Nonlocal Response in Plasmonic Nanostructures

  • Martijn Wubs
  • N. Asger Mortensen
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 185)


After a brief overview of nanoplasmonics experiments that defy explanation with classical electrodynamics, we introduce nonlocal response as a main reason for non-classical effects. This concept is first introduced phenomenologically, and afterwards based on the semi-classical hydrodynamic Drude model (HDM) that indeed exhibits nonlocal response. In particular, we discuss recent generalizations and extensions of the HDM, to include both convection and diffusion dynamics of the induced charges. This generalized nonlocal optical response (GNOR) model allows for the first time unified semi-classical explanations of known experimental phenomena for both monomers and dimers that previously seemed to require microscopic theory. Finally, we turn to Landau damping and discuss the microscopic origin of the size-dependent damping captured by the classical diffusion mechanism in the GNOR model.


Plasmonics Nonlocal response Spatial dispersion Linear-response theory Hydrodynamic Drude model Additional boundary conditions Semi-classical electrodynamics Quantum plasmonics Computational plasmonics Landau damping 



We acknowledge funding from the Danish National Research Foundation (CoE Project DNRF103) and the Danish Council for Independent Research–Natural Sciences (Project 1323-00087). Over the course of years we have benefited tremendously from numerous interactions with now former PhD students and postdocs as well as with our peers in the plasmonic community. In particular, many of the figures are by courtesy of PhD theses by Giuseppe Toscano [58], Søren Raza [75], and Thomas Christensen [73]. We also thank Wei Yan, Christin David, Nicolas Stenger, Sanshui Xiao, Yu Luo, Alexander Uskov, Uriel Levy, Javier García de Abajo, Antti-Pekka Jauho, Jacob Khurgin and Sergey Bozhevolnyi for long-term interactions.


  1. 1.
    T. Gruner, D.-G. Welsch, Phys. Rev. A 53, 1818 (1996)Google Scholar
  2. 2.
    L.G. Suttorp, M. Wubs, Phys. Rev. A 70, 013816 (2004)ADSCrossRefGoogle Scholar
  3. 3.
    D.E. Chang, A.S. Sørensen, P.R. Hemmer, M.D. Lukin, Phys. Rev. Lett. 97, 053002 (2006)ADSCrossRefGoogle Scholar
  4. 4.
    D.E. Chang, A.S. Sørensen, E.A. Demler, M.D. Lukin, Nat. Phys. 3(11), 807 (2007)CrossRefGoogle Scholar
  5. 5.
    M.S. Tame, K.R. McEnery, S.K. Özdemir, J. Lee, S.A. Maier, M.S. Kim, Nat. Phys. 9(6), 329 (2013)CrossRefGoogle Scholar
  6. 6.
    A. Delga, J. Feist, J. Bravo-Abad, F.J. García-Vidal, Phys. Rev. Lett. 112, 253601 (2014)ADSCrossRefGoogle Scholar
  7. 7.
    P.T. Kristensen, S. Hughes, ACS Photonics 1(1), 2 (2014)CrossRefGoogle Scholar
  8. 8.
    S.A. Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007)Google Scholar
  9. 9.
    M.L. Brongersma, Faraday Discuss. 178, 9 (2015)CrossRefGoogle Scholar
  10. 10.
    A. Baev, P.N. Prasad, H. Ågren, M. Samoć, M. Wegener, Phys. Rep. 594, 1 (2015)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    D.K. Gramotnev, S.I. Bozhevolnyi, Nat. Photonics 4(2), 83 (2010)ADSCrossRefGoogle Scholar
  12. 12.
    D.K. Gramotnev, S.I. Bozhevolnyi, Nat. Photonics 8(1), 14 (2014)ADSGoogle Scholar
  13. 13.
    L.M. Liz-Marzán, Langmuir 22(1), 32 (2006)CrossRefGoogle Scholar
  14. 14.
    E. Hao, G.C. Schatz, J. Chem. Phys. 120(1), 357 (2004)ADSCrossRefGoogle Scholar
  15. 15.
    M.I. Stockman, Phys. Rev. Lett. 93(13), 137404 (2004)ADSCrossRefGoogle Scholar
  16. 16.
    H. Duan, A.I. Fernández-Domínguez, M. Bosman, S.A. Maier, J.K.W. Yang, Nano Lett. 12(3), 1683 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    L.D. Landau, E.M. Lifshitz, L.P. Pitaevskii, in Electrodynamics of Continuous Media, Landau and Lifshitz Course on Theoretical Physics, vol. 8, 2nd edn. (Butterworth Heinemann, Oxford, 1984)Google Scholar
  18. 18.
    S. Raza, S.I. Bozhevolnyi, M. Wubs, N.A. Mortensen, J. Phys. Condens. Matter 27, 183204 (2015)ADSCrossRefGoogle Scholar
  19. 19.
    N.W. Ashcroft, N.D. Mermin, Solid State Physics (Saunders College Publishing, Fort Worth, 1976)zbMATHGoogle Scholar
  20. 20.
    I. Romero, J. Aizpurua, G.W. Bryant, F.J. García de Abajo, Opt. Express 14(21), 9988 (2006)ADSCrossRefGoogle Scholar
  21. 21.
    F.J. García de Abajo, J. Phys. Chem. C 112(46), 17983 (2008)CrossRefGoogle Scholar
  22. 22.
    J.M. McMahon, S.K. Gray, G.C. Schatz, Phys. Rev. Lett. 103, 097403 (2009)ADSCrossRefGoogle Scholar
  23. 23.
    C. David, F.J. García de Abajo, J. Phys. Chem. C 115(40), 19470 (2011)CrossRefGoogle Scholar
  24. 24.
    S. Raza, G. Toscano, A.P. Jauho, M. Wubs, N.A. Mortensen, Phys. Rev. B 84, 121412(R) (2011)ADSCrossRefGoogle Scholar
  25. 25.
    J. Kern, S. Grossmann, N.V. Tarakina, T. Häckel, M. Emmerling, M. Kamp, J.S. Huang, P. Biagioni, J. Prangsma, B. Hecht, Nano Lett. 12(11), 5504 (2012)ADSCrossRefGoogle Scholar
  26. 26.
    C. Ciracì, R.T. Hill, J.J. Mock, Y. Urzhumov, A.I. Fernández-Domínguez, S.A. Maier, J.B. Pendry, A. Chilkoti, D.R. Smith, Science 337(6098), 1072 (2012)ADSCrossRefGoogle Scholar
  27. 27.
    K.J. Savage, M.M. Hawkeye, R. Esteban, A.G. Borisov, J. Aizpurua, J.J. Baumberg, Nature 491(7425), 574 (2012)ADSCrossRefGoogle Scholar
  28. 28.
    J.A. Scholl, A.L. Koh, J.A. Dionne, Nature 483(7390), 421 (2012)ADSCrossRefGoogle Scholar
  29. 29.
    S. Raza, N. Stenger, S. Kadkhodazadeh, S.V. Fischer, N. Kostesha, A.P. Jauho, A. Burrows, M. Wubs, N.A. Mortensen, Nanophotonics 2(2), 131 (2013)ADSCrossRefGoogle Scholar
  30. 30.
    S. Raza, N. Stenger, A. Pors, T. Holmgaard, S. Kadkhodazadeh, J.B. Wagner, K. Pedersen, M. Wubs, S.I. Bozhevolnyi, N.A. Mortensen, Nat. Commun. 5, 4125 (2014)ADSCrossRefGoogle Scholar
  31. 31.
    S.F. Tan, L. Wu, J.K. Yang, P. Bai, M. Bosman, C.A. Nijhuis, Science 343(6178), 1496 (2014)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    D. Paria, K. Roy, H.J. Singh, S. Kumar, S. Raghavan, A. Ghosh, A. Ghosh, Adv. Mater. 27(10), 1751 (2015)Google Scholar
  33. 33.
    S. Raza, S. Kadkhodazadeh, T. Christensen, M. Di Vece, M. Wubs, N.A. Mortensen, N. Stenger, Nat. Commun. 6, 8788 (2015)ADSCrossRefGoogle Scholar
  34. 34.
    G. Toscano, S. Raza, A.P. Jauho, N.A. Mortensen, M. Wubs, Opt. Express 20(4), 4176 (2012)ADSCrossRefGoogle Scholar
  35. 35.
    F. Bloch, Z. Phys, A 81(5–6), 363 (1933)Google Scholar
  36. 36.
    A. Boardman, Electromagnetic surface modes. Hydrodynamic theory of plasmon-polaritons on plane surfaces. (John Wiley and Sons, Chichester, 1982)Google Scholar
  37. 37.
    J.M. Pitarke, V.M. Silkin, E.V. Chulkov, P.M. Echenique, Rep. Prog. Phys. 70, 1 (2007)ADSCrossRefGoogle Scholar
  38. 38.
    N.A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, S.I. Bozhevolnyi, Nat. Commun. 5, 3809 (2014)ADSGoogle Scholar
  39. 39.
    A.V. Uskov, I.E. Protsenko, N.A. Mortensen, E.P. O’Reilly, Plasmonics 9, 185 (2014)CrossRefGoogle Scholar
  40. 40.
    J.B. Khurgin, Faraday Discuss. 178, 109 (2015)CrossRefGoogle Scholar
  41. 41.
    W. Yan, M. Wubs, N.A. Mortensen, Phys. Rev. Lett. 115, 137403 (2015)ADSCrossRefGoogle Scholar
  42. 42.
    N.A. Mortensen, Phot. Nanostr. 11(4), 303 (2013)CrossRefGoogle Scholar
  43. 43.
    J. Monaghan, Rep. Prog. Phys. 68(8), 1703 (2005)ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    P. Ginzburg, A. Zayats, ACS Nano 7(5), 4334 (2013)CrossRefGoogle Scholar
  45. 45.
    G. Toscano, S. Raza, W. Yan, C. Jeppesen, S. Xiao, M. Wubs, A.P. Jauho, S.I. Bozhevolnyi, N.A. Mortensen, Nanophotonics 2(3), 161 (2013)ADSCrossRefGoogle Scholar
  46. 46.
    M. Wubs, Opt. Express 23(24), 31296 (2015)ADSCrossRefGoogle Scholar
  47. 47.
    W. Yan, M. Wubs, N.A. Mortensen, Phys. Rev. B 86(20), 205429 (2012)ADSCrossRefGoogle Scholar
  48. 48.
    P. Jewsbury, J. Phys. F: Met. Phys. 11, 195 (1981)ADSCrossRefGoogle Scholar
  49. 49.
    A. Liebsch, Phys. Rev. B 48(15), 11317 (1993)ADSCrossRefGoogle Scholar
  50. 50.
    R.C. Monreal, T.J. Antosiewicz, S.P. Apell, New J. Phys. 15(8), 083044 (2013)CrossRefGoogle Scholar
  51. 51.
    T.V. Teperik, P. Nordlander, J. Aizpurua, A.G. Borisov, Phys. Rev. Lett. 110, 263901 (2013)ADSCrossRefGoogle Scholar
  52. 52.
    M. Ichikawa, J. Phys. Soc. Jpn. 80(4), 044606 (2011)ADSCrossRefGoogle Scholar
  53. 53.
    Z.F. Öztürk, S. Xiao, M. Yan, M. Wubs, A.P. Jauho, N.A. Mortensen, J. Nanophot. 5, 051602 (2011)CrossRefGoogle Scholar
  54. 54.
    C. David, F.J. García de Abajo, ACS Nano 8(9), 9558 (2014)CrossRefGoogle Scholar
  55. 55.
    G. Toscano, J. Straubel, A. Kwiatkowski, C. Rockstuhl, F. Evers, H. Xu, N.A. Mortensen, M. Wubs, Nat. Commun. 6, 7132 (2015)ADSCrossRefGoogle Scholar
  56. 56.
    W. Yan, Phys. Rev. B 91, 115416 (2015)ADSCrossRefGoogle Scholar
  57. 57.
    X. Li, H. Fang, X. Weng, L. Zhang, X. Dou, A. Yang, X. Yuan, Opt. Express 23(23), 29738 (2015)ADSCrossRefGoogle Scholar
  58. 58.
    G. Toscano, Semiclassical theory of nonlocal plasmonic excitation in metallic nanostructures. Ph.D. thesis, Technical University of Denmark (2013)Google Scholar
  59. 59.
    B. Gallinet, J. Butet, O.J.F. Martin, Laser Phot. Rev. 9(6), 577 (2015)CrossRefGoogle Scholar
  60. 60.
    S. Raza, G. Toscano, A.P. Jauho, N.A. Mortensen, M. Wubs, Plasmonics 8(2), 193 (2013)CrossRefGoogle Scholar
  61. 61.
    T. Christensen, W. Yan, S. Raza, A.P. Jauho, N.A. Mortensen, M. Wubs, ACS Nano 8(2), 1745 (2014)CrossRefGoogle Scholar
  62. 62.
    D. Chulhai, L. Jensen, Generalized nonlocal optical response (2016). doi: 10.4231/D3V97ZS7X
  63. 63.
    A. Yanai, N.A. Mortensen, U. Levy, Phys. Rev. B 88, 205120 (2013)ADSCrossRefGoogle Scholar
  64. 64.
    K.R. Hiremath, L. Zschiedrich, F. Schmidt, J. Comp. Phys. 231(17), 5890 (2012)ADSCrossRefGoogle Scholar
  65. 65.
    W. Yan, N.A. Mortensen, M. Wubs, Phys. Rev. B 88, 155414 (2013)ADSCrossRefGoogle Scholar
  66. 66.
    T.J.R. Hughes, The Finite Element Method—Linear Static and Dynamic Finite Element Analysis (Dower Publications Inc, Mineola, New York, 1987)zbMATHGoogle Scholar
  67. 67.
    NanoPlasmonics Lab (2012),
  68. 68.
    L. Stella, P. Zhang, F.J. García-Vidal, A. Rubio, P. García-González, J. Phys. Chem. C 117(17), 8941 (2013)CrossRefGoogle Scholar
  69. 69.
    K. Andersen, K.L. Jensen, N.A. Mortensen, K.S. Thygesen, Phys. Rev. B 87, 235433 (2013)ADSCrossRefGoogle Scholar
  70. 70.
    U. Kreibig, M. Vollmer, Optical Properties of Metal Clusters (Springer-Verlag, Berlin, 1995)CrossRefGoogle Scholar
  71. 71.
    R. Esteban, A.G. Borisov, P. Nordlander, J. Aizpurua, Nat. Commun. 3, 825 (2012)ADSCrossRefGoogle Scholar
  72. 72.
    J.B. Khurgin, G. Sun, Opt. Express 23(24), 30739 (2015)ADSCrossRefGoogle Scholar
  73. 73.
    T. Christensen, From classical to quantum plasmonics in three and two dimensions. Ph.D. thesis, Technical University of Denmark (2015)Google Scholar
  74. 74.
    J.A. Scholl, A. Garcia-Etxarri, A.L. Koh, J.A. Dionne, Nano Lett. 13(2), 564 (2013)ADSCrossRefGoogle Scholar
  75. 75.
    S. Raza, Probing plasmonic nanostructures with electron energy-loss spectroscopy. Ph.D. thesis, Technical University of Denmark (2014)Google Scholar
  76. 76.
    R. Esteban, A. Zugarramurdi, P. Zhang, P. Nordlander, F.J. García-Vidal, A.G. Borisov, J. Aizpurua, Faraday Discuss. 178, 151 (2015)CrossRefGoogle Scholar
  77. 77.
    U. Hohenester, Phys. Rev. B 91(20), 205436 (2015)ADSCrossRefGoogle Scholar
  78. 78.
    S. Weiss, D. Botkin, D.F. Ogletree, M. Salmeron, D.S. Chemla, Phys. Stat. Sol. (b) 188(1), 343 (1995)ADSCrossRefGoogle Scholar
  79. 79.
    M. Grifoni, P. Hänggi, Phys. Rep. 304(5–6), 229 (1998)ADSMathSciNetCrossRefGoogle Scholar
  80. 80.
    M. Büttiker, H. Thomas, A. Prêtre, Phys. Lett. A 180(4–5), 364 (1993)ADSCrossRefGoogle Scholar
  81. 81.
    U.D. Keil, T. Ha, J.R. Jensen, J.M. Hvam, Appl. Phys. Lett. 72(23), 3074 (1998)ADSCrossRefGoogle Scholar
  82. 82.
    D. Jin, Q. Hu, D. Neuhauser, F. von Cube, Y. Yang, R. Sachan, T.S. Luk, D.C. Bell, N.X. Fang, Phys. Rev. Lett. 115, 193901 (2015)ADSCrossRefGoogle Scholar
  83. 83.
    T.V. Teperik, P. Nordlander, J. Aizpurua, A.G. Borisov, Opt. Express 21(22), 27306 (2013)ADSCrossRefGoogle Scholar
  84. 84.
    G. Toscano, S. Raza, S. Xiao, M. Wubs, A.P. Jauho, S.I. Bozhevolnyi, N.A. Mortensen, Opt. Lett. 37(13), 2538 (2012)ADSCrossRefGoogle Scholar
  85. 85.
    R. Filter, C. Bösel, G. Toscano, F. Lederer, C. Rockstuhl, Opt. Lett. 39(21), 6118 (2014)ADSCrossRefGoogle Scholar
  86. 86.
    C.L.C. Smith, N. Stenger, A. Kristensen, N.A. Mortensen, S.I. Bozhevolnyi, Nanoscale 7(21), 9355 (2015)ADSCrossRefGoogle Scholar
  87. 87.
    E. Bermudez-Urena, C. Gonzalez-Ballestero, M. Geiselmann, R. Marty, I.P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F.J. García-Vidal, S.I. Bozhevolnyi, R. Quidant, Nature Commun. 6, 7883 (2015)ADSCrossRefGoogle Scholar
  88. 88.
    A.V. Krasavin, P. Ginzburg, G.A. Wurtz, A.V. Zayats, Nature Commun. 7, 11497 (2016)ADSCrossRefGoogle Scholar
  89. 89.
    M.G. Blaber, M.D. Arnold, M.J. Ford, J. Phys. Chem. C 113(8), 3041 (2009)CrossRefGoogle Scholar

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© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Department of Photonics Engineering and Center for Nanostructured GrapheneTechnical University of DenmarkKongens LyngbyDenmark

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