Skip to main content
SpringerLink
Log in

Studying the possibility of extracting material parameters from reflection and transmission coefficients of plane wave for multilayer metamaterials based on metal nanogrids

  • Condensed-Matter Spectroscopy
  • Published:
Optics and Spectroscopy Aims and scope Submit manuscript

Abstract

To more adequately extract the effective refractive index and other so-called metamaterial parameters from the reflection and transmission coefficients of a wave for multilayer grid nanostructures in the near-IR spectral range, the Nicholson-Ross-Weir method was modified. The rate of convergence of each extracted metamaterial parameter to a certain limit is studied with increasing number of layers of the structure. For each frequency of the light field, this limit is obviously equal to the value of the parameter that corresponds to an infinite number of layers. The effect of a separation layer of a dielectric between pairs of grids on the convergence rate of extracted parameters is studied. Bulk electrodynamic parameters of the structure are discussed.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).

    Article  ADS  Google Scholar 

  2. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84(18), 4184 (2000).

    Article  ADS  Google Scholar 

  3. D. R. Smith and N. Knoll, Phys. Rev. Lett. 85, 2933 (2000).

    Article  ADS  Google Scholar 

  4. C. Caloz, C. C. Chang, and T. Itoh, J. Appl. Phys. 11(11), 5483 (2001).

    Article  ADS  Google Scholar 

  5. R. W. Ziolkowski and E. Heyman, Phys. Rev. E 64, 056625 (2001).

    Article  ADS  Google Scholar 

  6. R. W. Ziolkowski, IEEE Trans. Antennas Propag. 51, 1516 (2003).

    Article  ADS  Google Scholar 

  7. C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, Phys. Rev. Lett. 90, 107401 (2003).

    Article  ADS  Google Scholar 

  8. V. G. Veselago, 92(3), 517 (1967).

  9. D. V. Sivukhin, Opt. Spektrosk. 3(2), 308 (1957).

    Google Scholar 

  10. L. I. Mandelstam, Zh. Éksp. Teor. Fiz. 15, 475 (1945).

    MathSciNet  Google Scholar 

  11. V. E. Pafomov, Zh. Éksp. Teor. Fiz. 36, 1853 (1959).

    Google Scholar 

  12. V. E. Pafomov, Zh. Éksp. Teor. Fiz. 30, 761 (1956).

    Google Scholar 

  13. J. Pendry, Phys. Rev. Lett. 85, 3966 (2000).

    Article  ADS  Google Scholar 

  14. Theory and Phenomena of Metamaterials, Ed. by F. Capolino (CRC Press, New York, 2009).

    Google Scholar 

  15. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 8: Electrodynamics of Continuous Media, 3rd ed. (Nauka, Moscow, 1992; Pergamon, New York, 1984).

    Google Scholar 

  16. S. Tretyakov, Metamaterials 1, 40 (2007).

    Article  ADS  Google Scholar 

  17. X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, Phys. Rev. E 70, 016608 (2004).

    Article  ADS  Google Scholar 

  18. S. Zhang, W. Fan, K. J. Malloy, S. R. Brueck, N. C. Panoiu, and R. M. Osgood, Opt. Expr. 13, 4922 (2005).

    Article  ADS  Google Scholar 

  19. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett. 95, 137404 (2005).

    Article  ADS  Google Scholar 

  20. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, J. Opt. Soc. Am. B 23, 434 (2006).

    Article  ADS  Google Scholar 

  21. G. Dolling, M. Wegener, C. Enkrich, and S. Linden, Opt. Lett. 31, 1800 (2006).

    Article  ADS  Google Scholar 

  22. V. M. Shalaev, W. Cai, U. K. Chettiar, H. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, Opt. Lett. 30, 3356 (2005).

    Article  ADS  Google Scholar 

  23. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, Opt. Lett. 32, 53 (2007).

    Article  ADS  Google Scholar 

  24. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, Science 312, 892 (2006).

    Article  ADS  Google Scholar 

  25. C. Garcia-Meca, R. Ortuno, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, Opt. Lett. 34, 1603 (2009).

    Article  ADS  Google Scholar 

  26. A. M. Bratkovski, A. Cano, and A. P. Levanyuk, Appl. Phys. Lett. 87, 103507 (2005).

    Article  ADS  Google Scholar 

  27. R. Marques and J. Baena, Microwave Opt. Technol. Lett. 41, 290 (2004).

    Article  Google Scholar 

  28. Z. Liu, H. Lee, Y. Xiong, C. Sung, and X. Zhang, Science 315, 1686 (2007).

    Article  ADS  Google Scholar 

  29. I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315(5819), 1699 (2007).

    Article  ADS  Google Scholar 

  30. L. A. Vaĭnshteĭn, Usp. Fiz. Nauk 118, 339 (1976).

    Google Scholar 

  31. M. Wegener, private communication.

  32. V. M. Shalaev, Nat. Photonics 1, 41 (2007).

    Article  ADS  Google Scholar 

  33. J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).

    Article  MathSciNet  ADS  Google Scholar 

  34. C. R. Simovski, Opt. Spektrosk. 107(4), 623 (2009).

    Google Scholar 

  35. R. Ortuno, C. Garcia-Meca, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, Phys. Rev. B 79, 075 425 (2009).

    Article  Google Scholar 

  36. S. Zhang, W. Fan, N. C. Panoiu, K. Malloy, R. M. Osgood, and S. R. J. Brueck, Opt. Expr. 14, 6778 (2006).

    Article  ADS  Google Scholar 

  37. C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, T. Zentgraf, T. P. Meyrath, and H. Giessen, Phys. Rev. B 77, 035 126 (2008).

    Article  Google Scholar 

  38. G. Dolling, M. Wegener, and S. Linden, Opt. Lett. 32, 551 (2007).

    Article  ADS  Google Scholar 

  39. C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, Phys. Rev. B 77, 195328 (2008).

    Article  ADS  Google Scholar 

  40. C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, and F. Lederer, Phys. Rev. B 78, 155102 (2008).

    Article  ADS  Google Scholar 

  41. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).

    Article  ADS  Google Scholar 

  42. J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, Photon. Nanostr. Fund. Appl. 6, 96 (2008).

    Article  ADS  Google Scholar 

  43. R. Marqués, L. Jelinek, F. Mesa, and F. Medina, Opt. Expr. 17, 11582 (2009).

    Article  ADS  Google Scholar 

  44. X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, Jr., Phys. Rev. E 70, 016608 (2004).

    Article  ADS  Google Scholar 

  45. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).

    Article  ADS  Google Scholar 

  46. C. R. Simovski and S. A. Tretyakov, Phys. Rev. B 75, 195111 (2007).

    Article  ADS  Google Scholar 

  47. C. R. Simovski, Metamaterials 1, 62 (2007).

    Article  ADS  Google Scholar 

  48. C. R. Simovski, Metamaterials 2, 169 (2008).

    Article  ADS  Google Scholar 

  49. C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. A. Azad, and A. J. Taylor, Metamaterials 3, 100 (2009).

    Article  ADS  Google Scholar 

  50. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Petersburg State University of Information Technologies, Mechanics, and Optics, St. Petersburg, 197101, Russia

    P. A. Belov, E. A. Yankovskaya, I. V. Melchakova & C. R. Simovski

  2. Helsinki University of Technology, Helsinki, Finland

    C. R. Simovski

  3. Queen Mary College, University of London, London, UK

    P. A. Belov

Authors
  1. P. A. Belov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. A. Yankovskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. V. Melchakova
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C. R. Simovski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. A. Belov.

Additional information

Original Russian Text © P.A. Belov, E.A. Yankovskaya, I.V. Melchakova, C.R. Simovski, 2010, published in Optika i Spektroskopiya, 2010, Vol. 109, No. 1, pp. 90–101.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Belov, P.A., Yankovskaya, E.A., Melchakova, I.V. et al. Studying the possibility of extracting material parameters from reflection and transmission coefficients of plane wave for multilayer metamaterials based on metal nanogrids. Opt. Spectrosc. 109, 85–96 (2010). https://doi.org/10.1134/S0030400X10070143

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0030400X10070143

Keywords

Search

Navigation