Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)3095010.22363/2658-4670-2022-30-2-115-126ArticlesСтатьиResearch ArticleOptimization of an isotropic metasurface on a substrateОптимизация изотропной метаповерхности на подложкеhttps://orcid.org/0000-0003-0609-1065DombrovskayaZhanna O.ДомбровскаяЖ. О.

Candidate of Physical and Mathematical Sciences, Junior Researcher of Faculty of Physics

dombrovskaya@physics.msu.ruLomonosov Moscow State UniversityМосковский государственный университет им. М.В. Ломоносова03052022302VOL 30, NO2 (2022)ТОМ 30, №2 (2022)11512603052022Copyright ©; 2022, Dombrovskaya Z.O.Copyright ©; 2022, Домбровская Ж.О.2022Dombrovskaya Z.O.Домбровская Ж.О.http://creativecommons.org/licenses/by/4.0https://journals.rudn.ru/miph/article/view/30950

Mathematical statement of one-wavelength antireflective coating based on two-dimensional metamaterial is formulated for the first time. The constraints on geometric parameters of the structure are found. We propose a penalty function, which ensures the applicability of physical model and provides the uniqueness of the desired minimum. As an example, we consider the optimization of metasurface composed of PbTe spheres located on germanium substrate. It is shown that the accuracy of the minimization with properly chosen penalty term is the same as for the objective function without it.

Впервые приведена математическая формулировка одноволнового безотражательного покрытия на основе двумерного метаматериала. Найдены ограничения на геометрические параметры конструкции. Предложена штрафная функция, которая обеспечивает применимость физической модели и обеспечивает единственность искомого минимума. В качестве примера рассмотрена оптимизация метаповерхности, состоящей из сфер PbTe, расположенных на германиевой подложке. Показано, что точность минимизации с правильно выбранным штрафным термином такая же, как и для целевой функции без него.

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