OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 22 — Oct. 24, 2011
  • pp: 22176–22190

Periodicity-induced effects in the scattering and absorption of light by infinite and finite gratings of circular silver nanowires

Denys M. Natarov, Volodymyr O. Byelobrov, Ronan Sauleau, Trevor M. Benson, and Alexander I. Nosich  »View Author Affiliations

Optics Express, Vol. 19, Issue 22, pp. 22176-22190 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (3988 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We study numerically the effect of periodicity on the plasmon-assisted scattering and absorption of visible light by infinite and finite gratings of circular silver nanowires. The infinite grating is a convenient object of analysis because of the possibility to reduce the scattering problem to one period. We use the well-established method of partial separation of variables however make an important improvement by casting the resulting matrix equation to the Fredholm second-kind type, which guarantees convergence. If the silver wires have sub-wavelength radii, then two types of resonances co-exist and may lead to enhanced reflection and absorption: the plasmon-type and the grating-type. Each type is caused by different complex poles of the field function. The low-Q plasmon poles cluster near the wavelength where dielectric function equals −1. The grating-type poles make multiplets located in close proximity of Rayleigh wavelengths, tending to them if the wires get thinner. They have high Q-factors and, if excited, display intensive near-field patterns. A similar interplay between the two types of resonances takes place for finite gratings of silver wires, the sharpness of the grating-type peak getting greater for longer gratings. By tuning carefully the grating period, one can bring together two resonances and enhance the resonant scattering of light per wire by several times.

© 2011 OSA

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1970) Diffraction and gratings : Diffractive optics
(290.0290) Scattering : Scattering

ToC Category:

Original Manuscript: July 20, 2011
Revised Manuscript: October 5, 2011
Manuscript Accepted: October 10, 2011
Published: October 24, 2011

Virtual Issues
Collective Phenomena (2011) Optics Express

Denys M. Natarov, Volodymyr O. Byelobrov, Ronan Sauleau, Trevor M. Benson, and Alexander I. Nosich, "Periodicity-induced effects in the scattering and absorption of light by infinite and finite gratings of circular silver nanowires," Opt. Express 19, 22176-22190 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. For example, examination of the single-cylinder field Fourier expansion coefficients (177) of [11] for ka=2πa/λ→0 shows that they have poles at λ=λnP, for which ε(λnP)≈−1−cn(ka)2(4n)−1, where the azimuthal index is n≥1 and cn>0 are known coefficients.
  2. J. Kottmann, O. Martin, D. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross-section,” Phys. Rev. B 64(23), 235402 (2001). [CrossRef]
  3. J. Kottmann and O. J. F. Martin, “Plasmon resonant coupling in metallic nanowires,” Opt. Express 8(12), 655–663 (2001). [CrossRef] [PubMed]
  4. V. Giannini and J. A. Sánchez-Gil, “Calculations of light scattering from isolated and interacting metallic nanowires of arbitrary cross section by means of Green’s theorem surface integral equations in parametric form,” J. Opt. Soc. Am. A 24(9), 2822–2830 (2007). [CrossRef] [PubMed]
  5. T. Søndergaard and S. J. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi B 245(1), 9–19 (2008). [CrossRef]
  6. F. J. G. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007). [CrossRef]
  7. V. Twersky, “On scattering of waves by the infinite grating of circular cylinders,” IRE Trans. Antennas Propag. 10(6), 737–765 (1962). [CrossRef]
  8. O. Kavaklioglu, “On diffraction of waves by the infinite grating of circular dielectric cylinders at oblique incidence: Floquet representation,” J. Mod. Phys. 48, 125–142 (2001).
  9. K. Yasumoto, H. Toyama, and T. Kushta, “Accurate analysis of 2-D electromagnetic scattering from multilayered periodic arrays of circular cylinders using lattice sums technique,” IEEE Trans. Antenn. Propag. 52(10), 2603–2611 (2004). [CrossRef]
  10. R. Gómez-Medina, M. Laroche, and J. J. Sáenz, “Extraordinary optical reflection from sub-wavelength cylinder arrays,” Opt. Express 14(9), 3730–3737 (2006). [CrossRef] [PubMed]
  11. M. Laroche, S. Albaladejo, R. Gomez-Medina, and J. J. Saenz, “Tuning the optical response of nanocylinder arrays: an analytical study,” Phys. Rev. B 74(24), 245422 (2006). [CrossRef]
  12. M. Laroche, S. Albaladejo, R. Carminati, and J. J. Sáenz, “Optical resonances in one-dimensional dielectric nanorod arrays: field-induced fluorescence enhancement,” Opt. Lett. 32(18), 2762–2764 (2007). [CrossRef] [PubMed]
  13. V. O. Byelobrov, J. Ctyroky, T. M. Benson, R. Sauleau, A. Altintas, and A. I. Nosich, “Low-threshold lasing eigenmodes of an infinite periodic chain of quantum wires,” Opt. Lett. 35(21), 3634–3636 (2010). [CrossRef] [PubMed]
  14. L. Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 79(532), 399–416 (1907). [CrossRef]
  15. A. Hessel and A. A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 4(10), 1275–1297 (1965). [CrossRef]
  16. D. W. Kerr and C. H. Palmer, “Anomalous behavior of thin-wire gratings,” J. Opt. Soc. Am. 61(4), 450–456 (1971). [CrossRef]
  17. S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120(23), 10871–10875 (2004). [CrossRef] [PubMed]
  18. S. Zou and G. C. Schatz, “Narrow plasmonic/photonic extinction and scattering line shapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121(24), 12606–12612 (2004). [CrossRef] [PubMed]
  19. S. Zou and G. C. Schatz, “Silver nanoparticle array structures that produce giant enhancements in electromagnetic fields,” Chem. Phys. Lett. 403(1-3), 62–67 (2005). [CrossRef]
  20. E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Käll, “Controlling plasmon line shapes through diffractive coupling in linear arrays of cylindrical nanoparticles fabricated by electron beam lithography,” Nano Lett. 5(6), 1065–1070 (2005). [CrossRef] [PubMed]
  21. N. Félidj, G. Laurent, J. Aubard, G. Lévi, A. Hohenau, J. R. Krenn, and F. R. Aussenegg, “Grating-induced plasmon mode in gold nanoparticle arrays,” J. Chem. Phys. 123(22), 221103 (2005). [CrossRef] [PubMed]
  22. V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008). [CrossRef] [PubMed]
  23. B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008). [CrossRef] [PubMed]
  24. S. V. Boriskina and L. Dal Negro, “Multiple-wavelength plasmonic nanoantennas,” Opt. Lett. 35(4), 538–540 (2010). [CrossRef] [PubMed]
  25. V. Twersky, “On a multiple scattering theory of the finite grating and the Wood anomalies,” J. Appl. Phys. 23(10), 1099–1118 (1952). [CrossRef]
  26. G. O. Olaofe, “Scattering by two cylinders,” Radio Sci. 5(11), 1351–1360 (1970). [CrossRef]
  27. H. A. Ragheb and M. Hamid, “Scattering by N parallel conducting circular cylinders,” Int. J. Electron. 59(4), 407–421 (1985). [CrossRef]
  28. A. Z. Elsherbeni and A. A. Kishk, “Modeling of cylindrical objects by circular dielectric and conducting cylinders,” IEEE Trans. Antenn. Propag. 40(1), 96–99 (1992). [CrossRef]
  29. D. Felbacq, G. Tayeb, and D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 11(9), 2526–2538 (1994). [CrossRef]
  30. X. Antoine, C. Chniti, and K. Ramdani, “On the numerical approximation of high-frequency acoustic multiple scattering problems by circular cylinders,” J. Comput. Phys. 227(3), 1754–1771 (2008). [CrossRef]
  31. Here, we imply convergence in mathematical sense, as a possibility to minimise the error in the solution by inverting progressively greater matrices. Non-convergent numerical solutions are often able to provide a couple of correct digits however fail to achieve better accuracy.
  32. X. Antoine, K. Ramdani, and B. Thierry, “Etude numerique de la resolution par equations integrales de la diffraction multiple par des disques,” in Proc. Congres Français d’Acoustique, Lyon (2010).
  33. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. 6(12), 4370–4379 (1972). [CrossRef]
  34. A. I. Nosich, “Radiation conditions, limiting absorption principle, and general relations in open waveguide scattering,” J. Electromagn. Waves Appl. 8(3), 329–353 (1994). [CrossRef]
  35. C. M. Linton, “The Green’s function for the two-dimensional Helmholtz equation in periodic domains,” J. Eng. Math. 33(4), 377–401 (1998). [CrossRef]
  36. V. Giannini, G. Vecchi, and J. Gómez Rivas, “Lighting up multipolar surface plasmon polaritons by collective resonances in arrays of nanoantennas,” Phys. Rev. Lett. 105(26), 266801 (2010). [CrossRef] [PubMed]
  37. R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009). [CrossRef] [PubMed]
  38. W. Zhou and T. W. Odom, “Tunable subradiant lattice plasmons by out-of-plane dipolar interactions,” Nat. Nanotechnol. 6(7), 423–427 (2011). [CrossRef] [PubMed]

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