Skip to main content
Log in

Optical diffraction by two-dimensional photonic structures with hexagonal symmetry

  • Optical Properties
  • Published:
Physics of the Solid State Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. M. Cowley, Diffraction Physics (Elsevier, Oxford, 1985).

  2. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).

    Article  ADS  Google Scholar 

  3. S. John, Phys. Rev. Lett. 58, 2486 (1987).

    Article  ADS  Google Scholar 

  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).

    MATH  Google Scholar 

  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. 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).

    Article  ADS  Google Scholar 

  7. Yu. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, Nature (London) 414, 289 (2001).

    Article  ADS  Google Scholar 

  8. K. Wostyn, Y. Zhao, B. Yee, K. Clays, A. Persoons, G. Shaetzen, and L. Hellemans, J. Chem. Phys. 118, 10752 (2003).

    Article  ADS  Google Scholar 

  9. A. V. Baryshev, A. A. Kaplyanskii, V. A. Kosobukin, M. F. Limonov, and A. P. Skvortsov, Phys. Solid State 46 (7), 1331 (2004).

    Article  ADS  Google Scholar 

  10. F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, Phys. Rev. B: Condens. Matter 71, 195112 (2005).

    Article  ADS  Google Scholar 

  11. M. V. Rybin, K. B. Samusev, and M. F. Limonov, Photonics Nanostruct: Fundam. Appl., No. 5, 119 (2007).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  14. V. G. Golubev, V. A. Kosobukin, D. A. Kurdyukov, A. V. Medvedev, and A. B. Pevtsov, Semiconductors 35 (6), 680 (2001).

    Article  ADS  Google Scholar 

  15. J. F. Galisteo-López, M. Ibisate, R. Sapienza, L. S. Froufe-Pérez, Á. Blanco, and C. López, Adv. Mater. (Weinheim) 23, 30 (2011).

    Article  Google Scholar 

  16. K. B. Samusev, G. N. Yushin, M. V. Rybin, and M. F. Limonov, Phys. Solid State 50 (7), 1280 (2008).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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. 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).

    Article  Google Scholar 

  20. L. M. Goldenberg, J. Wagner, J. Stumpe, B. R. Paulke, and E. Gornitz, Physica E (Amsterdam) 17, 433 (2003).

    Article  ADS  Google Scholar 

  21. B. Bru[umlaut]ser, I. Staude, G. von Freymann, M. Wegener, and U. Pietsch, Appl. Opt. 51, 6732 (2012).

    Article  ADS  Google Scholar 

  22. K. B. Samusev, M. V. Rybin, A. K. Samusev, and M. F. Limonov, Phys. Solid State 57 (12), 2494 (2015).

    Article  ADS  Google Scholar 

  23. M. Farsari and B. N. Chichkov, Nat. Photonics 3, 450 (2009).

    Article  ADS  Google Scholar 

  24. S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, Nature (London) 412, 697 (2001).

    Article  ADS  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  28. V. A. Kosobukin, Phys. Solid State 47 (11), 2035 (2005).

    Article  ADS  Google Scholar 

  29. A. Guinier, X-Ray Diffraction in Crystals, Imperfect Crystals, and Amorphous Bodies (Dover, New York, 2013).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. V. Rybin.

Additional information

Original Russian Text © K.B. Samusev, M.V. Rybin, S.Yu. Lukashenko, P.A. Belov, M.F. Limonov, 2016, published in Fizika Tverdogo Tela, 2016, Vol. 58, No. 7, pp. 1364–1370.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Samusev, K.B., Rybin, M.V., Lukashenko, S.Y. et al. Optical diffraction by two-dimensional photonic structures with hexagonal symmetry. Phys. Solid State 58, 1412–1419 (2016). https://doi.org/10.1134/S1063783416070301

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063783416070301

Navigation