OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 4 — Feb. 13, 2012
  • pp: 3663–3674

Polarizability of nanowires at surfaces: exact solution for general geometry

Jesper Jung and Thomas G. Pedersen  »View Author Affiliations

Optics Express, Vol. 20, Issue 4, pp. 3663-3674 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (1202 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The polarizability of a nanostructure is an important parameter that determines the optical properties. An exact semi-analytical solution of the electrostatic polarizability of a general geometry consisting of two segments forming a cylinder that can be arbitrarily buried in a substrate is derived using bipolar coordinates, cosine-, and sine-transformations. Based on the presented expressions, we analyze the polarizability of several metal nanowire geometries that are important within plasmonics. Our results provide physical insight into the interplay between the multiple resonances found in the polarizability of metal nanowires at surfaces.

© 2012 OSA

OCIS Codes
(000.3860) General : Mathematical methods in physics
(230.5750) Optical devices : Resonators
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Optics at Surfaces

Original Manuscript: October 28, 2011
Revised Manuscript: December 12, 2011
Manuscript Accepted: January 27, 2012
Published: January 31, 2012

Jesper Jung and Thomas G. Pedersen, "Polarizability of nanowires at surfaces: exact solution for general geometry," Opt. Express 20, 3663-3674 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  2. L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge2006).
  3. A. V. Zayats and I. I. Smolyaninov, “Near-field photonics: surface plasmon polaritons and localized surface plasmons,” J. Opt. A: Pure Appl. Opt.5, S16–S50 (2003). [CrossRef]
  4. 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]
  5. W. A. Murray and W. L. Barnes, “Plasmonic materials,” Adv. Mater.19, 3771–3782 (2007). [CrossRef]
  6. S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics1, 641–648 (2007). [CrossRef]
  7. M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys.57, 783–826 (1985). [CrossRef]
  8. Y. C. Coa, R. Jin, and C. A. Mirkin, “Nanoparticles with Raman spectroscopic fingerprints for DNA and RNA detection,” Science297, 1536–1540 (2002). [CrossRef]
  9. A. J. Haes and R. P. V. Duyne, “A nanoscale optical biosensor: sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles,” J. Am. Chem. Soc.124, 10596–10604 (2002). [CrossRef] [PubMed]
  10. K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express16, 21793–21800 (2008). [CrossRef] [PubMed]
  11. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9, 205–213 (2010). [CrossRef] [PubMed]
  12. V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater.22, 4794–4808 (2010). [CrossRef] [PubMed]
  13. L. Lorenz, “Lysbevægelsen i og udenfor en af plane lysbølger belyst kugle,” K. Dan. Vidensk. Selsk. Skr.6, 1–62 (1890).
  14. G. Mie, “Beitrage zur optik truber medien speziell kolloidaler metallosungen,” Ann. Physik.330, 337–445 (1908). [CrossRef]
  15. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  16. L. Rayleigh, “The dispersal of light by a dielectric cylinder,” Phil. Mag.36, 365–376 (1918).
  17. J. R. Wait, “Scattering of a plane wave from a circular cylinder at oblique incidence,” Can. J. Phys.33, 189–195 (1955). [CrossRef]
  18. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).
  19. J. Jin, The Finite Element Method in Electrodynamics (Wiley, 2002).
  20. T. Søndergaard, “Modeling of plasmonic nanostructures: Green’s function integral equation methods,” Phys. Status Solidi B244, 3448–3462 (2007). [CrossRef]
  21. O. J. F. Martin, C. Girard, and A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett.74, 526–529 (1995). [CrossRef] [PubMed]
  22. F. J. Garcia de Abajo and A. Howie, “Retarded field calculation of electron energy loss in inhomogenous dielectrics,” Phys. Rev. B65, 115418 (2002). [CrossRef]
  23. J. Jung, T. G. Pedersen, T. Søndergaard, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Electrostatic plasmon resonances of metal nanospheres in layered geometries,” Phys. Rev. B81, 125413 (2010). [CrossRef]
  24. F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. V. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A205, 2844–2861 (2008). [CrossRef]
  25. J. W. Yoon, W. J. Park, K. J. Lee, S. H. Song, and R. Magnusson, “Surface-plasmon mediated total absorption of light into silicon,” Opt. Express19, 20673–20680 (2011). [CrossRef] [PubMed]
  26. P. C. Waterman, “Surface fields and the T matrix,” J. Opt. Soc. Am. A16, 2968–2977 (1999). [CrossRef]
  27. A. V. Radchik, A. V. Paley, G. B. Smith, and A. V. Vagov, “Polarization and resonant absorption in intersecting cylinders and spheres,” J. Appl. Phys.76, 4827–4835 (1994). [CrossRef]
  28. A. Salandrino, A. Alu, and N. Engheta, “Parallel, series, and intermediate interconnects of optical nanocircuit elements. 1. Analytical solution,” J. Opt. Soc. Am. B24, 3007–3013 (2007). [CrossRef]
  29. M Pitkonen, “A closed-form solution for the polarizability of a dielectric double half-cylinder,” J. Electromagn. Waves Appl.24, 1267–1277 (2010). [CrossRef]
  30. H. Kettunen, H. Wallen, and A. Sihvola, “Polarizability of a dielectic hemisphere,” J. Appl. Phys.102, 044105 (2007). [CrossRef]
  31. Y. Luo, J. B. Pendry, and A. Aubry, “Surface plasmons and singularities,” Nano Lett.10, 4186–4191 (2010). [CrossRef]
  32. Y. Luo, A. Aubry, and J. B. Pendry, “Electromagnetic contribution to surface-enhanced Raman scattering from rough metal surfaces: a transformation optics approach,” Phys. Rev. B83, 155422 (2011). [CrossRef]
  33. J. Jung and T. G. Pedersen, “Exact polarizability and plasmon resonances of partly buried nanowires,” Opt. Express19, 22775–22785 (2011). [CrossRef] [PubMed]
  34. P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill Book Company Inc., 1953).
  35. H. E. Lockwood, A Book of Curves (Cambridge University Press, 1963).
  36. A. Jonquiere, “Note sur la serie ∑n=1∞xnns,” Bulletin de la Socit Mathmatique de France17, 142–152 (1889).
  37. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 4370–4379 (1972). [CrossRef]
  38. J. R. Arias-Gonzalez and M. Nieto-Vesperinas, “Resonant near-field eigenmodes of nanocylinders on flat surfaces under both homogenous and inhomogenous lightwave excitation,” J. Opt. Soc. Am. A18, 657–665 (2001). [CrossRef]
  39. A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Plasmonic hybridization between nanowires and a metallic surface: a transformation optics approach,” ACS Nano53293–3308 (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