DOI: https://doi.org/10.26089/NumMet.v18r438

Design of an isotropic all-dielectric metasurface on a substrate

Authors

  • Zh.O. Dombrovskaya

Keywords:

optimization problem
penalty function method
dielectric metasurface on substrate
antireflective coating

Abstract

A mathematical statement of the problem of one-wavelength antireflective coating based on a metasurface is formulated. The constraints on geometric parameters of the structure are found. A penalty function is proposed to ensure the applicability of the physical model and to provide the uniqueness of the desired minimum. As an example, the problem of antireflective metasurface composed of PbTe spheres located on a germanium substrate is considered. The reflectance spectrum of such a structure is found in the range 8-12 um and is compared with the spectrum of the metasurface without a substrate and with the spectrum of an uncovered substrate.

New computational technologies

Downloads

Published

2017-11-06

Issue

Vol. 18 (2017): Issue 4.

Section

Section 1. Numerical methods and applications

Author Biography

Zh.O. Dombrovskaya

Lomonosov Moscow State University,
Faculty of Physics
• PhD Student

References

  1. H. A. Atwater and A. Polman, “Plasmonics for Improved Photovoltaic Devices,” Nat. Mater. 9 (3), 205-213 (2010).
  2. M. Albooyeh, D. Morits, and C. R. Simovski, “Electromagnetic Characterization of Substrated Metasurfaces,” Metamaterials 5 (4), 178-205 (2011).
  3. M. Gu, Z. Ouyang, B. Jia, et al., “Nanoplasmonics: A Frontier of Photovoltaic Solar Cells,” Nanophotonics 1 (3-4), 235-248 (2012).
  4. K. V. Baryshnikova, M. I. Petrov, V. E. Babicheva, and P. A. Belov, “Plasmonic and Silicon Spherical Nanoparticle Antireflective Coatings,” Sci. Rep. 6 (2016).
    doi 10.1038/srep22136
  5. 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,” J. Opt. Soc. Am. B 34 (7), D18-D28 (2017).
  6. N. N. Kalitkin and E. A. Al’shina, Numerical Methods , Book 1: Numerical Analysis (Akademiya, Moscow, 2013) [in Russian].
  7. A. N. Tikhonov, “Solution of Incorrectly Formulated Problems and the Regularization Method,” Dokl. Akad. Nauk SSSR 151 (3), 501-504 (1963) [Sov. Math. Dokl. 4 (4), 1035-1038 (1963)].
  8. A. G. Sveshnikov and A. S. Il’inskii, “Design Problems in Electrodynamics,” Dokl. Akad. Nauk SSSR 204 (5), 1077-1080 (1972) [Sov. Phys. Dokl. 17, 527-530 (1972)].
  9. V. B. Glasko, A. N. Tikhonov, and A. V. Tikhonravov, “The Synthesis of Multilayer Coatings,” Zh. Vychisl. Mat. Mat. Fiz. 14 (1), 135-144 (1974) [USSR Comput. Math. Math. Phys. 14 (1), 135-143 (1974)].
  10. A. V. Tikhonravov, V. G. Zhupanov, V. N. Fedoseev, and M. K. Trubetskov, “Design and Production of Antireflection Coating for the 8-10 μm Spectral Region,” Opt. Express 22 (26), 32174-32179 (2014).
  11. A. E. Miroshnichenko, A. B. Evlyukhin, Y. S. Kivshar, and B. N. Chichkov, “Substrate-Induced Resonant Magnetoelectric Effects for Dielectric Nanoparticles,” ACS Photonics 2 (10), 1423-1428 (2015).
  12. A. B. Evlyukhin, C. Reinhardt, A. Seidel, et al., “Optical Response Features of Si-Nanoparticle Arrays,” Phys. Rev. B 82 (2010).
    doi 10.1103/PhysRevB.82.045404
  13. Zh. O. Dombrovskaya and A. V. Zhuravlev, “Investigation of the Possibility of Metafilm Modeling as a Conventional Thin Film,” Appl. Phys. A 123 (2017).
    doi 10.1007/s00339-016-0642-2
  14. C. L. Holloway, A. Dienstfrey, E. F. Kuester, et al., “A Discussion on the Interpretation and Characterization of Metafilms/Metasurfaces: The Two-Dimensional Equivalent of Metamaterials,” Metamaterials 3 (2), 100-112 (2009).
  15. D. Morits and C. Simovski, “Electromagnetic Characterization of Planar and Bulk Metamaterials: A Theoretical Study,” Phys. Rev. B 82 (2010).
    doi 10.1103/PhysRevB.82.165114
  16. Zh. O. Dombrovskaya, A. V. Zhuravlev, G. V. Belokopytov, and A. N. Bogolyubov, “Inverse Problem for Recovering of Meta-Atom Characteristics by Transmittance and Reflectance of a Metafilm,” Izv. Akad. Nauk, Ser. Fiz. 79 (12), 1708-1710 (2015) [Bull. Russ. Acad. Sci.: Phys. 79 (12), 1496-1498 (2015)].
  17. E. F. Kuester, M. A. Mohamed, M. Piket-May, and C. L. Holloway, “Averaged Transition Conditions for Electromagnetic Fields at a Metafilm,” IEEE Trans. Antennas Propag. 51 (10), 2641-2651 (2003).
  18. C. L. Holloway, E. F. Kuester, and A. Dienstfrey, “Characterizing Metasurfaces/Metafilms: The Connection between Surface Susceptibilities and Effective Material Properties,” IEEE Antennas Wireless Propag. Lett. 10, 1507-1511 (2011).
  19. G. V. Belokopytov and A. V. Zhuravlev, “Dipole Polarizability of Spherical Particles,” Fiz. Volnovykh Protses. Radiotekh. Sis. 11 (1), 41-49 (2008).
  20. Zh. O. Dombrovskaya, A. V. Zhuravlev, G. V. Belokopytov, and A. N. Bogolyubov, “Phonon-Polariton Meta-Atoms for Far Infrared Range,” Phys. Wave Phenom. 24 (2), 96-102 (2016).
  21. A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, et al., “Magnetic Light,” Sci. Rep. 2 (2012).
    doi 10.1038/srep00492
  22. F. Weiting and Y. Yixun, “Temperature Effects on the Refractive Index of Lead Telluride and Zinc Selenide,” Infrared Phys. 30 (4), 371-373.
  23. H. W. Icenogle, B. C. Platt, and W. L. Wolfe, “Refractive Indexes and Temperature Coefficients of Germanium and Silicon,” Appl. Opt. 15 (10), 2348-2351 (1976).
  24. H. H. Li, “Refractive Index of Silicon and Germanium and Its Wavelength and Temperature Derivatives,” J. Phys. Chem. Ref. Data 9 (3), 561-658 (1980).
  25. R. H. Byrd, M. E. Hribar, and J. Nocedal, “An Interior Point Algorithm for Large-Scale Nonlinear Programming,” SIAM J. Optim. 9 (4), 877-900 (1999).

License

Copyright (c) 2017 Вычислительные методы и программирование

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.