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Modeling of aperiodic structures with optical scaling characteristics


A.M. Zotov – Ph.D. (Phys.-Math.), Senior Researcher, Department of Optics and Spectroscopy, Physics Faculty of Moscow State University
E.G. Kim – Student, Department of Optics and Spectroscopy, Physics Faculty of Moscow State University
P.V. Korolenko – Dr.Sc. (Phys.-Math.), Professor, Department of Optics and Spectroscopy, Physics Faculty of Moscow State University
Yu.V. Ryzhikova – Ph.D. (Phys.-Math.), Researcher, Department of Optics and Spectroscopy, Physics Faculty of Moscow State University

Methods for the numerical simulation of various types of aperiodic structures and the analysis of scaling in their optical characteristics are developed. 1D – 3D gratings, multilayer systems and inhomogeneous phase plates are considered as such structures. When constructing systems with internal symmetry of self-similarity are used properties of Thue-Morse, double-period and Fibonacci sequences. Multiparametric fractal analysis allowed to establish a quantitative relationship between the structural features of their morphology and properties of the probing light beam. Estimation of scaling parameters in the optical characteristics was carried out in two ways. The first method is based on the calculation of the structure function, by which the "mass" fractal dimension is defined. The second – used the covering-blanket method. The self-consistent procedure for the determination of parameters such as the width of the area and the scaling coefficients and fractal dimensions is described in detail. It is shown that the characteristic self-similar elements corresponding to a particular type of aperiodic gratings (local fractal patterns) that can be registered in the structure of the scattered radiation have a high degree of stability to changes in lighting conditions and the presence of random structural defects in aperiodic gratings. Results of numerical experiments specify a direct relationship between fractal attributes of researched objects and their optical characteristics. In particular, there is an almost full coincidence the mass fractal dimensions of the profile of a randomly inhomogeneous phase plate and the intensity distribution of the scattered light beam.

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