Optical and Quantum Electronics

, Volume 47, Issue 10, pp 3337–3347 | Cite as

Utilizing the plasmonic resonance to enhance three wave mixing effects in nano-scale cut-wire



In this paper, quantitative study of the enhanced three wave mixing effects from periodic array of nano-scale golden cut-wires embedded in nonlinear dielectric is performed. Geometrical parameters of the considered structure are chosen so that the plasmonic resonance occurs in the wavelength 1.5 μm. Plasmonic resonance of this structure gives rise to the localization factor significantly larger than that of the cut-wire structures with no plasmonic resonance. Considering the surrounding medium of the cut-wire a typical second-order nonlinear optical medium, enhancement of the nonlinearity of this nonlinear medium is illustrated. Since the mentioned structure can be considered a homogeneous nonlinear medium with the effective nonlinear susceptibility, nonlinear retrieval method is used to determine the effective nonlinear susceptibility for all four frequency combinations. Maximum enhancement of the effective susceptibility is obtained for the second harmonic generation of the applied wave with the frequency corresponding to the plasmonic resonance, with the enhancement up to two orders of magnitude. Efficiency of the second harmonic generation in this resonant structure surrounded with nonlinear dielectric is calculated to be 30 times more than that of the nonlinear dielectric with the same dimensions.


Plasmonic resonance Electric field localization Effective susceptibility Enhanced nonlinearity 


  1. Bar-Lev, D., Scheuer, J.: Efficient second harmonic generation using nonlinear substrates patterned by nano-antenna arrays. Opt. Express 21(24), 29165–29178 (2013)CrossRefADSGoogle Scholar
  2. Bouhelier, A., Beversluis, M., Hartschuh, A., Novotny, L.: Near-field second-harmonic generation induced by local field enhancement. Phys. Rev. Lett. 90(1), 013903 (2003)CrossRefADSGoogle Scholar
  3. Boyd, R.W.: Nonlinear Optics. Academic press, New York (2003)Google Scholar
  4. Canfield, B.K., Husu, H., Laukkanen, J., Bai, B., Kuittinen, M., Turunen, J., Kauranen, M.: Local field asymmetry drives second-harmonic generation in noncentrosymmetric nanodimers. Nano Lett. 7(5), 1251–1255 (2007)CrossRefADSGoogle Scholar
  5. Dadap, J., Shan, J., Eisenthal, K., Heinz, T.: Second-harmonic Rayleigh scattering from a sphere of centrosymmetric material. Phys. Rev. Lett. 83(20), 4045–4048 (1999)CrossRefADSGoogle Scholar
  6. Fan, W., Zhang, S., Malloy, K., Brueck, S., Panoiu, N., Osgood, R.: Second harmonic generation from patterned GaAs inside a subwavelength metallic hole array. Opt. Express 14(21), 9570–9575 (2006)CrossRefADSGoogle Scholar
  7. Fietz, C., Soukoulis, C.M.: Finite element simulation of microphotonic lasing system. Opt. Express 20(10), 11548–11560 (2012)CrossRefADSGoogle Scholar
  8. Günter, P.: Nonlinear Optical Effects and Materials. Springer, Berlin (2000)CrossRefGoogle Scholar
  9. Guo, J., Xiang, Y., Dai, X., Wen, S.: Enhanced nonlinearities in double-fishnet negative-index photonic metamaterials. Prog. Electromagn. Res. 136, 269–282 (2013)CrossRefGoogle Scholar
  10. Kauranen, M., Zayats, A.V.: Nonlinear plasmonics. Nat. Photonics 6(11), 737–748 (2012)CrossRefADSGoogle Scholar
  11. Kawata, S.: Plasmonics: future outlook. Jpn. J. Appl. Phys. 52(1R), 010001 (2013)CrossRefADSGoogle Scholar
  12. Krenn, J., Schider, G., Rechberger, W., Lamprecht, B., Leitner, A., Aussenegg, F., Weeber, J.: Design of multipolar plasmon excitations in silver nanoparticles. Appl. Phys. Lett. 77(21), 3379–3381 (2000)CrossRefADSGoogle Scholar
  13. Lapine, M., Shadrivov, I.V., Kivshar, Y.S.: Colloquium: nonlinear metamaterials. Rev. Mod. Phys. 86(3), 1093–1123 (2014)CrossRefADSGoogle Scholar
  14. Larouche, S., Smith, D.R.: A retrieval method for nonlinear metamaterials. Opt. Commun. 283(8), 1621–1627 (2010)CrossRefADSGoogle Scholar
  15. Linden, S., Enkrich, C., Wegener, M., Zhou, J., Koschny, T., Soukoulis, C.M.: Magnetic response of metamaterials at 100 terahertz. Science 306, 1351–1353 (2004)CrossRefADSGoogle Scholar
  16. Linden, S., Niesler, F., Förstner, J., Grynko, Y., Meier, T., Wegener, M.: Collective effects in second-harmonic generation from split-ring-resonator arrays. Phys. Rev. Lett. 109(1), 015502 (2012)CrossRefADSGoogle Scholar
  17. McPhedran, R.C., Shadrivov, I.V., Kuhlmey, B.T., Kivshar, Y.S.: Metamaterials and metaoptics. NPG Asia Mater. 3(11), 100–108 (2011)CrossRefGoogle Scholar
  18. Niesler, F., Feth, N., Linden, S., Niegemann, J., Gieseler, J., Busch, K., Wegener, M.: Second-harmonic generation from split-ring resonators on a GaAs substrate. Opt. Lett. 34(13), 1997–1999 (2009)CrossRefADSGoogle Scholar
  19. Pendry, J.B., Holden, A.J., Robbins, D.J., Stewart, W.J.: Magnetism from conductors, and enhanced non-linear phenomena. IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999)Google Scholar
  20. Puscasu, I., Schaich, W., Boreman, G.D.: Modeling parameters for the spectral behavior of infrared frequency-selective surfaces. Appl. Opt. 40(1), 118–124 (2001)CrossRefADSGoogle Scholar
  21. Rose, A., Larouche, S., Huang, D., Poutrina, E., Smith, D.R.: Nonlinear parameter retrieval from three-and four-wave mixing in metamaterials. Phys. Rev. E 82(3), 036608 (2010)CrossRefADSGoogle Scholar
  22. Rose, A., Larouche, S., Smith, D.R.: Quantitative study of the enhancement of bulk nonlinearities in metamaterials. Phys. Rev. A 84(5), 053805 (2011) CrossRefADSGoogle Scholar
  23. Sabet, R.A., Khoshsima, H., Namdar, A., Ahmadi, V.: Enhanced second order nonlinearity using plasmonic resonance of nano-scale metallic cut-wires. Eur. Phys. J. Appl. Phys. 69(2), 20503 (2015)CrossRefGoogle Scholar
  24. Schaich, W., Schider, G., Krenn, J., Leitner, A., Aussenegg, F., Puscasu, I., Monacelli, B., Boreman, G.: Optical resonances in periodic surface arrays of metallic patches. Appl. Opt. 42(28), 5714–5721 (2003)CrossRefADSGoogle Scholar
  25. Schider, G., Krenn, J., Hohenau, A., Ditlbacher, H., Leitner, A., Aussenegg, F., Schaich, W.L., Puscasu, I., Monacelli, B., Boreman, G.: Plasmon dispersion relation of Au and Ag nanowires. Phys. Rev. B 68(15), 155427 (2003)CrossRefADSGoogle Scholar
  26. Shalaev, V.M.: Optical negative-index metamaterials. Nat. Photonics 1(1), 41–48 (2007)MathSciNetCrossRefADSGoogle Scholar
  27. Smith, D., Schultz, S., Markoš, P., Soukoulis, C.: Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients. Phys. Rev. B 65(19), 195104 (2002)CrossRefADSGoogle Scholar
  28. Smith, D., Vier, D., Koschny, T., Soukoulis, C.: Electromagnetic parameter retrieval from inhomogeneous metamaterials. Phys. Rev. E 71(3), 036617 (2005)CrossRefADSGoogle Scholar
  29. Stockman, M.I.: Nanoplasmonics: past, present, and glimpse into future. Opt. Express 19(22), 22029–22106 (2011)CrossRefADSGoogle Scholar
  30. Tuovinen, H., Kauranen, M., Jefimovs, K., Vahimaa, P., Vallius, T., Turunen, J., Tkachenko, N.V., Lemmetyinen, H.: Linear and second-order nonlinear optical properties of arrays of noncentrosymmetric gold nanoparticles. J. Nonlinear Opt. Phys. Mater. 11(04), 421–432 (2002)CrossRefADSGoogle Scholar
  31. Veselago, V., Braginsky, L., Shklover, V., Hafner, C.: Negative refractive index materials. J. Comput. Theor. Nanosci. 3(2), 189–218 (2006)Google Scholar
  32. Zheludev, N.I.: The road ahead for metamaterials. Science 328(5978), 582–583 (2010)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Research Institute for Applied Physics and AstronomyUniversity of TabrizTabrizIran

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