Applied Physics B

, 122:242 | Cite as

Simulations of high harmonic generation from plasmonic nanoparticles in the terahertz region

  • Yevgen GrynkoEmail author
  • Thomas Zentgraf
  • Torsten Meier
  • Jens Förstner
Part of the following topical collections:
  1. Ultrafast Nanooptics


Metallic nanostructures are known for enhancing weak nonlinear processes when a resonant and coherent excitation takes place. With proper structural design, an additional boost of particular nonlinear processes is expected to be possible. Here, we present a numerical technique that is capable of simulating high harmonic generation from resonantly excited metallic nanoparticles in the terahertz frequency range. We demonstrate our method by investigating the nonlinear emission of arrays of plasmonic split-ring resonators at the range of ten terahertzs. Our multiscale, non-perturbative, and microscopic approach is based on a self-consistent combination of a hydrodynamic model for the nonlinear electronic material response and the discontinuous Garlerkin time-domain technique for the evaluation of the propagation of the electromagnetic field. It is predicted that the electronic nonlinearities of plasmonic nanoparticles give rise to several harmonics in the light emission when excited by intense terahertz radiation. Furthermore, our analysis predicts a non-perturbative scaling of higher harmonics at high excitation intensities.


Second Harmonic Generation High Harmonic Generation Plasmonic Nanostructures Second Harmonic Generation Signal High Excitation Intensity 
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.



This work was supported by the Deutsche Forschungsgemeinschaft (DFG) through the priority program SPP 1391, the Emmy-Noether program, and the SFB TRR 142. Computing time was granted by the Paderborn Center for Parallel Computing (PC\(^2\)) and Jülich Supercomputing Center.


  1. 1.
    R.A. Shelby, D.R. Smith, S. Schultz, Science 292, 77–79 (2001)ADSCrossRefGoogle Scholar
  2. 2.
    J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D.A. Genov, G. Bartal, X. Zhang, Nature 355, 376–379 (2008)ADSCrossRefGoogle Scholar
  3. 3.
    A.J. Ward, J.B. Pendry, J. Mod. Opt. 43, 773–793 (1996)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    U. Leonhardt, T.G. Philbin, New J. Phys. 8, 247 (2006)ADSCrossRefGoogle Scholar
  5. 5.
    U. Leonhardt, Science 312, 1777–1780 (2006)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    J.B. Pendry, D. Schurig, D.R. Smith, Science 312, 1780–1782 (2006)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    J.B. Pendry, A.J. Holden, D.J. Robbins, W.J. Stewart, IEEE Trans. Microw. Theory Technol. 47, 2075–2084 (1999)ADSCrossRefGoogle Scholar
  8. 8.
    M.W. Klein, C. Enkrich, M. Wegener, J. Förstner, J.V. Moloney, W. Hoyer, T. Stroucken, M. Meier, S.W. Koch, S. Linden: Photonic Metamaterials: From Random to Periodic Technical Digest (Optical Society of America), paper TuC5 (2006)Google Scholar
  9. 9.
    N. Feth, M. König, M. Husnik, K. Stannigel, J. Niegemann, K. Busch, M. Wegener, S. Linden, Opt. Express 18, 6545–6554 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    Y. Zeng, W. Hoyer, J. Liu, S.W. Koch, J.V. Moloney, Phys. Rev. B 79, 235109 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    F.B.P. Niesler, N. Feth, S. Linden, M. Wegener, Opt. Lett. 36, 1533 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    Y. Grynko, T. Meier, S. Linden, F.B.P. Niesler, M. Wegener, J. Förstner, SPIE OPTO, 86230L-86230L-9 (2013)Google Scholar
  13. 13.
    S. Chen, G. Li, F. Zeuner, W.H. Wong, E.Y.B. Pun, T. Zentgraf, K.W. Cheah, S. Zhang, Phys. Rev. Lett. 113, 033901 (2014)ADSCrossRefGoogle Scholar
  14. 14.
    G. Li, S. Chen, N. Pholchai, B. Reineke, P.W.H. Wong, E.Y.B. Pun, K.W. Cheah, T. Zentgraf, S. Zhang, Nat. Mater. 14, 607 (2015)ADSCrossRefGoogle Scholar
  15. 15.
    J.I. Dadap, J. Shan, K.B. Eisenthal, T.F. Heinz, Phys. Rev. Lett. 83, 4045 (1999)ADSCrossRefGoogle Scholar
  16. 16.
    C.I. Valencia, E.R. Mendez, B.S. Mendoza, JOSA B 20, 2150–2161 (2003)ADSCrossRefGoogle Scholar
  17. 17.
    A. Dähn, W. Hübner, K.H. Bennemann, Phys. Rev. Lett. 77, 3929 (1996)ADSCrossRefGoogle Scholar
  18. 18.
    J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, P.F. Brevet, Nano Lett. 10, 1717 (2010)ADSCrossRefGoogle Scholar
  19. 19.
    I. Russier-Antoine, E. Benichou, G. Bachelier, C. Jonin, P.F. Brevet, J. Phys. Chem. C 111(111), 9044 (2007)CrossRefGoogle Scholar
  20. 20.
    S. Kujala, B.K. Canfield, M. Kauranen, Y. Svirko, J. Turunen, Opt. Exp. 16, 17196–17208 (2008)ADSCrossRefGoogle Scholar
  21. 21.
    J. Butet, P.F. Brevet, O.J.F. Martin, ACS Nano 9, 10545–10562 (2015)CrossRefGoogle Scholar
  22. 22.
    M. Gentile, M. Hentschel, R. Taubert, H. Guo, H. Giessen, M. Fiebig, Appl. Phys. B 105, 149–162 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    S. Linden, F.B.P. Niesler, J. Förstner, Y. Grynko, T. Meier, M. Wegener, Phys. Rev. Lett. 109, 015502 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    M. Kauranen, A.V. Zayats, Nat. Photon. 6, 737 (2012)ADSCrossRefGoogle Scholar
  25. 25.
    N. Bloembergen, R.K. Chang, S.S. Jha, C.H. Lee, Phys. Rev. 174, 813–822 (1968)ADSCrossRefGoogle Scholar
  26. 26.
    T. Utikal, T. Zentgraf, T. Paul, K. Rockstuhl, F. Lederer, M. Lippitz, H. Giessen, Phys. Rev. Lett. 106, 133901 (2011)ADSCrossRefGoogle Scholar
  27. 27.
    B.S. Mendoza, W.L. Mochan, Phys. Rev. B 53, 4999 (1995)ADSCrossRefGoogle Scholar
  28. 28.
    J.E. Sipe, V.C.Y. So, M. Fukui, G.I. Stegeman, Phys. Rev. B 21, 4389–4402 (1980)ADSCrossRefGoogle Scholar
  29. 29.
    A. Capretti, C. Forestiere, L. Dal Negro, G. Miano, Plasmonics 9, 151 (2014)CrossRefGoogle Scholar
  30. 30.
    R. Alaee, C. Menzel, A. Banas, K. Banas, S. Xu, H. Chen, H.O. Moser, F. Lederer, C. Rockstuhl, Phys. Rev. B 87, 075110 (2013)ADSCrossRefGoogle Scholar
  31. 31.
    J.S. Hesthaven, T. Warburton, J. Comp. Phys. 181, 186–221 (2002)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    J.S. Hesthaven, T. Warburton, Nodal Discontinuous Galerkin Methods (Springer, New York, 2008)CrossRefzbMATHGoogle Scholar
  33. 33.
    J. Niegemann, M. König, K. Stannigel, K. Busch, Photon. Nanostruct. Fundam. Appl. 7, 2 (2009)ADSCrossRefGoogle Scholar
  34. 34.
    K. Stannigel, M. König, J. Niegemann, K. Busch, Opt. Express 17, 14934–14947 (2009)ADSCrossRefGoogle Scholar
  35. 35.
    J. Niegemann, W. Pernice, K. Busch, J. Opt. A Pure Appl. Opt. 11, 114015 (2009)ADSCrossRefGoogle Scholar
  36. 36.
    A. Hille, R. Kullock, S. Grafstrom, L.M. Eng, J. Comput. Theor. Nanosci. 7, 1581–1586 (2010)CrossRefGoogle Scholar
  37. 37.
    M. König, J. Niegemann, K. Busch, Photon. Nanostruct. Fundam. Appl. 8, 303 (2010)ADSCrossRefGoogle Scholar
  38. 38.
    J. Niegemann, R. Diehl, K. Busch, J. Comp. Phys. 231, 364–372 (2012)ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    K. Busch, M. König, J. Niegemann, Laser Photon. Rev. 5, 773 (2011)CrossRefGoogle Scholar
  40. 40.
    M. H. Carpenter, C. A. Kennedy: Tech. Re NASA-TM-109112, NASA Langley Research Center, VA, USA (1994)Google Scholar
  41. 41.
  42. 42.
    J. Liu, M. Brio, Y. Zeng, A. Zakharian, W. Hoyer, S.W. Koch, J.V. Moloney, J. Comput. Phys. 229, 5921–5932 (2010)ADSCrossRefGoogle Scholar
  43. 43.
    I. Akhiezer, Plasma Electrodynamics, vol. II (Pergamon Press, Oxford, New York, 1975)Google Scholar
  44. 44.
    M.A. Ordal, L.L. Long, R.J. Bell, S.E. Bell, R.R. Bell, R.W. Alexander, C.A. Ward, Appl. Opt. 22, 1099–1119 (1983)ADSCrossRefGoogle Scholar
  45. 45.
    P. Bodenheimer et al., Numerical Methods in Astrophysics: An Introduction (CRC Press, Boca Raton, 2006)Google Scholar
  46. 46.
    P. Guyot-Sionnest, W. Chen, Y.R. Shen, Phys. Rev. B 33, 8254 (1986)ADSCrossRefGoogle Scholar
  47. 47.
    W.J. Padilla, Opt. Express 15, 1639–1646 (2007)ADSMathSciNetCrossRefGoogle Scholar
  48. 48.
    N.A. Papadogiannis, S.D. Moustaizis, Opt. Commun. 137, 174–180 (1997)ADSCrossRefGoogle Scholar
  49. 49.
    N.A. Papadogiannis, P.A. Loukakos, S.D. Moustaizis, Opt. Commun. 166, 133–139 (1999)ADSCrossRefGoogle Scholar
  50. 50.
    A.T. Georges, N.E. Karatzas, Appl. Phys. B 81, 479–485 (2005)ADSCrossRefGoogle Scholar
  51. 51.
    J. Alberti, H. Linnenbank, S. Linden, Y. Grynko, J. Förstner, Appl. Phys. B 122, 45 (2016)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Yevgen Grynko
    • 1
    Email author
  • Thomas Zentgraf
    • 2
  • Torsten Meier
    • 2
  • Jens Förstner
    • 1
  1. 1.Theoretical Electrical Engineering Group and CeOPPUniversity PaderbornPaderbornGermany
  2. 2.Department of Physics and CeOPPUniversity PaderbornPaderbornGermany

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