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Plasmonics

, Volume 14, Issue 2, pp 321–326 | Cite as

Nonlocal Plasmonic Modes and Plasmonic Band Structures in Cylindrically Curved Graphene

  • Y. ZhouEmail author
  • C. Q. Shao
Article
  • 104 Downloads

Abstract

In this paper, hydrodynamic model has been analytically solved to investigate the nonlocal plasmons in cylindrically curved graphene layers. Within the quasi-static approximation, the dispersion relations for both local and nonlocal cases have been derived; the nonlocal effect is found to shift the dispersion relations upwards. High-order azimuthal modes possess different cutoff frequencies due to such nonlocality, which may occur even in large-scale highly doped structures. In periodically doped cases, the nonlocal effect can modify the corresponding plasmonic band structures, i.e., moving the locations of the bandgaps. The periodicity has made the material more sensitive to the plasmon nonlocality. Our investigations may lead to more attentions to the nonlocal plasmonic responses in graphene which are important for graphene-plasmon-based photonic devices.

Keywords

Graphene plasmonics Photonic bandgap materials Waveguides 

Notes

Acknowledgments

We thank C. Q. Shao for the use of their computer cluster.

Funding

This work was supported by the National Natural Science Foundation of China (11647117) and the Natural Science Foundation of Zhejiang Province (LQ17A040003). C. Q. Shao was supported by the National Natural Science Foundation of China (11747073).

References

  1. 1.
    Koppens FHL, Chang DE, García de Abajo FJ (2011) Graphene plasmonics: a platform for strong light matter interactions. Nano Lett 11(8):3370–3377.  https://doi.org/10.1021/nl201771h CrossRefGoogle Scholar
  2. 2.
    Grigorenko AN, Polini M, Novoselov KS (2012) Graphene plasmonics. Nat Photonics 6(11):749–758.  https://doi.org/10.1038/nphoton.2012.262 CrossRefGoogle Scholar
  3. 3.
    Bao Q, Loh KP (2012) Graphene photonics, plasmonics, and broadband optoelectronic devices. ACS Nano 6(5):3677–3694.  https://doi.org/10.1021/nn300989g@proofing CrossRefGoogle Scholar
  4. 4.
    García de Abajo FJ (2014) Graphene plasmonics: challenges and opportunities. ACS Photonics 1(3):135–152.  https://doi.org/10.1021/ph400147y CrossRefGoogle Scholar
  5. 5.
    Nikitin AY, Guinea F, Garcia-Vidal FJ, Martin-Moreno L (2011) Fields radiated by a nanoemitter in a graphene sheet. Phys Rev B 84(19):195446.  https://doi.org/10.1103/PhysRevB.84.195446 CrossRefGoogle Scholar
  6. 6.
    Zhan TR, Zhao FY, Hu XH, Liu XH, Zi J (2012) Band structure of plasmons and optical absorption enhancement in grapheneon subwavelength dielectric gratings at infrared frequencies. Phys Rev B 86:165416.  https://doi.org/10.1103/PhysRevB.86.165416 CrossRefGoogle Scholar
  7. 7.
    Thongrattanasiri S, Koppens FHL, García de Abajo FJ (2012) Complete optical absorption in periodically patterned graphene. Phys Rev Lett 108(4):047401.  https://doi.org/10.1103/PhysRevLett.108.047401 CrossRefGoogle Scholar
  8. 8.
    Thongrattanasiri S, García de Abajo FJ (2013) Optical field enhancement by strong plasmon interaction in graphene nanostructures. Phys Rev Lett 110(18):187401.  https://doi.org/10.1103/PhysRevLett.110.187401 CrossRefGoogle Scholar
  9. 9.
    Stauber T, Gómez-Santos G, García de Abajo FJ (2014) Extraordinary absorption of decorated undoped graphene. Phys Rev Lett 112(7):077401.  https://doi.org/10.1103/PhysRevLett.112.077401 CrossRefGoogle Scholar
  10. 10.
    Mikhailov SA, Ziegler K (2007) New electromagnetic mode in graphene. Phys Rev Lett 99(1):016803.  https://doi.org/10.1103/PhysRevLett.99.016803 CrossRefGoogle Scholar
  11. 11.
    Jablan M, Buljan H, Soljačić M (2009) Plasmonics in graphene at infrared frequencies. Phys Rev B 80(24):245435.  https://doi.org/10.1103/PhysRevB.80.245435 CrossRefGoogle Scholar
  12. 12.
    Nikitin AY, Guinea F, García-Vidal FJ, Martín-Moreno L (2011) Edge and waveguide terahertz surface plasmon modes in graphene microribbons. Phys Rev B 84(16):161407.  https://doi.org/10.1103/PhysRevB.84.161407 CrossRefGoogle Scholar
  13. 13.
    Wang W, Apell SP, Kinaret JM (2012) Edge magnetoplasmons and the optical excitations in graphene disks. Phys Rev B 86(12):125450.  https://doi.org/10.1103/PhysRevB.86.125450 CrossRefGoogle Scholar
  14. 14.
    Christensen J, Manjavacas A, Thongrattanasiri S, Koppens FHL, García de Abajo FJ (2012) Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons. ACS Nano 6(1):431–440.  https://doi.org/10.1021/nn2037626 CrossRefGoogle Scholar
  15. 15.
    Croy A, Midtvedt D, Isacsson A, Kinaret JM (2012) Nonlinear damping in graphene resonators. Phys Rev B 86(23):235435CrossRefGoogle Scholar
  16. 16.
    Thongrattanasiri S, Silveiro I, García de Abajo FJ (2012) Plasmons in electrostatically doped graphene. Appl Phys Lett 100(20):201105.  https://doi.org/10.1063/1.4714688 CrossRefGoogle Scholar
  17. 17.
    Nikitin AY, Guinea F, Garcia-Vidal FJ, Martin-Moreno L (2012) Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons. Phys Rev B 85(8):081405.  https://doi.org/10.1103/PhysRevB.85.081405 CrossRefGoogle Scholar
  18. 18.
    Wang W, Kinaret JM (2013) Plasmons in graphene nanoribbons: Interband transitions and nonlocal effects. Phys Rev B 87(19):195424.  https://doi.org/10.1103/PhysRevB.87.195424 CrossRefGoogle Scholar
  19. 19.
    Gullans M, Chang DE, Koppens FHL, García de Abajo FJ, Lukin MD (2013) Single-photon nonlinear optics with graphene plasmons. Phys Rev Lett 111(24):247401.  https://doi.org/10.1103/PhysRevLett.111.247401 CrossRefGoogle Scholar
  20. 20.
    Nikitin AY, Low T, Martin-Moreno L (2014) Anomalous reflection phase of graphene plasmons and its influence on resonators. Phys Rev B 90(4):041407.  https://doi.org/10.1103/PhysRevB.90.041407 CrossRefGoogle Scholar
  21. 21.
    Zhan T, Han D, Hu X, Liu X, Chui ST, Zi J (2014) Tunable terahertz radiation from graphene induced by moving electrons. Phys Rev B 89(24):245434.  https://doi.org/10.1103/PhysRevB.89.245434 CrossRefGoogle Scholar
  22. 22.
    Fan HM, Wang TB, Liu NH, Liu JT, Liao QH, Yu TB (2014) Tunable plasmonic band gap and defect mode in one-dimensional photonic crystal covered with graphene. J Opt 16:125005.  https://doi.org/10.1088/2040-8978/16/12/125005 CrossRefGoogle Scholar
  23. 23.
    Wang W, Christensen T, Jauho AP, Thygesen KS, Wubs M, Mortensen NA (2015) Plasmonic eigenmodes in individual and bow-tie graphene nanotriangles. Sci Rep 5:9535.  https://doi.org/10.1038/srep09535 CrossRefGoogle Scholar
  24. 24.
    Gao Y, Ren G, Zhu B, Liu H, Lian Y, Jian S (2014) Analytical model for plasmon modes in graphene-coated nanowire. Opt Express 22(20):24322–24331.  https://doi.org/10.1364/OE.22.024322 CrossRefGoogle Scholar
  25. 25.
    Gao Y, Ren G, Zhu B, Wang J, Jian S (2014) Single-mode graphene-coated nanowire plasmonic waveguide. Opt Lett 39(20):5909–5912.  https://doi.org/10.1364/OL.39.005909 CrossRefGoogle Scholar
  26. 26.
    Lamata IS, Alonso-González P, Hillenbrand R, Nikitin AY (2015) Plasmons in cylindrical 2D materials as a platform for nanophotonic circuits. ACS Photonics 2(2):280–286.  https://doi.org/10.1021/ph500377u CrossRefGoogle Scholar
  27. 27.
    Li RJ, Lin X, Lin SS, Liu X, Chen HS (2015) Tunable deep-subwavelength superscattering using graphene monolayers. Opt Lett 40(8):1651–1654.  https://doi.org/10.1364/OL.40.001651 CrossRefGoogle Scholar
  28. 28.
    Xiao TH, Gan L, Li ZY (2015) Graphene surface plasmon polaritons transport on curved substrates. Photon Res 3(6):300–307.  https://doi.org/10.1364/PRJ.3.000300 CrossRefGoogle Scholar
  29. 29.
    Silveiro I, Manjavacas A, Thongrattanasiri S, García de Abajo FJ (2013) Plasmonic energy transfer in periodically doped graphene. New J Phys 15:033042.  https://doi.org/10.1088/1367-2630/15/3/033042 CrossRefGoogle Scholar
  30. 30.
    Yeung KYM, Chee J, Yoon H, Song Y, Kong J, Ham D (2014) Far-infrared graphene plasmonic crystals for plasmonic band engineering. Nano Lett 14(5):2479–2484.  https://doi.org/10.1021/nl500158y CrossRefGoogle Scholar
  31. 31.
    Shi B, Cai W, Zhang X, Xiang Y, Zhan Y, Geng J, Ren M, Xu J (2016) Tunable band-stop filters for graphene plasmons based on periodically modulated graphene. Sci Rep 6:26796.  https://doi.org/10.1038/srep26796 CrossRefGoogle Scholar
  32. 32.
    Zhou Y, Zhu YY, Zhang K, Wu HW, Peng RW, Fan RH, Wang M (2017) Plasmonic band structures in doped graphene tubes. Opt Express 25(11):12081–12089.  https://doi.org/10.1364/OE.25.012081 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of ScienceHangzhou Dianzi UniversityHangzhouChina

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