Optimization of an isotropic metasurface on a substrate

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Abstract

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.

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1. Introduction Last few years the designs of nanostructured coatings with the reflection coefficient close to zero attract a great attention. Such coatings are promising for solar cells and other photovoltaic elements which work both in the visible and in the infrared ranges. Nowadays, high refractive index all-dielectric meta-atoms are used [1], [2] instead of plasmonics [3], [4] in order to reduce Joule losses. Commonly, the properties of substrated metasurfaces are calculated numerically. The computations are complicated due to big divergence of characteristic scales: resonator size can be 3-20 times smaller then the wavelength
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About the authors

Zhanna O. Dombrovskaya

Lomonosov Moscow State University

Author for correspondence.
Email: dombrovskaya@physics.msu.ru
ORCID iD: 0000-0003-0609-1065

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

1, bld. 2, Leninskie Gory, Moscow, 119991, Russian Federation

References

  1. K. V. Baryshnikova, M. I. Petrov, V. E. Babicheva, and P. A. Belov, “Plasmonic and silicon nanoparticle anti-reflective coatings”, Scientific Reports, vol. 6, p. 22136, 2016. doi: 10.1038/srep22136.
  2. V. E. Babicheva, M. I. Petrov, K. V. Baryshnikova, and P. A. Belov, “Reflection compensation mediated by electric and magnetic resonances of all-dielectric metasurfaces”, Journal of the Optical Society of America B, vol. 34, no. 7, pp. D18-D28, 2017. doi: 10.1364/JOSAB.34.000D18.
  3. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices”, Nature Materials, vol. 9, pp. 205-213, 2010. doi: 10.1038/nmat2629.
  4. M. Albooyeh, D. Morits, and C. R. Simovski, “Electromagnetic characterization of substrated metasurfaces”, Metamaterials, vol. 5, pp. 178-205, 2011. doi: 10.1016/j.metmat.2011.08.002.
  5. Z. O. Dombrovskaya et al., “Inverse problem for recovering of meta-atom characteristics by transmittance and reflectance of a metafilm”, Bulletin of the Russian Academy of Sciences: Physics, vol. 79, no. 12, pp. 1496- 1498, 2015. doi: 10.3103/S1062873815120151.
  6. A. B. Evlyukhin et al., “Optical response features of Si-nanoparticle arrays”, Physical Review B, vol. 82, p. 045404, 2010. doi: 10.1103/PhysRevB.82.045404.
  7. N. N. Kalitkin and E. A. Al’shina, Numerical Methods [Chislennye metody], book 1, in Russian. Moscow: Akademiya, 2013.
  8. R. H. Byrd, M. E. Hribar, and J. Nocedal, “An interior point algorithm for large-scale nonlinear programming”, SIAM Journal on Optimization, vol. 9, no. 4, pp. 877-900, 1999. doi: 10.1137/S1052623497325107.
  9. A. G. Sveshnikov and A. S. Ilinskiy, “Design problems in electrodynamics [Zadachi proyektirovaniya v elektrodinamike]”, in Russian, Proceedings of the USSR Academy of Sciences, vol. 204, pp. 1077-1080, 1972.
  10. V. B. Glasko, A. N. Tikhonov, and A. V. Tikhonravov, “On the synthesis of multilayer coatings [O sinteze mnogosloynykh pokrytiy]”, USSR Computational Mathematics and Mathematical Physics, vol. 14, p. 135, 1974, in Russian.
  11. A. V. Tikhonravov et al., “Design and production of antireflection coating for the 8 - 10 mm spectral region”, Optics Express, vol. 22, pp. 32174-32179, 2014. doi: 10.1364/OE.22.032174.
  12. Z. O. Dombrovskaya and A. V. Zhuravlev, “Investigation of the possibility of metafilm modeling as a conventional thin film”, Applied Physics A, vol. 123, p. 27, 2017. doi: 10.1007/s00339-016-0642-2.
  13. A. E. Miroshnichenko et al., “Substrate-induced resonant magnetoelectric effects with dielectric nanoparticles”, ACS Photonics, vol. 2, pp. 1423-1428, 2015. doi: 10.1021/acsphotonics.5b00117.
  14. G. V. Belokopytov and A. V. Zhuravlev, “Dipole polarizability of spherical particles [Dipol’naya polyarizuyemost’ sfericheskikh chastits]”, in Russian, Physics of Wave Processes and Radio Systems, vol. 2, pp. 41- 49, 2008.
  15. Z. O. Dombrovskaya et al., “Phonon-polariton meta-atoms for far infrared range”, Physics of Wave Phenomena, vol. 24, pp. 96-102, 2016. doi: 10.3103/S1541308X16020023.
  16. A. I. Kuznetsov et al., “Magnetic light”, Scientific Reports, vol. 2, p. 492, 2012. doi: 10.1038/srep004092.
  17. D. G. Baranov et al., “All-dielectric nanophotonics: the quest for better materials and fabrication techniques”, Optica, vol. 4, no. 7, pp. 814-825, 2017. doi: 10.1364/OPTICA.4.000814.

Copyright (c) 2022 Dombrovskaya Z.O.

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