Interaction of a two-dimensional electromagnetic pulse with an electron inhomogeneity in an array of carbon nanotubes in the presence of field inhomogeneity

  • Alexander V. Zhukov
  • Roland Bouffanais
  • Hervé Leblond
  • Dumitru Mihalache
  • Eduard G. Fedorov
  • Mikhail B. Belonenko
Regular Article

Abstract

In this study, we address the challenging problem of propagation of infrared electromagnetic two-dimensional bipolar pulses of extremely short duration in a heterogeneous array of semiconductor carbon nanotubes. Heterogeneity is defined here as a region of high electron density. The evolutions of the electromagnetic field and charge density in the sample are described by Maxwell’s equations and the continuity equation respectively, wherein the inhomogeneity of the field along the nanotube axis is integrated and incorporated into the modeling framework. Our numerical solution to this problem shows the possibility of a stable propagation of two-dimensional electromagnetic pulses through a heterogeneous array of carbon nanotubes. This propagation of electromagnetic pulses is accompanied by a redistribution of the electron density in the sample. For the first time to the best of our knowledge, this latter effect is fully accounted for in our study. Specifically, we demonstrate that depending on the initial speed of the electromagnetic pulse two possible outcomes might ensue: either (i) the pulse overcomes the region of increased electron concentration, or alternatively (ii) it is reflected therefrom. As a result, a near-infrared pulse is transmitted, while the long-wavelength infrared pulse is reflected, on an obstacle that is much smaller than its wavelength.

Graphical abstract

Keywords

Ultraintense and Ultra-short Laser Fields 

References

  1. 1.
    P.J.F. Harris, Carbon Nanotubes and Related Structures: New Materials for the Twenty-First Century (Cambridge University Press, 1999)Google Scholar
  2. 2.
    S. Iijima, Nature 354, 56 (1991)CrossRefADSGoogle Scholar
  3. 3.
    S.A. Maksimenko, G.Ya. Slepyan, J. Commun. Technol. Electron. 47, 261 (2002)Google Scholar
  4. 4.
    S.A. Maksimenko, G. Ya. Slepyan, Handbook of Nanotechnology. Nanometer Structure: Theory, Modeling, and Simulation (SPIE Press, Bellingham, 2004)Google Scholar
  5. 5.
    S.A. Akhmanov, V.A. Vysloukh, A.S. Chirkin, Optics of Femtosecond Laser Pulses (AIP, New York, 1992)Google Scholar
  6. 6.
    M.B. Belonenko, E.V. Demushkina, N.G. Lebedev, J. Russ. Laser Res. 27, 457 (2006)CrossRefGoogle Scholar
  7. 7.
    M.B. Belonenko, E.V. Demushkina, N.G. Lebedev, Phys. Solid State 50, 383 (2008)CrossRefADSGoogle Scholar
  8. 8.
    M.B. Belonenko, E.V. Demushkina, N.G. Lebedev, Technol. Phys. 53, 817 (2008)CrossRefADSGoogle Scholar
  9. 9.
    M.B. Belonenko, E.V. Demushkina, N.G. Lebedev, Russ. J. Phys. Chem. B 2, 964 (2008)CrossRefGoogle Scholar
  10. 10.
    N.N. Yanyushkina, M.B. Belonenko, N.G. Lebedev, A.V. Zhukov, M. Paliy, Int. J. Mod. Phys. B 25, 3401 (2011)MATHCrossRefADSGoogle Scholar
  11. 11.
    M.B. Belonenko, A.S. Popov, N.G. Lebedev, A.V. Pak, A.V. Zhukov, Phys. Lett. A 375, 946 (2011)CrossRefADSGoogle Scholar
  12. 12.
    P. Mandel, M. Tlidi, J. Opt. B 6, R60 (2004)CrossRefADSGoogle Scholar
  13. 13.
    B.A. Malomed, D. Mihalache, F. Wise, L. Torner, J. Opt. B 7, R53 (2005)CrossRefADSGoogle Scholar
  14. 14.
    Y.V. Kartashov, B.A. Malomed, L. Torner, Rev. Mod. Phys. 83, 247 (2011)CrossRefADSGoogle Scholar
  15. 15.
    P. Grelu, N. Akhmediev, Nat. Photon. 6, 84 (2012)CrossRefADSGoogle Scholar
  16. 16.
    Z. Chen, M. Segev, D. Christodoulides, Rep. Prog. Phys. 75, 086401 (2012)CrossRefADSGoogle Scholar
  17. 17.
    D. Mihalache, Rom. J. Phys. 57, 352 (2012)Google Scholar
  18. 18.
    M. Tlidi, K. Staliunas, K. Panajotov, A.G. Vladimirov, M.G. Clerc, Philos. Trans. R. Soc. A 372, 20140101 (2014)CrossRefADSGoogle Scholar
  19. 19.
    D. Mihalache, Rom. J. Phys. 59, 295 (2014)Google Scholar
  20. 20.
    B.A. Malomed, J. Opt. Soc. Am. B 31, 2460 (2014)CrossRefADSGoogle Scholar
  21. 21.
    N.N. Rosanov, G.B. Sochilin, V.D. Vinokura, N.V. Vysotina, Philos. Trans. R. Soc. A 372, 20140012 (2014)CrossRefADSGoogle Scholar
  22. 22.
    V.S. Bagnato, D.J. Frantzeskakis, P.G. Kevrekidis, B.A. Malomed, D. Mihalache, Rom. Rep. Phys. 67, 5 (2015)Google Scholar
  23. 23.
    S.V. Sazonov, Bull. Russ. Acad. Sci. Phys. 75, 157 (2011)MathSciNetCrossRefGoogle Scholar
  24. 24.
    H. Leblond, H. Triki, D. Mihalache, Rom. Rep. Phys. 65, 925 (2013)Google Scholar
  25. 25.
    H. Leblond, D. Mihalache, Phys. Rep. 523, 61 (2013)MathSciNetCrossRefADSGoogle Scholar
  26. 26.
    D.J. Frantzeskakis, H. Leblond, D. Mihalache, Rom. J. Phys. 59, 767 (2014)Google Scholar
  27. 27.
    M.B. Belonenko, S. Yu. Glazov, N.G. Lebedev, N.E. Meshcheryakova, Phys. Sol. State 51, 1758 (2009)CrossRefADSGoogle Scholar
  28. 28.
    M.B. Belonenko, N.G. Lebedev, A.S. Popov, J. Exp. Theor. Phys. Lett. 91, 461 (2010)CrossRefGoogle Scholar
  29. 29.
    H. Leblond, D. Mihalache, Phys. Rev. A 86, 043832 (2012)CrossRefADSGoogle Scholar
  30. 30.
    M.B. Belonenko, A.S. Popov, N.G. Lebedev, Techn. Phys. Lett. 37, 119 (2011)CrossRefADSGoogle Scholar
  31. 31.
    A.S. Popov, M.B. Belonenko, N.G. Lebedev, A.V. Zhukov, M. Paliy, Eur. Phys. J. D 65, 635 (2011)CrossRefADSGoogle Scholar
  32. 32.
    A.S. Popov, M.B. Belonenko, N.G. Lebedev, A.V. Zhukov, T.F. George, Int. J. Theor. Phys. Group Theory Nonlinear Opt. 15, 5 (2011)Google Scholar
  33. 33.
    E.G. Fedorov, A.V. Zhukov, M.B. Belonenko, T.F. George, Eur. Phys. J. D 66, 219 (2012)CrossRefADSGoogle Scholar
  34. 34.
    A.V. Zhukov, R. Bouffanais, M.B. Belonenko, E.G. Federov, Mod. Phys. Lett. B 27, 1350045 (2013)CrossRefADSGoogle Scholar
  35. 35.
    M.B. Belonenko, E.G. Fedorov, Phys. Sol. State 55, 1238 (2013)CrossRefGoogle Scholar
  36. 36.
    A.V. Zhukov, R. Bouffanais, E.G. Fedorov, M.B. Belonenko, J. Appl. Phys. 114, 143106 (2013)CrossRefADSGoogle Scholar
  37. 37.
    A.V. Zhukov, R. Bouffanais, E.G. Fedorov, M.B. Belonenko, J. Appl. Phys. 115, 203109 (2014)CrossRefADSGoogle Scholar
  38. 38.
    L.D. Landau, E.M. Lifshitz, L.P. Pitaevskii, Electrodynamics of Continuous Media, 2nd edn. (Elsevier, Oxford, 2004)Google Scholar
  39. 39.
    L.D. Landau, E.M. Lifshitz, The Classical Theory of Fields, 4th edn. (Butterworth-Heinemann, Oxford, 2000)Google Scholar
  40. 40.
    Yu.S. Kivshar, B.A. Malomed, Rev. Mod. Phys. 61, 763 (1989)CrossRefADSGoogle Scholar
  41. 41.
    S.V. Kryuchkov, K.A. Popov, Semiconductors 30, 1130 (1996)ADSGoogle Scholar
  42. 42.
    J.W. Thomas, Numerical Partial Differential Equations – Finite Difference Methods (Springer Verlag, New York, 1995)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Alexander V. Zhukov
    • 1
  • Roland Bouffanais
    • 1
  • Hervé Leblond
    • 2
  • Dumitru Mihalache
    • 3
    • 4
  • Eduard G. Fedorov
    • 5
    • 6
  • Mikhail B. Belonenko
    • 7
    • 8
  1. 1.Singapore University of Technology & DesignSingaporeSingapore
  2. 2.Laboratoire de Photonique d’AngersLUNAM Université, Université d’AngersAngersFrance
  3. 3.Academy of Romanian ScientistsBucharestRomania
  4. 4.Horia Hulubei National Institute of Physics and Nuclear EngineeringMagureleRomania
  5. 5.Scientific and Industrial Corporation “Vavilov State Optical Institute”Saint PetersburgRussia
  6. 6.ITMO UniversitySaint PetersburgRussia
  7. 7.Laboratory of NanotechnologyVolgograd Institute of BusinessVolgogradRussia
  8. 8.Volgograd State UniversityVolgogradRussia

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