Physics of the Solid State

, Volume 58, Issue 7, pp 1412–1419 | Cite as

Optical diffraction by two-dimensional photonic structures with hexagonal symmetry

  • K. B. Samusev
  • M. V. Rybin
  • S. Yu. Lukashenko
  • P. A. Belov
  • M. F. Limonov
Optical Properties


Photonic structures with hexagonal symmetry have been prepared by the additive technology of two-photon laser lithography, and their optical properties have been investigated. The structure of the samples has been examined using scanning electron microscopy. The calculations have been performed for the optical diffraction in the Born approximation of the scattering theory for structures with a limited number of scatterers. The images formed in the monochromatic light on a flat screen located behind the sample have been calculated. The diffraction patterns on the screen have C 6v symmetry and consist of three straight lines intersecting at an angle of 120° and hyperbolas, the number of which is a multiple of six. An important feature of these diffraction patterns is the superstructure, i.e., the partition of straight lines and hyperbolas into individual diffraction reflections, the number of which is determined by the number of scatterers of a particular sample. The results of the experimental investigation of the diffraction patterns completely coincide with the calculated data, including the number and arrangement of the superstructure reflections.


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  1. 1.
    J. M. Cowley, Diffraction Physics (Elsevier, Oxford, 1985).Google Scholar
  2. 2.
    E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).ADSCrossRefGoogle Scholar
  3. 3.
    S. John, Phys. Rev. Lett. 58, 2486 (1987).ADSCrossRefGoogle Scholar
  4. 4.
    J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, New Jersey, United States, 2008).zbMATHGoogle Scholar
  5. 5.
    Optical Properties of Photonic Structures: Interplay of Order and Disorder, Ed. by M. F. Limonov and R. M. Rue (CRC Press, Boca Raton, Florida, United States, 2012).Google Scholar
  6. 6.
    V. N. Astratov, V. N. Bogomolov, A. A. Kaplyanskii, A. V. Prokofiev, L. A. Samoilovich, S. M. Samoilovich, and Yu. A. Vlasov, Nuovo Cimento Soc. Ital. Fis., D 17, 1349 (1995).ADSCrossRefGoogle Scholar
  7. 7.
    Yu. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, Nature (London) 414, 289 (2001).ADSCrossRefGoogle Scholar
  8. 8.
    K. Wostyn, Y. Zhao, B. Yee, K. Clays, A. Persoons, G. Shaetzen, and L. Hellemans, J. Chem. Phys. 118, 10752 (2003).ADSCrossRefGoogle Scholar
  9. 9.
    A. V. Baryshev, A. A. Kaplyanskii, V. A. Kosobukin, M. F. Limonov, and A. P. Skvortsov, Phys. Solid State 46 (7), 1331 (2004).ADSCrossRefGoogle Scholar
  10. 10.
    F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, Phys. Rev. B: Condens. Matter 71, 195112 (2005).ADSCrossRefGoogle Scholar
  11. 11.
    M. V. Rybin, K. B. Samusev, and M. F. Limonov, Photonics Nanostruct: Fundam. Appl., No. 5, 119 (2007).ADSCrossRefGoogle Scholar
  12. 12.
    H. Miguez, C. López, F. Meseguer, A. Blanco, L. Vázquez, R. Mayoral, M. Ocana, V. Fornés, and A. Mifsud, Appl. Phys. Lett. 71, 1148 (1997).ADSCrossRefGoogle Scholar
  13. 13.
    A. V. Baryshev, A. V. Ankudinov, A. A. Kaplyanskii, V. A. Kosobukin, M. F. Limonov, K. B. Samusev, and D. E. Usvyat, Phys. Solid State 44 (9), 1648 (2002).ADSCrossRefGoogle Scholar
  14. 14.
    V. G. Golubev, V. A. Kosobukin, D. A. Kurdyukov, A. V. Medvedev, and A. B. Pevtsov, Semiconductors 35 (6), 680 (2001).ADSCrossRefGoogle Scholar
  15. 15.
    J. F. Galisteo-López, M. Ibisate, R. Sapienza, L. S. Froufe-Pérez, Á. Blanco, and C. López, Adv. Mater. (Weinheim) 23, 30 (2011).CrossRefGoogle Scholar
  16. 16.
    K. B. Samusev, G. N. Yushin, M. V. Rybin, and M. F. Limonov, Phys. Solid State 50 (7), 1280 (2008).ADSCrossRefGoogle Scholar
  17. 17.
    A. K. Samusev, K. B. Samusev, M. V. Rybin, M. F. Limonov, E. Yu. Trofimova, D. A. Kurdyukov, and V. G. Golubev, Phys. Solid State 53 (5), 1056 (2011).ADSCrossRefGoogle Scholar
  18. 18.
    M. V. Rybin, I. S. Sinev, A. K. Samusev, K. B. Samusev, E. Yu. Trofimova, D. A. Kurdyukov, V. G. Golubev, and M. F. Limonov, Phys. Rev. B: Condens. Matter 87, 125131(1–8) (2013).Google Scholar
  19. 19.
    R. M. Amos, J. G. Rarity, P. R. Tapster, T. J. Shepherd, and S. C. Kitson, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 61, 2929 (2000).CrossRefGoogle Scholar
  20. 20.
    L. M. Goldenberg, J. Wagner, J. Stumpe, B. R. Paulke, and E. Gornitz, Physica E (Amsterdam) 17, 433 (2003).ADSCrossRefGoogle Scholar
  21. 21.
    B. Bru[umlaut]ser, I. Staude, G. von Freymann, M. Wegener, and U. Pietsch, Appl. Opt. 51, 6732 (2012).ADSCrossRefGoogle Scholar
  22. 22.
    K. B. Samusev, M. V. Rybin, A. K. Samusev, and M. F. Limonov, Phys. Solid State 57 (12), 2494 (2015).ADSCrossRefGoogle Scholar
  23. 23.
    M. Farsari and B. N. Chichkov, Nat. Photonics 3, 450 (2009).ADSCrossRefGoogle Scholar
  24. 24.
    S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, Nature (London) 412, 697 (2001).ADSCrossRefGoogle Scholar
  25. 25.
    A. Ovsianikov, J. Viertl, B. Chichkov, M. Oubaha, B. MacCraith, I. Sakellari, A. Giakoumaki, D. Gray, M. Vamvakaki, M. Farsari, and C. Fotakis, ACS Nano 2, 2257 (2008).CrossRefGoogle Scholar
  26. 26.
    I. I. Shishkin, K. B. Samusev, M. V. Rybin, M. F. Limonov, Yu. S. Kivshar’, A. Gaidukeviichute, R. V. Kiyan, and B. N. Chichkov, JETP Lett. 95 (9), 457 (2012).ADSCrossRefGoogle Scholar
  27. 27.
    I. I. Shishkin, M. V. Rybin, K. B. Samusev, M. F. Limonov, R. V. Kiyan, B. N. Chichkov, Yu. S. Kivshar’, and P. A. Belov, JETP Lett. 99 (9), 531 (2014).ADSCrossRefGoogle Scholar
  28. 28.
    V. A. Kosobukin, Phys. Solid State 47 (11), 2035 (2005).ADSCrossRefGoogle Scholar
  29. 29.
    A. Guinier, X-Ray Diffraction in Crystals, Imperfect Crystals, and Amorphous Bodies (Dover, New York, 2013).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  • K. B. Samusev
    • 1
    • 2
  • M. V. Rybin
    • 1
    • 2
  • S. Yu. Lukashenko
    • 2
    • 3
  • P. A. Belov
    • 2
  • M. F. Limonov
    • 1
    • 2
  1. 1.Ioffe Physical-Technical InstituteRussian Academy of SciencesSt. PetersburgRussia
  2. 2.St. Petersburg National Research University of Information Technologies, Mechanics and OpticsSt. PetersburgRussia
  3. 3.Institute for Analytical InstrumentationRussian Academy of SciencesSt. PetersburgRussia

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