approximants of quasicrystalline systems are developed. 2D aperiodic grating and multilayer system (1D aperiodic photonic crystals) are considered as such systems. For their construction are used properties of Cantor, Thue-Morse, double-period and Fibonacci sequences. The possibility of identifying for 1D and 2D quasicrystalline structure approximants has appeared by determining patterns which are separate fragments in the optical characteristics and determine the scaling parameters in the fields probing light beams. Numerical simulation results specify a direct relationship between the scaling characteristics of the light fields and the morphological features of approximant structures. Calculations showed that the scaling properties have all considered optical characteristics as fractal objects (based on the Cantor set) and a fractal-like structures constructed by means of the double period, Thue-Morse and Fibonacci numerical sequences. It is received that the approximants with different levels of generation of elementary cells and belong to one class self-similarity symmetry despite the significant external differences are characterized by same shape patterns and the same scaling coefficients. The proposed algorithms for constructing approximants with different geometry and calculation of their optical characteristics allowed to establish a high degree of pattern stability in the scaling distributions of the aperiodic 1D photonic crystals and 2D diffraction gratings.

 

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