, Volume 14, Issue 6, pp 1911–1918 | Cite as

Grating-Assisted Surface Plasmon Resonance for Enhancement of Optical Harmonic Generation in Graphene

  • Yan Zhao
  • Yanyan Huo
  • Baoyuan Man
  • Tingyin NingEmail author


We investigate nonlinear optical second- and third-harmonic generation from graphene covered on dielectric gratings. The nonlinear optical response in graphene is dramatically enhanced when surface plasmon of graphene is excited. Compared with graphene on a flat dielectric, the enhancement factor of second- and third-harmonic generation is up to 106 and 108, respectively. We, in detail, studied the second- and third-harmonic generation intensity influenced by the angle of incidence, the Fermi level, and carrier mobility of graphene.


Graphene Nonlinear effects Surface plasmon 


Funding information

This work was supported by the Natural Science Foundation of China (11404195, 11504209) and China Postdoctoral Science Foundation (2015M582127).


  1. 1.
    Mikhailov SA, Ziegler K (2008) Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects. J Phys Condens Matter 20(38):384204PubMedGoogle Scholar
  2. 2.
    Bao Q, Loh KP (2012) Graphene photonics, plasmonics, and broadband optoelectronic devices. ACS Nano 6(5):3677–3694Google Scholar
  3. 3.
    Bonaccorso F, Sun Z, Hasan T, Ferrari AC (2010) Graphene photonics and optoelectronics. Nat Photonics 4(9):611–622Google Scholar
  4. 4.
    Ooi KJA, Tan DTH (2017) Nonlinear graphene plasmonics. Proc R Soc A 473(2206):20170433PubMedGoogle Scholar
  5. 5.
    Sun Z (2018) Electrically tuned nonlinearity. Nat Photonics 12(7):383–385Google Scholar
  6. 6.
    Martinez A, Sun Z (2013) Nanotube and graphene saturable absorbers for fibre lasers. Nat Photonics 7(11):842–845Google Scholar
  7. 7.
    Bao Q, Zhang H, Wang Y, Ni Z, Yan Y, Shen ZX, Loh KP, Tang DY (2009) Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers. Adv Funct Mater 19(19):3077–3083Google Scholar
  8. 8.
    Song YW, Jang SY, Han WS, Bae MK (2010) Graphene mode-lockers for fiber lasers functioned with evanescent field interaction. Appl Phys Lett 96(5):051122Google Scholar
  9. 9.
    Mikhailov SA (2011) Theory of the giant plasmon-enhanced second-harmonic generation in graphene and semiconductor two-dimensional electron systems. Phys Rev B 84(4):045432Google Scholar
  10. 10.
    Glazov MM, Ganichev SD (2014) High frequency electric field induced nonlinear effects in graphene. Phys Rep 535:101–138Google Scholar
  11. 11.
    Soavi G, Wang G, Rostami H, Purdie DG, De Fazio D, Ma T, Luo B, Wang J, Ott AK, Yoon D, Bourelle S, Muench JE, Goykhman I, Dal Conte S, Celebrano M, Tomadin A, Polini M, Cerullo G, Ferrari AC (2018) Broadband, electrically tunable third-harmonic generation in graphene. Nat Nanotechnol 13:583–588PubMedGoogle Scholar
  12. 12.
    Jiang T, Huang D, Cheng J, Fan X, Zhang Z, Shan Y, Yi Y, Dai Y, Shi L, Liu K, Zeng C, Zi J, Sipe JE, Shen Y, Liu WT, Wu S (2018) Gate tunable third-order nonlinear optical response of massless Dirac fermions in graphene. Nat Photonics 12:430–436Google Scholar
  13. 13.
    Smirnova DA, Shadrivov IV, Smirnov AI, Kivshar YS (2014) Dissipative plasmon-solitons in multilayer graphene. Laser Photonics Rev 8(2):291–296Google Scholar
  14. 14.
    Savin AV, Kivshar YS (2010) Surface solitons at the edges of graphene nanoribbons. Europhys Lett 89(4):46001Google Scholar
  15. 15.
    Horvath C, Bachman D, Indoe R, Van V (2013) Photothermal nonlinearity and optical bistability in a graphene–silicon waveguide resonator. Opt Lett 38(23):5036–5039PubMedGoogle Scholar
  16. 16.
    Dai X, Jiang L, Xiang Y (2015) Low threshold optical bistability at terahertz frequencies with graphene surface plasmons. Sci Rep 5:12271PubMedPubMedCentralGoogle Scholar
  17. 17.
    Chen PY, Argyropoulos C, Alu A (2013) Terahertz antenna phase shifters using integrally-gated graphene transmission-lines. IEEE Trans Antennas Propag 61(4):1528–1237Google Scholar
  18. 18.
    Argyropoulos C (2015) Enhanced transmission modulation based on dielectric metasurfaces loaded with graphene. Opt Express 23(18):23787–23797PubMedGoogle Scholar
  19. 19.
    Gu T, Petrone N, McMillan JF, van der Zande A, Yu M, Lo GQ, Kwong DL, Hone J, Wong CW (2012) Regenerative oscillation and four-wave mixing in graphene optoelectronics. Nat Photonics 6(8):554–559Google Scholar
  20. 20.
    Wu R, Zhang Y, Yan S, Bian F, Wang W, Bai X, Lu X, Zhao J, Wang E (2011) Purely coherent nonlinear optical response in solution dispersions of graphene sheets. Nano Lett 11(12):5159–5164PubMedGoogle Scholar
  21. 21.
    Zhang H, Virally S, Bao Q, Ping LK, Massar S, Godbout N, Kockaert P (2012) Z-scan measurement of the nonlinear refractive index of graphene. Opt Lett 37(11):1856–1858PubMedGoogle Scholar
  22. 22.
    Yang H, Feng X, Wang Q, Huang H, Chen W, Wee AT, Ji W (2011) Giant two-photon absorption in bilayer graphene. Nano Lett 11(7):2622–2627PubMedGoogle Scholar
  23. 23.
    Dremetsika E, Dlubak B, Gorza SP, Ciret C, Martin MB, Hofmann S, Seneor P, Dolfi D, Massa S, Emplit P, Kockaert P (2016) Measuring the nonlinear refractive index of graphene using the optical Kerr effect method. Opt Lett 41(14):3281–3284PubMedGoogle Scholar
  24. 24.
    Vermeulen N, Castelló-Lurbe D, Cheng J, Pasternak I, Krajewska A, Ciuk T, Strupinski W, Thienpont H, Van Erps J (2016) Negative Kerr nonlinearity of graphene as seen via chirped-pulse-pumped self-phase modulation. Phys Rev Appl 6(4):044006Google Scholar
  25. 25.
    Ciesielski R, Comin A, Handloser M, Donkers K, Piredda G, Lombardo A, Ferrari AC, Hartschuh A (2015) Graphene near-degenerate four-wave mixing for phase characterization of broadband pulses in ultrafast microscopy. Nano Lett 15(8):4968–4972PubMedGoogle Scholar
  26. 26.
    Sun D, Divin C, Rioux J, Sipe JE, Berger C, De Heer WA, First PN, Norris TB (2010) Coherent control of ballistic photocurrents in multilayer epitaxial graphene using quantum interference. Nano Lett 10(4):1293–1296PubMedGoogle Scholar
  27. 27.
    Nair RR, Blake P, Grigorenko AN, Novoselov KS, Booth TJ, Stauber T, Peres NMR, Geim AK (2008) Fine structure constant defines visual transparency of graphene. Science 320(5881):1308–1308PubMedGoogle Scholar
  28. 28.
    Mak KF, Sfeir MY, Wu Y, Lui CH, Misewich JA, Heinz TF (2008) Measurement of the optical conductivity of graphene. Phys Rev Lett 101(19):196405PubMedGoogle Scholar
  29. 29.
    Furchi M, Urich A, Pospischil A, Lilley G, Unterrainer K, Detz H, Klang P, Andrews AM, Schrenk W, Strasser G, Thomas Mueller T (2012) Microcavity-integrated graphene photodetector. Nano Lett 12(6):2773–2777PubMedPubMedCentralGoogle Scholar
  30. 30.
    Savostianova NA, Mikhailov SA (2015) Giant enhancement of the third harmonic in graphene integrated in a layered structure. Appl Phys Lett 107(18):181104Google Scholar
  31. 31.
    Liu Y, Cheng R, Liao L, Zhou H, Bai J, Liu G, Liu L, Huang Y, Duan X (2011) Plasmon resonance enhanced multicolour photodetection by graphene. Nat Commun 2:579PubMedPubMedCentralGoogle Scholar
  32. 32.
    Fei Z, Andreev GO, Bao W, Zhang LM, McLeod AS, Chen Wang C, Stewart MK, Zhao Z, Dominguez G, Thiemens M, Fogler MM, Tauber MJ, Castro-Neto AH, Lau CN, Keilmann F, Basov DN (2011) Infrared nanoscopy of Dirac plasmons at the graphene-SiO2 interface. Nano Lett 11(11):4701–4705PubMedGoogle Scholar
  33. 33.
    Wang X, Cheng Z, Xu K, Tsang HK, Xu JB (2013) High-responsivity graphene/silicon-heterostructure waveguide photodetectors. Nat Photonics 7(11):888–891Google Scholar
  34. 34.
    Pospischil A, Humer M, Furchi MM, Bachmann D, Guider R, Fromherz T, Mueller T (2013) CMOS-compatible graphene photodetector covering all optical communication bands. Nat Photonics 7(11):892–896Google Scholar
  35. 35.
    Wang T, Zhang X (2017) Improved third-order nonlinear effect in graphene based on bound states in the continuum. Photon Res 5(6):629–639Google Scholar
  36. 36.
    Nasari H, Abrishamian MS (2016) Nonlinear terahertz frequency conversion via graphene microribbon array. Nanotechnology 27(30):305202PubMedGoogle Scholar
  37. 37.
    Cox JD, Marini A, De Abajo FJG (2017) Plasmon-assisted high-harmonic generation in graphene. Nat Commun 8:14380PubMedPubMedCentralGoogle Scholar
  38. 38.
    Chen PY, Argyropoulos C, Farhat M, Gomez-Diaz JS (2017) Flatland plasmonics and nanophotonics based on graphene and beyond. Nanophotonics 6(6):1239–1262Google Scholar
  39. 39.
    Koppens FHL, Chang DE, de Abajo FJG (2011) Graphene plasmonics: a platform for strong light-matter interactions. Nano Lett 11(8):3370–3377PubMedPubMedCentralGoogle Scholar
  40. 40.
    Kim Y, Kwon MS (2017) Mid-infrared subwavelength modulator based on grating-assisted coupling of a hybrid plasmonic waveguide mode to a graphene plasmon. Nanoscale 9(44):17429–17438PubMedGoogle Scholar
  41. 41.
    Gao W, Shu J, Qiu C, Xu Q (2012) Excitation of plasmonic waves in graphene by guided-mode resonances. ACS Nano 6(9):7806–7813PubMedPubMedCentralGoogle Scholar
  42. 42.
    Gao W, Shi G, Jin Z, Shu J, zhang Q, Vajtai R, Ajayan PM, Kono J, Xu Q (2013) Excitation and active control of propagating surface plasmon polaritons in graphene. Nano Lett 13(8):3698–3702PubMedGoogle Scholar
  43. 43.
    Nasari H, Abrishamian MS (2016) Electrically tunable, plasmon resonance enhanced, terahertz third harmonic generation via graphene. RSC Adv 6(55):50190–50200Google Scholar
  44. 44.
    Li J, Zhang T, Chen L (2018) High-efficiency plasmonic third-harmonic generation with graphene on a silicon diffractive grating in mid-infrared region. Nanoscale Res Lett 13(1):338PubMedPubMedCentralGoogle Scholar
  45. 45.
    Cao J, Kong Y, Gao S (2018) Plasmon resonance enhanced mid-infrared generation by graphene on gold gratings through difference frequency mixing. Opt Commun 406:183–187Google Scholar
  46. 46.
    Guo J, Jiang L, Jia Y, Dai X, Xiang Y, Fan D (2017) Low threshold optical bistability in one-dimensional gratings based on graphene plasmonics. Opt Express 25(6):5972–5981PubMedGoogle Scholar
  47. 47.
    Hanson GW (2008) Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene. J Appl Phys 103(6):064302Google Scholar
  48. 48.
    Smirnova D, Kivshar YS (2014) Second-harmonic generation in subwavelength graphene waveguides. Phys Rev B 90(16):165433Google Scholar
  49. 49.
    Jin B, Guo T, Argyropoulos C (2017) Enhanced third harmonic generation with graphene metasurfaces. J Opt 19(9):094005Google Scholar
  50. 50.
    COMSOL Multiphysics®. Accessed 18 March 2019
  51. 51.
    Lu J, Ding B, Huo Y, Ning T (2018) Geometric effect on second harmonic generation from gold grating. Opt Commun 415:146–150Google Scholar
  52. 52.
    Zhang Y, Killeen T (2016) CO2 lasers-progressing from a varied past to an application-specific future. Laser Focus World 52(11):29–32Google Scholar
  53. 53.
    Hendry E, Hale PJ, Moger J, Savchenko AK, Mikhailov SA (2010) Coherent nonlinear optical response of graphene. Phys Rev Lett 105:097401PubMedGoogle Scholar
  54. 54.
    An YQ, Nelson F, Lee JU, Diebold AC (2013) Enhanced optical second-harmonic generation from the current-biased graphene/SiO2/Si(001) structure. Nano Lett 13(5):2104–2109PubMedGoogle Scholar
  55. 55.
    Klein J, Wierzbowski J, Steinhoff A, Florian M, Roesner M, Heimbach F, Mueller K, Jahnke F, Wehling TO, Finley JJ, Kaniber M (2016) Electric-field switchable second-harmonic generation in bilayer MoS2 by inversion symmetry breaking. Nano Lett 17(1):392–398PubMedGoogle Scholar
  56. 56.
    Lu B, Zhou S, Song Y, Fu S (2019) Enhancement of second harmonic generation in MnF2/graphene sandwich structure. Appl Phys A Mater Sci Process 125(4):254Google Scholar
  57. 57.
    Beckerleg C, Constant TJ, Zeimpekis I, Hornett SM, Craig C, Hewak DW, Hendry E (2018) Cavity enhanced third harmonic generation in graphene. Appl Phys Lett 112(1):011102Google Scholar
  58. 58.
    Zhao Y, Lu J, Huo Y, Man B, Ning T (2019) Enhanced third harmonic generation from graphene embedded in dielectric resonant waveguide gratings. Opt Commun 447:30–35Google Scholar
  59. 59.
    Xiao-Ya Y (2011) Progress in preparation of graphene. J Inorg Mater 26(6):561–570Google Scholar
  60. 60.
    Fan X, Wagner S, Schädlich P, Speck F, Kataria S, Haraldsson T, Seyller T, Lemme MC, Niklaus F (2018) Direct observation of grain boundaries in graphene through vapor hydrofluoric acid (VHF) exposure. Sci Adv 4(5):eaar5170PubMedPubMedCentralGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Yan Zhao
    • 1
  • Yanyan Huo
    • 1
  • Baoyuan Man
    • 1
  • Tingyin Ning
    • 1
    Email author
  1. 1.Shandong Provincial Key Laboratory of Optics and Photonic Devices & Shandong Provincial Engineering and Technical Center of Light Manipulations, School of Physics and ElectronicsShandong Normal UniversityJinanChina

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