Skip to main content
SpringerLink
Log in

Influence of the sign of the refractive index in the reflectivity of a metamaterial surface with localized roughness

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

To study the scattering properties of metamaterials, we generalize two scattering methods developed for conventional (non-magnetic) isotropic materials to the case of materials with arbitrary values (positive or negative) of magnetic permeability and electric permittivity. The generalized methods are used to study the changes produced in the reflectivity of a metamaterial surface with localized roughness when the relative refractive index changes sign. Our results show that, unlike the case of a plane surface whose reflectivity is unaffected by the change of sign of the relative refractive index, in rough surfaces the change of sign is manifested in the reflectivity, even for very low roughness, particularly in observation directions away from the specular direction.

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. A. Sihvola, Metamaterials in electromagnetics, Metamaterials 1, 2 (2007)

  2. R. Marqués, F. Martín, M. Sorolla, Metamaterials with Negative Parameters: Theory, Design and Microwave Applications (Wiley, 2008)

  3. L. Solymar, E. Shamonina, Waves in Metamaterials (Oxford University Press, New York, 2009)

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

    Article  ADS  Google Scholar 

  5. V.G. Veselago, Soviet Physics Uspekhi 10, 509 (1968)

    Article  ADS  Google Scholar 

  6. R.A. Depine, A. Lakhtakia, Microwaves Opt. Technol. Lett. 41, 315 (2004)

    Article  Google Scholar 

  7. A. Lakhtakia, T.G. Mackay, J.B. Geddes, Microwaves Opt. Technol. Lett. 51, 1230 (2009)

    Article  Google Scholar 

  8. A. Lakhtakia, Beltrami Fields in Chiral Media, World Scientific Series in Contemporary Chemical Physics (1994), Vol. 2

  9. M.W. McCall, A. Lakhtakia, W.S. Weiglhofer, Eur. J. Phys. 23, 353 (2002)

    Article  Google Scholar 

  10. R. Ruppin, J. Phys. Condens. Matter 16, 5991 (2004)

    Article  ADS  Google Scholar 

  11. S. Ancey, Y. Décanini, A. Folacci, P. Gabrielli, Phys. Rev. B 72, 085458 (2005)

    Article  ADS  Google Scholar 

  12. S. Ancey, Y. Décanini, A. Folacci, P. Gabrielli, Phys. Rev. B 76, 195413 (2007)

    Article  ADS  Google Scholar 

  13. R. Ruppin, Solid State Commun. 116, 411 (2000)

    Article  ADS  Google Scholar 

  14. R.A. Depine, A. Lakhtakia, Opt. Commun. 233, 277 (2004)

    Article  ADS  Google Scholar 

  15. R.A. Depine, A. Lakhtakia, Phys. Rev. E 69, 057602 (2004)

    Article  ADS  Google Scholar 

  16. R.A. Depine, A. Lakhtakia, Optik 116, 31 (2005)

    Article  ADS  Google Scholar 

  17. R.A. Depine, A. Lakhtakia, D.R. Smith, Phys. Lett. A 337, 155 (2005)

    Article  ADS  MATH  Google Scholar 

  18. R.A. Depine, A. Lakhtakia, New J. Phys. 7, 158 (2005)

    Article  ADS  Google Scholar 

  19. R.A. Depine, M.E. Inchaussandague, A. Lakhtakia, Opt. Commun. 258, 90 (2006)

    Article  ADS  Google Scholar 

  20. U. Leonhardt, Science 312, 1777 (2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. C. Henkel, K. Joulain, Europhys. Lett. 72, 929 (2005)

    Article  ADS  Google Scholar 

  24. M. Cuevas, R.A. Depine, Phys. Rev. B 78, 125412 (2008)

    Article  ADS  Google Scholar 

  25. M. Cuevas, R.A. Depine, Phys. Rev. Lett. 103, 097401 (2009)

    Article  ADS  Google Scholar 

  26. T. Driscoll, D.N. Basov, W.J. Padilla, J.J. Mock, D.R. Smith, Phys. Rev. B 75, 115114 (2007)

    Article  ADS  Google Scholar 

  27. A. Lakhtakia, Microw. Opt. Technol. Lett. 40, 160 (2004)

    Article  Google Scholar 

  28. L. Rayleigh, Proc. R. Soc. Lond A 79, 399 (1907)

    ADS  MATH  Google Scholar 

  29. B.A. Lippmann, J. Opt. Soc. Am. 43, 408 (1953)

    Article  Google Scholar 

  30. L. Kazandjian, Phys. Rev. E 54, 6802 (1996)

    Article  ADS  Google Scholar 

  31. J.B. Keller, J. Opt. Soc. Am. A 17, 456 (2000)

    Article  ADS  Google Scholar 

  32. T. Watanabe, Y. Choyal, K. Minami, V.L. Granatstein, Phys. Rev. E 69, 056606 (2004)

    Article  ADS  Google Scholar 

  33. T. Elfouhaily, Phys. Rev. Lett. 97, 120404 (2006)

    Article  ADS  Google Scholar 

  34. P. Prabasaj, Opt. Commun. 278, 204 (2007)

    Article  ADS  Google Scholar 

  35. J. Wauer, T. Rother, Opt. Commun. 282, 339 (2009)

    Article  ADS  Google Scholar 

  36. A.G. Voronovich, Rayleigh Hypothesis, in Light scattering and nanoscale surface roughness, edited by A.A. Maradudin (Springer, 2006), pp. 93–105

  37. A.V. Tishchenko, Opt. Express 17, 17102 (2009)

    Article  Google Scholar 

  38. A.V. Tishchenko, Optics Photonics News 21, 50 (2010)

    Article  ADS  Google Scholar 

  39. F. Toigo , A. Marvin , V. Celli , N.R. Hill , Phys. Rev. B 15, 12, 5618 (1977)

    Article  ADS  Google Scholar 

  40. S.O. Rice, Commun. Pure Appl. Math. 4, 351 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  41. M. Born, E. Wolf, Principles of Optics, 6th. edn. (Pergamon Press, Oxford, 1980)

  42. M. Lester, R.A. Depine, Opt. Commun. 127, 189 (1996)

    Article  ADS  Google Scholar 

  43. J.A. DeSanto, J. Opt. Soc. Am. 2, 2202 (1985)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Grupo de Electromagnetismo Aplicado, Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria Pabellón I, C1428, EHA Buenos Aires, Argentina

    V. Grünhut & R. A. Depine

Authors
  1. V. Grünhut
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. A. Depine
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. A. Depine.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grünhut, V., Depine, R.A. Influence of the sign of the refractive index in the reflectivity of a metamaterial surface with localized roughness. Eur. Phys. J. D 62, 227–236 (2011). https://doi.org/10.1140/epjd/e2011-10438-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjd/e2011-10438-4

Keywords

Search

Navigation