OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 16 — Aug. 11, 2014
  • pp: 18958–18965

Exact solution for velocity of plasmon-polariton in metallic nano-chain

Witold A. Jacak  »View Author Affiliations

Optics Express, Vol. 22, Issue 16, pp. 18958-18965 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (836 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



In equidistant infinite chain of metallic nanospheres the collective mode of surface plasmons propagates without radiative losses, i.e., the Lorentz friction losses in each nanosphere are compensated by energy income in near-, medium- and far-field from the rest of the chain. Within an approximate approach including numerical studies in Green function framework it has been indicated superluminal propagation of some plasmon-polariton modes. By the exact solution of the nonlinear dynamic equation we demonstrate that the superluminal modes were an artifact of the perturbation solution type and we show that the group velocities for both polarizations are limited by light velocity, though vary in large range depending on chain parameters and are typically one order lower than the light velocity.

© 2014 Optical Society of America

OCIS Codes
(240.5420) Optics at surfaces : Polaritons
(250.5403) Optoelectronics : Plasmonics

ToC Category:

Original Manuscript: May 26, 2014
Revised Manuscript: July 6, 2014
Manuscript Accepted: July 8, 2014
Published: July 29, 2014

Witold A. Jacak, "Exact solution for velocity of plasmon-polariton in metallic nano-chain," Opt. Express 22, 18958-18965 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. S. Citrin, “Plasmon polaritons in finite-length metal-nanoparticle chains: The role of chain length unravelled,” Nano Lett.5, 985–989 (2005). [CrossRef] [PubMed]
  2. L. L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B107, 7343–7350 (2003). [CrossRef]
  3. S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys.120, 10871–10875 (2004). [CrossRef] [PubMed]
  4. J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett.82, 2590–2593 (1999). [CrossRef]
  5. M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B62, R16356 (2000). [CrossRef]
  6. S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, “Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy,” Phys. Rev. B65, 193408 (2002). [CrossRef]
  7. S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B67, 205402 (2003). [CrossRef]
  8. S. A. Maier, P. G. Kik, L. A. Sweatlock, H. A. Atwater, J. J. Penninkhof, A. Polman, S. Meltzer, E. Harel, A. Requicha, and B. E. Koel, “Energy transport in metal nanoparticle plasmon waveguides,” Mat. Res. Soc. Symp. Proc.777, T7.1.1 (2003).
  9. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit inmetal nanoparticle plasmon waveguides,” Nat. Mater.2, 229–232 (2003). [CrossRef] [PubMed]
  10. S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys.98, 011101 (2005). [CrossRef]
  11. I. L. Rasskazov, S. V. Karpov, and V. A. Markel, “Nondecaying surface plasmon polaritons in linear chains of silver nanospheroids,” Opt. Lett.38, 4743–4746 (2013). [CrossRef] [PubMed]
  12. A. A. Govyadinov and V. A. Markel, “From slow to superluminal propagation: Dispersive properties of surface plasmon polaritons in linear chains of metallic nanospheroids,” Phys. Rev. B78, 035403 (2008). [CrossRef]
  13. Y. Hadad and B. Z. Steinberg, “Greens function theory for infinite and semi-infinite particle chains,” Phys. Rev. B84, 125402 (2011). [CrossRef]
  14. V. A. Markel and A. K. Sarychev, “Comment on Greens function theory for infinite and semi-infinite particle chains,” Phys. Rev. B86, 037401 (2012). [CrossRef]
  15. L. D. Landau and E. M. Lifshitz, Field Theory (Nauka, 1973).
  16. J. D. Jackson, Classical Electrodynamics (John Willey and Sons Inc., 1998).
  17. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett.96, 113002 (2006). [CrossRef] [PubMed]
  18. W. A. Jacak, “On plasmon polariton propagation along metallic nano-chain,” Plasmonics8, 1317–1333 (2013). [CrossRef] [PubMed]
  19. C. Yannouleas, R. A. Broglia, M. Brack, and P. F. Bortignon, “Fragmentation of the photoabsorption strength in neutral and charged metal microclusters,” Phys. Rev. Lett.63, 255–258 (1989). [CrossRef] [PubMed]
  20. W. Ekardt, “Anomalous inelastic electron scattering from small metal particles,” Phys. Rev. B33, 8803–8805 (1986). [CrossRef]
  21. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals Series and Products (Academic Press, Inc., 1994).
  22. V. A. Markel and A. K. Sarychev, “Propagation of surface plasmons in ordered and disordered chains of metal nanospheres,” Phys. Rev. B75, 085426 (2007). [CrossRef]
  23. W. Jacak, J. Krasnyj, J. Jacak, R. Gonczarek, A. Chepok, L. Jacak, D. Hu, and D. Schaadt, “Radius dependent shift in surface plasmon frequency in large metallic nanospheres: Theory and experiment,” J. Appl. Phys.107, 124317 (2010). [CrossRef]
  24. T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett.80, 4249–4252 (1998). [CrossRef]
  25. E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Stationary behavior of a chain of interacting spasers,” Phys. Rev. B85, 165419 (2012). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited