Applied Physics B

, 122:94 | Cite as

Investigation of the nonlinear refractive index of single-crystalline thin gold films and plasmonic nanostructures

  • Sebastian Goetz
  • Gary Razinskas
  • Enno Krauss
  • Christian Dreher
  • Matthias Wurdack
  • Peter Geisler
  • Monika Pawłowska
  • Bert Hecht
  • Tobias Brixner
Part of the following topical collections:
  1. Ultrafast Nanooptics


The nonlinear refractive index of plasmonic materials may be used to obtain nonlinear functionality, e.g., power-dependent switching. Here, we investigate the nonlinear refractive index of single-crystalline gold in thin layers and nanostructures on dielectric substrates. In a first step, we implement a z-scan setup to investigate ~100-µm-sized thin-film samples. We determine the nonlinear refractive index of fused silica, n 2(SiO2) = 2.9 × 10−20 m2/W, in agreement with literature values. Subsequent z-scan measurements of single-crystalline gold films reveal a damage threshold of 0.22 TW/cm2 and approximate upper limits of the real and imaginary parts of the nonlinear refractive index, |n 2′(Au)| < 1.2 × 10−16 m2/W and |n 2″(Au)| < 0.6 × 10−16 m2/W, respectively. To further determine possible effects of a nonlinear refractive index in plasmonic circuitry, interferometry is proposed as a phase-sensitive probe. In corresponding nanostructures, relative phase changes between two propagating near-field modes are converted to amplitude changes by mode interference. Power-dependent experiments using sub-10-fs near-infrared pulses and diffraction-limited resolution (NA = 1.4) reveal linear behavior up to the damage threshold (0.23 times relative to that of a solid single-crystalline gold film). An upper limit for the nonlinear power-dependent phase change between two propagating near-field modes is determined to Δφ < 0.07 rad.


Output Port Damage Threshold Nonlinear Refractive Index Antenna Length Spatial Contrast 
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 German Science Foundation (DFG) within the Priority Program “Ultrafast Nanooptics” (SPP 1391).


  1. 1.
    S.A. Maier, Plasmonics: Fundamentals and Applications (Springer, Berlin, 2007)Google Scholar
  2. 2.
    W.L. Barnes, A. Dereux, T.W. Ebbesen, Nature 424, 824 (2003)ADSCrossRefGoogle Scholar
  3. 3.
    M. Stockman, Opt. Express 19, 22029 (2011)ADSCrossRefGoogle Scholar
  4. 4.
    L. Novotny, N. van Hulst, Nat. Photonics 5, 83 (2011)ADSCrossRefGoogle Scholar
  5. 5.
    P. Biagioni, J.-S. Huang, B. Hecht, Rep. Prog. Phys. 75, 024402 (2012)ADSCrossRefGoogle Scholar
  6. 6.
    Y. Fang, Z. Li, Y. Huang, S. Zhang, P. Nordlander, N.J. Halas, H. Xu, Nano Lett. 10, 1950 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    H. Wei, Z. Wang, X. Tian, M. Käll, H. Xu, Nat. Commun. 2, 387 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    C. Rewitz, G. Razinskas, P. Geisler, E. Krauss, S. Goetz, M. Pawłowska, B. Hecht, T. Brixner, Phys. Rev. Appl. 1, 014007 (2014)ADSCrossRefGoogle Scholar
  9. 9.
    G. Lenz, J. Zimmermann, T. Katsufuji, M.E. Lines, H.Y. Hwang, S. Spälter, R.E. Slusher, S.-W. Cheong, J.S. Sanghera, I.D. Aggarwal, Opt. Lett. 25, 254 (2000)ADSCrossRefGoogle Scholar
  10. 10.
    A. Reiserer, J.-S. Huang, B. Hecht, T. Brixner, Opt. Express 18, 11810 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    P. Ginzburg, A. Hayat, N. Berkovitch, M. Orenstein, Opt. Lett. 35, 1551 (2010)ADSCrossRefGoogle Scholar
  12. 12.
    S. Palomba, L. Novotny, Phys. Rev. Lett. 101, 056802 (2008)ADSCrossRefGoogle Scholar
  13. 13.
    J. Renger, R. Quidant, N. van Hulst, L. Novotny, Phys. Rev. Lett. 104, 046803 (2010)ADSCrossRefGoogle Scholar
  14. 14.
    M. Lippitz, M.A. van Dijk, M. Orrit, Nano Lett. 5, 799 (2005)ADSCrossRefGoogle Scholar
  15. 15.
    T. Hanke, G. Krauss, D. Träutlein, B. Wild, R. Bratschitsch, A. Leitenstorfer, Phys. Rev. Lett. 103, 257404 (2009)ADSCrossRefGoogle Scholar
  16. 16.
    M. Hentschel, T. Utikal, H. Giessen, M. Lippitz, Nano Lett. 12, 3778 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    R.W. Boyd, Z. Shi, I. De Leon, Opt. Commun. 326, 74 (2014)ADSCrossRefGoogle Scholar
  18. 18.
    D.D. Smith, Y. Yoon, R.W. Boyd, J.K. Campbell, L.A. Baker, R.M. Crooks, M. George, J. Appl. Phys. 86, 6200 (1999)ADSCrossRefGoogle Scholar
  19. 19.
    P. Wang, Y. Lu, L. Tang, J. Zhang, H. Ming, J. Xie, F.-H. Ho, H.-H. Chang, H.-Y. Lin, D.-P. Tsai, Opt. Commun. 229, 425 (2004)ADSCrossRefGoogle Scholar
  20. 20.
    N. Rotenberg, A.D. Bristow, M. Pfeiffer, M. Betz, H.M. van Driel, Phys. Rev. B 75, 155426 (2007)ADSCrossRefGoogle Scholar
  21. 21.
    E. Xenogiannopoulou, P. Aloukos, S. Couris, E. Kaminska, A. Piotrowska, E. Dynowska, Opt. Commun. 275, 217 (2007)ADSCrossRefGoogle Scholar
  22. 22.
    M. Sheik-Bahae, A.A. Said, E.W. Van Stryland, Opt. Lett. 14, 955 (1989)ADSCrossRefGoogle Scholar
  23. 23.
    M. Sheik-Bahae, A. Said, T.-H. Wei, D.J. Hagan, E.W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990)ADSCrossRefGoogle Scholar
  24. 24.
    R. Sutherland, Handbook of Nonlinear Optics, 2nd edn. (CRC Press, London, 2003)CrossRefGoogle Scholar
  25. 25.
    P.B. Chapple, J. Staromlynska, R.G. McDuff, JOSA B 11, 975 (1994)ADSCrossRefGoogle Scholar
  26. 26.
    R. Trebino, K.W. DeLong, D.N. Fittinghoff, J.N. Sweetser, M.A. Krumbügel, B.A. Richman, D.J. Kane, Rev. Sci. Instrum. 68, 3277 (1997)ADSCrossRefGoogle Scholar
  27. 27.
    D. Milam, Appl. Opt. 37, 546 (1998)ADSCrossRefGoogle Scholar
  28. 28.
    H.I. Elim, W. Ji, F. Zhu, Appl. Phys. B 82, 439 (2006)ADSCrossRefGoogle Scholar
  29. 29.
    R. DeSalvo, A.A. Said, D.J. Hagan, E.W. van Stryland, M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996)ADSCrossRefGoogle Scholar
  30. 30.
    T. Olivier, F. Billard, H. Akhouayri, Opt. Express 12, 1377 (2004)ADSCrossRefGoogle Scholar
  31. 31.
    J.-S. Huang, V. Callegari, P. Geisler, C. Brüning, J. Kern, J.C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, U. Sennhauser, B. Hecht, Nat. Commun. 1, 150 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    X. Wu, R. Kullock, E. Krauss, B. Hecht, Cryst. Res. Technol. 50, 595 (2015)CrossRefGoogle Scholar
  33. 33.
    C. Kern, M. Zürch, J. Petschulat, T. Pertsch, B. Kley, T. Käsebier, U. Hübner, C. Spielmann, Appl. Phys. A 104, 15 (2011)ADSCrossRefGoogle Scholar
  34. 34.
    P.B. Johnson, R.W. Christy, Phys. Rev. B 6, 4370 (1972)ADSCrossRefGoogle Scholar
  35. 35.
    R. de Nalda, R. del Coso, J. Requejo-Isidro, J. Olivares, A. Suarez-Garcia, J. Solis, C.N. Afonso, JOSA B 19, 289 (2002)ADSCrossRefGoogle Scholar
  36. 36.
    P. Geisler, G. Razinskas, E. Krauss, X.-F. Wu, C. Rewitz, P. Tuchscherer, S. Goetz, C.-B. Huang, T. Brixner, B. Hecht, Phys. Rev. Lett. 111, 183901 (2013)ADSCrossRefGoogle Scholar
  37. 37.
    P. Mühlschlegel, H.-J. Eisler, O.J.F. Martin, B. Hecht, D.W. Pohl, Science 308, 1607 (2005)ADSCrossRefGoogle Scholar
  38. 38.
    J.-S. Huang, T. Feichtner, P. Biagioni, B. Hecht, Nano Lett. 9, 1897 (2009)ADSCrossRefGoogle Scholar
  39. 39.
    M. Schnell, P. Alonso-González, L. Arzubiaga, F. Casanova, L.E. Hueso, A. Chuvilin, R. Hillenbrand, Nat. Photonics 5, 283 (2011)ADSCrossRefGoogle Scholar
  40. 40.
    P.M. Krenz, R.L. Olmon, B.A. Lail, M.B. Raschke, G.D. Boreman, Opt. Express 18, 21678 (2010)ADSCrossRefGoogle Scholar
  41. 41.
    E. Verhagen, M. Spasenović, A. Polman, L. (Kobus) Kuipers, Phys. Rev. Lett. 102, 203904 (2009)ADSCrossRefGoogle Scholar
  42. 42.
    M. Cinchetti, A. Gloskovskii, S.A. Nepjiko, G. Schönhense, H. Rochholz, M. Kreiter, Phys. Rev. Lett. 95, 047601 (2005)ADSCrossRefGoogle Scholar
  43. 43.
    L. Lepetit, G. Cheriaux, M. Joffre, JOSA B 12, 2467 (1995)ADSCrossRefGoogle Scholar
  44. 44.
    C. Rewitz, T. Keitzl, P. Tuchscherer, J.-S. Huang, P. Geisler, G. Razinskas, B. Hecht, T. Brixner, Nano Lett. 12, 45 (2012)ADSCrossRefGoogle Scholar
  45. 45.
    C. Rewitz, T. Keitzl, P. Tuchscherer, S. Goetz, P. Geisler, G. Razinskas, B. Hecht, T. Brixner, Opt. Express 20, 14632 (2012)ADSCrossRefGoogle Scholar
  46. 46.
    M. Pawłowska, S. Goetz, C. Dreher, M. Wurdack, E. Krauss, G. Razinskas, P. Geisler, B. Hecht, T. Brixner, Opt. Express 22, 31496 (2014)ADSCrossRefGoogle Scholar
  47. 47.
    T. Wu, J. Tang, B. Hajj, M. Cui, Opt. Express 19, 12961 (2011)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Sebastian Goetz
    • 1
  • Gary Razinskas
    • 2
  • Enno Krauss
    • 2
  • Christian Dreher
    • 1
  • Matthias Wurdack
    • 1
  • Peter Geisler
    • 2
  • Monika Pawłowska
    • 1
    • 3
  • Bert Hecht
    • 2
    • 4
  • Tobias Brixner
    • 1
    • 4
  1. 1.Institut für Physikalische und Theoretische ChemieUniversität WürzburgWürzburgGermany
  2. 2.Nano-Optics and Biophotonics Group, Experimentelle Physik 5Universität WürzburgWürzburgGermany
  3. 3.Nencki Institute for Experimental BiologyPolish Academy of SciencesWarsawPoland
  4. 4.Röntgen Research Center for Complex Material Systems (RCCM)Universität WürzburgWürzburgGermany

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