OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 11 — Nov. 1, 2008
  • pp: 2767–2775

Optical response of linear chains of metal nanospheres and nanospheroids

Stephen J. Norton and Tuan Vo-Dinh  »View Author Affiliations

JOSA A, Vol. 25, Issue 11, pp. 2767-2775 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (193 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A semi-analytical method for computing the electric field surrounding a finite linear chain of metal nanospheres and nanospheroids is described. In treating chains or clusters of spheres, a common approach is to use the spherical-harmonic addition theorem to relate the multipole expansion coefficients between different spheres. A method is described here that avoids the use of spherical-harmonic addition theorems, which are not applicable to spheroidal chains. Simulations are given that illustrate the large field enhancements that can occur in the gaps between silver nanoparticles arising from plasmon resonances.

© 2008 Optical Society of America

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(260.5740) Physical optics : Resonance
(290.4210) Scattering : Multiple scattering
(290.5850) Scattering : Scattering, particles
(290.5860) Scattering : Scattering, Raman
(240.6695) Optics at surfaces : Surface-enhanced Raman scattering

ToC Category:
Optics at Surfaces

Original Manuscript: May 22, 2008
Revised Manuscript: August 2, 2008
Manuscript Accepted: August 21, 2008
Published: October 17, 2008

Virtual Issues
Vol. 4, Iss. 1 Virtual Journal for Biomedical Optics

Stephen J. Norton and Tuan Vo-Dinh, "Optical response of linear chains of metal nanospheres and nanospheroids," J. Opt. Soc. Am. A 25, 2767-2775 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. T. Vo-Dinh, M. Y. K. Hiromoto, G. M. Begun, and R. L. Moody, “Surface-enhanced Raman spectrometry for trace organic-analysis,” Anal. Chem. 56, 1667-1670 (1984). [CrossRef]
  2. T. Vo-Dinh, “Surface-enhanced Raman spectroscopy using metallic nanostructures,” Trends Analyt. Chem. 17, 557-570 (1998). [CrossRef]
  3. M. Wabuyele and T. Vo-Dinh, “Detection of HIV Type 1 DNA sequence using plasmonics nanoprobes,” Anal. Chem. 77, 7810-7815 (2005). [CrossRef] [PubMed]
  4. M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783-826 (1985). [CrossRef]
  5. G. C. Schatz, M. A. Young, and R. P. Van Duyne, “Electromagnetic mechanism of SERS,” in Surface-Enhanced Raman Scattering--Physics and Applications, K.Kneipp, M.Moskovits, and H.Kneipp, eds., Top. Appl. Phys. 103, 19-46 (2006). [CrossRef]
  6. H. Xu, J. Aizpurua, M. Kall, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318-4324 (2000). [CrossRef]
  7. Selected Papers on Surface-Enhanced Raman Scattering, M.Kerker, ed., SPIE Milestone Series, Vol. MS 10 (Proc. SPIE, 1990).
  8. J. M. Gerardy and M. Ausloos, “Absorption spectrum of clusters of spheres from the general solution of Maxwell's equations. The long-wavelength limit,” Phys. Rev. B 22, 4950-4959 (1980). [CrossRef]
  9. M. Schmeits and L. Dambly, “Fast electron scattering by bispherical surface-plasmon modes,” Phys. Rev. B 44, 12706-12711 (1991). [CrossRef]
  10. M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, “Electromagnetic energy transport via linear chains of silver nanoparticles,” Opt. Lett. 23, 1331-1333 (1998). [CrossRef]
  11. K. Li, M. I. Stockman, and D. J. Bergman, “Self-similar chain of metal nanospheres as an efficient nanolens,” Phys. Rev. Lett. 91, 227402-1-4 (2003). [CrossRef]
  12. M. I. Stockman, K. Li, X. Li, and D. J. Bergman, “An efficient nanolens: Self-similar chain of metal nanospheres,” Proc. SPIE 5512, 87-99 (2004). [CrossRef]
  13. U. Evra and D. J. Bergman, “Lifetime of nano-plasmonic states,” Proc. SPIE 6324, 63240H (2006). [CrossRef]
  14. W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE, 1995), Appendix D.
  15. Translational addition theorems applicable to spheroids have been derived in , but, at least in our opinion, their complexity renders them extremely unwieldy at best and unuseable at worst. They involve double infinite summations with coefficients that themselves require numerical evaluation.
  16. B. P. Sinha and R. H. Macphie, “Translational addition theorems for spheroidal scalar and vector wave functions,” Q. Appl. Math. 38, 143-158 (1980).
  17. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998).
  18. The set of parameters used in our paper is the same set employed in the commercial finite-difference time-domain electromagnetic code Fullwave 6.0 (RSoft Design Group, Inc.), which were derived from the data in . These values are:Δϵk={1759.471,135.344,258.1946,22.90436,1749.06,11756.18},ak={1,1,1,1,1,1},bk={0.243097,19.68071,2.289161,0.329194,4.639097,12.25} andck={0,17.07876,515.022,1718.357,2116.092,10559.42}.
  19. M. J. Caola, “Solid harmonics and their addition theorems,” J. Phys. A 11, L23-L25 (1978). [CrossRef]
  20. P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, 1953), p. 1284.
  21. P. F. Liao and A. Wokaun, “Lightning rod effect in surface enhanced Raman scattering,” J. Chem. Phys. 76, 751-752 (1982). [CrossRef]
  22. K. Kneipp, Y. Yang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667-1670 (1997). [CrossRef]
  23. P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part I (McGraw-Hill, New York, 1953), p. 599.

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited