Advertisement

Spatial Dispersion, Polaritons, and Negative Refraction

  • Vladimir M. Agranovich
  • Yuri N. Gartstein
Chapter
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 98)

Negative refraction occurs at an interface as a natural consequence of negative group velocity waves in one of the interfacing media. We briefly comment on the history of this understanding of the phenomenon. Several physical systems are discussed that may be capable of exhibiting normal electromagnetic waves (polaritons) with negative group velocities at optical frequencies. These systems are analyzed in a unified way on the basis of a framework provided by spatial dispersion. This framework utilizes the notion of the generalized dielectric tensor εij(ω, k) representing the electromagnetic response of the medium to perturbations of frequency ω and wave vector k. Polaritons with negative group velocity can occur in the medium (whether in natural materials or in artificial metamaterials) when spatial dispersion is strong enough. Our examples include both chiral and nonchiral systems, and bulk and surface polariton waves. We also discuss the relationship between the spatial dispersion approach and the more familiar description based on the dielectric permittivity ε(ω) and magnetic permeability μ(ω).

Keywords

Wave Vector Group Velocity Dielectric Function Spatial Dispersion Negative Refraction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L.I. Mandelstam, Complete Works, vol. 5 (USSR Academy of Sciences, Moscow, 1950), Lectures given on 26 February 1940 and on 5 May 1944.Google Scholar
  2. 2.
    L.I. Mandelstam, Zh. Eksp. Teor. Fiz., 15, 475 (1945).Google Scholar
  3. 3.
    L.I. Mandelstam, Lectures on Optics, Relativity and Quantum Mechanics (Nauka, Moscow, 1972).Google Scholar
  4. 4.
    L. Brillouin, Wave Propagation and Group Velocity(Academic, New York, 1960).zbMATHGoogle Scholar
  5. 5.
    L.D. Landau, E.M. Lifshitz,Electrodynamics of Continuous Media. (Butterworth-Heinemann, Oxford, 1984).Google Scholar
  6. 6.
    V.M. Agranovich, V.L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons (Springer, Berlin Heidelberg New York, 1984).Google Scholar
  7. 7.
    V.M. Agranovich, Y.R. Shen, R. Baughman, A.A. Zakhidov, Phys. Rev. B, 69, 165112(2004).CrossRefADSGoogle Scholar
  8. 8.
    V.M. Agranovich, Y.R. Shen, R. Baughman, A.A. Zakhidov, J. Lumin. 110, 167(2004).CrossRefGoogle Scholar
  9. 9.
    V.G. Veselago, Sov. Phys. Uspekhi 10, 509 (1968).CrossRefADSGoogle Scholar
  10. 10.
    A.L. Pokrovsky, A.L. Efros, Solid State Commun. 124, 283 (2002).CrossRefADSGoogle Scholar
  11. 11.
    R.A. Shelby, D.R. Smith, S. Schultz, Science 292, 77 (2001).CrossRefADSGoogle Scholar
  12. 12.
    J.B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).CrossRefADSGoogle Scholar
  13. 13.
  14. 14.
    A. Boardman, N. King, L. Velasco, Electromagnetics 25, 365 (2005).CrossRefGoogle Scholar
  15. 15.
    K.T. McDonald, Am. J. Phys. 69, 607 (2001).CrossRefADSGoogle Scholar
  16. 16.
    H. Lamb, Proc. Lond. Math. Soc. 1, 473 (1904).CrossRefGoogle Scholar
  17. 17.
    M. Laue, Ann. Phys. (Leipzig) 18, 523 (1905).ADSGoogle Scholar
  18. 18.
    A. Schuster, An Introduction to the Theory of Optics (Edward Arnold, London, 1904).zbMATHGoogle Scholar
  19. 19.
    E.L. Feinberg, Phys. Uspekhi 45, 81 (2002).CrossRefADSGoogle Scholar
  20. 20.
    D.V. Sivukhin, Opt. Spektrosk. 3, 308 (1957) .Google Scholar
  21. 21.
    V.E. Pafomov, Sov. Phys. JETP 9, 1321 (1959).Google Scholar
  22. 22.
    V.L. Ginzburg, Applications of Electrodynamics in Theoretical Physics and Astrophysics (Gordon and Breach, New York, 1989), Chap. 7.Google Scholar
  23. 23.
    V.E. Pafomov, Sov. Phys. JETP 5, 307 (1957).Google Scholar
  24. 24.
    J.D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).zbMATHGoogle Scholar
  25. 25.
    V.M. Agranovich, V.E. Pafomov, A.A. Rukhadze, Sov. Phys. JETP 9, 160. (1959).zbMATHGoogle Scholar
  26. 26.
    I.M. Frank, Sov. Phys. JETP 9, 580 (1959).Google Scholar
  27. 27.
    K.A. Barsukov, Sov. Phys. JETP 9, 1052 (1959).MathSciNetGoogle Scholar
  28. 28.
    Yu.A. Il’inskii, L.V. Keldysh, Electromagnetic Response of Material Media. (Plenum, New York, 1994).Google Scholar
  29. 29.
    D.B. Melrose, R.C. McPhedran, Electromagnetic Processes in Dispersive Media. (Cambridge University Press, Cambridge, 1991).CrossRefGoogle Scholar
  30. 30.
    S.M. Rytov, Zh. Eksp. Teor. Fiz. 17, 930 (1947).Google Scholar
  31. 31.
    M.E. Gertsenshtein, Zh. Eksp. Teor. Fiz. 26, 680 (1954).Google Scholar
  32. 32.
    A.A. Golubkov, V.A. Makarov, Phys. Uspekhi 38, 325 (1995).CrossRefADSGoogle Scholar
  33. 33.
    A.P. Vinogradov, Phys. Uspekhi 45, 331 (2002).CrossRefADSGoogle Scholar
  34. 34.
    D. Bedeaux, M. Osipov, J. Vlieger, J. Opt. Soc. Am. A 12, 2431 (2004).CrossRefADSGoogle Scholar
  35. 35.
    L. Keldysh, D. Kirzhnitz, A. Dolgov (eds.), The Dielectric Function of Condensed Systems (North-Holland, Amsterdam, 1989).Google Scholar
  36. 36.
    G.D. Mahan, Many-Particle Physics (Kluwer, New York, 2000).Google Scholar
  37. 37.
    Y. Toyozawa, Optical Processes in Solids(Cambridge University Press, Cambridge, 2003).CrossRefGoogle Scholar
  38. 38.
    D.P. Craig, T. Thirunamachandran, Molecular Quantum Electrodynamics (Academic, London, 1984).Google Scholar
  39. 39.
    L.D. Barron, Molecular Light Scattering and Optical Activity (Cambridge University Press, Cambridge, 2004).CrossRefGoogle Scholar
  40. 40.
    V.L. Ginzburg, Sov. Phys. JETP 7, 1096 (1958).MathSciNetGoogle Scholar
  41. 41.
    S.I. Pekar, Sov. Phys. JETP 6, 785 (1958).MathSciNetADSGoogle Scholar
  42. 42.
    L. Silvestri, O.A. Dubovski, G.C. La Rocca, F. Bassani, V.M. Agranovich, Nuovo Cimento Soc. Ital. Fis. C 27, 437 (2004).ADSGoogle Scholar
  43. 43.
    V.M. Agranovich, Sov. Phys. Uspekhi 3, 427 (1961).CrossRefADSGoogle Scholar
  44. 44.
    V.S. Pine, G. Dresselhaus, Phys. Rev. 188, 1489 (1969).CrossRefADSGoogle Scholar
  45. 45.
    J.B. Pendry, Science 306, 1353 (2004).CrossRefADSGoogle Scholar
  46. 46.
    S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, C. Simovski, J. Electromagn. Waves Appl. 17, 695 (2003).CrossRefGoogle Scholar
  47. 47.
    T.G. Mackay, Microw. Opt. Technol. Lett. 45, 120 (2005).CrossRefGoogle Scholar
  48. 48.
    Y. Jin, S. He, Opt. Express 13, 4974 (2005).CrossRefADSGoogle Scholar
  49. 49.
    C. Monzon, D.W. Forester, Phys. Rev. Lett. 95, 123904 (2005).CrossRefADSGoogle Scholar
  50. 50.
    V.M. Agranovich, Yu.N. Gartstein, A.A. Zakhidov, Phys. Rev. B 73, 045114. (2006).CrossRefADSGoogle Scholar
  51. 51.
    V.M. Agranovich, in Surface Polaritons, ed. by V.M. Agranovich, D.L. Mills. (North-Holland, Amsterdam, 1982), p. 187.Google Scholar
  52. 52.
    T. Lopez-Rios, F. Abeles, G. Vuye, J. Physique 39, 645 (1978).CrossRefGoogle Scholar
  53. 53.
    E.A. Vinogradov, T.A. Leskova, Phys. Rep. 194, 273 (1990).CrossRefADSGoogle Scholar
  54. 54.
    V.A. Yakovlev, G.N. Zhizhin, Opt. Commun. 15, 293 (1975).CrossRefADSGoogle Scholar
  55. 55.
    I. Pockrand, A. Brillante, D. Mobius, J. Chem. Phys. 77, 6289 (1982).CrossRefADSGoogle Scholar
  56. 56.
    J. Bellessa, C. Bonnand, J.C. Plenet, J. Mugnier, Phys. Rev. Lett. 93, 036404. (2004).CrossRefADSGoogle Scholar
  57. 57.
    V.M. Agranovich, T.A. Leskova, Prog. Surf. Sci. 29, 169 (1988).CrossRefADSGoogle Scholar
  58. 58.
    J.B. Pendry, Phys. Rev. Lett. 85, 3965 (2000).CrossRefADSGoogle Scholar
  59. 59.
    A.N. Grigorenko, A.K. Geim, H.F. Gleeson, Y. Zhang, A.A. Firsov, I.Y. Khrushchev, J. Petrovic, Nature 438, 355 (2005).CrossRefADSGoogle Scholar
  60. 60.
    V.M. Shalaev, W. Cai, U. Chettiar, H.K. Yuan, A.K. Sarychev, V.P. Drachev, V. KIldishev, Opt. Lett. 30, 3356 (2005).CrossRefADSGoogle Scholar
  61. 61.
    A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, 1995).zbMATHGoogle Scholar
  62. 62.
    I.V. Shadrivov, A.A. Zharov, Yu.S. Kivshar, arXiv:physics/0506092 (2005).Google Scholar
  63. 63.
    O.S. Tarasenko, S.V. Tarasenko, V.M. Yurchenko, JETP Lett. 80, 484 (2004).CrossRefADSGoogle Scholar
  64. 64.
    A.B. Kozyrev, H. Kim, A. Karbassi, D.W. van der Weide, Appl. Phys. Lett. 87,121109 (2005).CrossRefADSGoogle Scholar
  65. 65.
    M. Lapin, M. Gorkunov, K.H. Rinhofer, Phys. Rev. E 67, 065601 (2003).CrossRefADSGoogle Scholar
  66. 66.
    A.A. Zharov, I.V. Shadrivov, Yu.S. Kivshar, Phys. Rev. Lett. 91, 037401 (2003).CrossRefADSGoogle Scholar
  67. 67.
    S. O’Brien, D. McPeake, S.A. Ramakrishna, J.B. Pendry, Phys. Rev. B 69, 241101 (R) (2004).CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Vladimir M. Agranovich
    • 1
  • Yuri N. Gartstein
    • 2
  1. 1.Institute of Spectroscopy Russian Academy of SciencesTroitskRussia
  2. 2.Department of PhysicsThe University of Texas at DallasRichardsonUSA

Personalised recommendations