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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 13 — Jun. 20, 2011
  • pp: 12208–12219

Localized surface-plasmon resonances on single and coupled nanoparticles through surface integral equations for flexible surfaces

Rogelio Rodríguez-Oliveros and José A. Sánchez-Gil  »View Author Affiliations

Optics Express, Vol. 19, Issue 13, pp. 12208-12219 (2011)

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We present an advanced numerical formulation to calculate the optical properties of 3D nanoparticles (single or coupled) of arbitrary shape and lack of symmetry. The method is based on the (formally exact) surface integral equation formulation, implemented for parametric surfaces describing particles with arbitrary shape through a unified treatment (Gielis’ formula). Extinction, scattering, and absorption spectra of a variety of metal nanoparticles are shown, thus determining rigorously the localised surface-plasmon resonances of nanocubes, nanostars, and nanodimers. Far-field and near-field patterns for such resonances are also calculated, revealing their nature. The flexibility and reliability of the formulation makes it specially suitable for complex scattering problems in Nano-Optics & Plasmonics.

© 2011 OSA

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(290.5850) Scattering : Scattering, particles
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Optics at Surfaces

Original Manuscript: March 29, 2011
Revised Manuscript: May 19, 2011
Manuscript Accepted: May 22, 2011
Published: June 8, 2011

Rogelio Rodríguez-Oliveros and José A. Sánchez-Gil, "Localized surface-plasmon resonances on single and coupled nanoparticles through surface integral equations for flexible surfaces," Opt. Express 19, 12208-12219 (2011)

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  1. X. Lu, M. Rycenga, S. E. Skrabalak, B. Wiley, and Y. Xia, “Chemical synthesis of novel plasmonic nanoparticles,” Annu. Rev. Phys. Chem. 60, 167–92 (2009). [CrossRef]
  2. T. R. Jensen, G. C. Schatz, and R. P. V. Duyne, “Nanosphere lithography: surface plasmon resonance spectrum of a periodic array of silver nanoparticles by ultraviolet-visible extinction spectroscopy and electrodynamic modeling,” J. Phys. Chem. B 103, 2394–2401 (1999). [CrossRef]
  3. A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95, 267407 (2005). [CrossRef]
  4. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006). [CrossRef] [PubMed]
  5. V. Giannini, A. Fernandez-Dominguez, Y. Sonnefraud, T. Roschuk, R. Fernandez-García, and S. A. Maier, “Controlling light localization and light–matter interactions with nanoplasmonics,” Small 6, 2498–2507 (2010). [CrossRef] [PubMed]
  6. L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5, 83–90 (2011). [CrossRef]
  7. J. A. Sánchez-Gil and J. V. García-Ramos, “Local and average electromagnetic enhancement in surface-enhanced Raman scattering from self-affine fractal metal substrates with nanoscale irregularities,” Chem. Phys. Lett. 367, 361–366 (2003). [CrossRef]
  8. E. J. Zeman and G. C. Schatz, “An accurate electromagnetic theory study of surface enhancement factors for Ag, Au, Cu, Li, Na, Al, Ga, In, Zn, and Cd,” J. Phys. C 91, 634–643 (1987).
  9. H. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface- enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000). [CrossRef]
  10. P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, and B. Hecht, “Resonant optical antennas,” Science 308, 1607–1609 (2005). [CrossRef] [PubMed]
  11. J. J. Greffet, “Nanoantennas for light emission,” Science 308, 1561–1563 (2005). [CrossRef] [PubMed]
  12. O. L. Muskens, V. Giannini, J. A. Sánchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7, 2871–2875 (2007). [CrossRef] [PubMed]
  13. T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. V. Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28–33 (2007). [CrossRef] [PubMed]
  14. C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998). [CrossRef]
  15. W. L. Barnes, “Comparing experiment and theory in plasmonics,” J. Opt. A, Pure Appl. Opt. 11, 114002 (2009). [CrossRef]
  16. K. S. Yee, “Numerical Solution of initial value problems of Maxwells equations,” IEEE Trans. Antenn. Propag. 14, 302–307 (1966). [CrossRef]
  17. R. Clough, “The finite element method after twenty-five years: a personal view,” Comput. Struct. 12, 361–370 (1980). [CrossRef]
  18. C. Girard and A. Dereux, “Near-field optics theories,” Rep. Progr. Phys. 59, 657 (1996). [CrossRef]
  19. B. T. Draine and P. J. Flatau, “Discrete-Dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491 (1994). [CrossRef]
  20. M. I. Mishchenko, N. T. Zakharova, G. Videen, N. G. Khlebtsov, and T. Wriedt, “Comprehensive T-matrix reference database: a 2007–2009 update,” J. Quant. Spectrosc. Radiat. Tranfer. 111, 650–658 (2010). [CrossRef]
  21. V. Myroshnychenko, E. Carbó-Argibay, I. Pastoriza-Santos, J. Pérez-Juste, L. M. Liz-Marzán, and F. García de Abajo, “Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20, 4288–4293 (2008). [CrossRef]
  22. A. A. Maradudin, T. R. Michel, A. Mcgurn, and E. R. Mendez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990). [CrossRef]
  23. J. A. Sanchez-Gil and M. Nieto-Vesperinas, “Light scattering from random rough dielectric surfaces,” J. Opt. Soc. Am A 8, 1270 (1991). [CrossRef]
  24. S. Rao, D. Wilton, and A. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antenn. Propag. 30, 409–418 (1982). [CrossRef]
  25. A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3D simulations of plasmonics and high permittivity nanostructures,” J. Opt. Soc. Am. A 26, 732–740 (2009). [CrossRef]
  26. P. Tran and A. Maradudin, “The scattering of electromagnetic waves from two-dimensional randomly rough perfectly conducting surfaces: the full angular intensity distribution,” Opt. Commun. 110, 269–273 (1994). [CrossRef]
  27. K. Pak, L. Tsang, and J. Johnson, “Numerical simulations and backscattering enhancement of electromagnetic waves from two-dimensional dielectric random rough surfaces with the sparse-matrix canonical grid method,” J. Opt. Soc. Am. A 14, 1515 (1997). [CrossRef]
  28. I. Simonsen, A. A. Maradudin, and T. A. Leskova, “The scattering of electromagnetic waves from two-dimensional randomly rough perfectly conducting surfaces: the full angular intensity distribution,” Phys. Rev. A 81, 013,806 (2009).
  29. I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of Electromagnetic Waves from Two-Dimensional Randomly Rough Penetrable Surfaces,” Phys. Rev. Lett. 104, 223,904 (2010). [CrossRef] [PubMed]
  30. C. I. Valencia, E. R. Méndez, and B. S. Mendoza, “Second-harmonic generation in the scattering of light by two dimensional nanoparticles,” J. Opt. Soc. Am. B 20, 2150–2161 (2003). [CrossRef]
  31. 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, 2822 (2007). [CrossRef]
  32. U. Hohenester and J. Krenn, “Surface plasmon resonances of single and coupled metallic nanoparticles: a boundary integral method approach,” Phys. Rev. B 72, 1–9 (2005). [CrossRef]
  33. J. Jung and T. Sodergaard, “Greens function surface integral equation method for theoretical analysis of scatterers close to a metal interface,” Phys. Rev. B 77, 245310 (2008). [CrossRef]
  34. P. I. Geshev, U. Fischer, and H. Fuchs, “Calculation of tip enhanced Raman scattering caused by nanoparticle plasmons acting on a molecule placed near a metallic film,” Phys. Rev. B 81, 125,441 (2010). [CrossRef]
  35. J. Gielis, “A generic geometric transformation that unifies a wide range of natural and abstract shapes,” Am. J. Bot. 90, 333–338 (2003). [CrossRef] [PubMed]
  36. J. Stratton and L. Chu, “Diffraction theory of electromagnetic waves,” Phys. Rev. 56, 99–107 (1939). [CrossRef]
  37. M. Born and E. Wolf, Principles of Optics , 6th ed. (Pergamon, 1980).
  38. H. Ying Yao and Y. Bing Gan, “Regularization of the combined field integral equation on parametric surface for EM scattering problems,” Electromagnetics 26, 423–438 (2006). [CrossRef]
  39. P. Bourke, “SuperShape in 3D,” URL http://local.wasp.uwa.edu.au/~{}pbourke/geometry/supershape3d/ .
  40. H. Van De Hulst, Light Scattering by Small Particles , 1st ed. (Dover, 1981).
  41. P. B. Johnson and R. W. Christie, “Optical constants of nobel metals,” Phys. Rev. B 6, 4370 (1972). [CrossRef]
  42. S. Y. Lee, L. Hung, G. S. Lang, J. E. Cornett, I. D. Mayergoyz, and O. Rabin, “Dispersion in the SERS enhancement with silver nanocube dimers,” ACS Nano 4, 5763–5772 (2010). [CrossRef] [PubMed]
  43. A. L. González and C. Noguez, “Optical properties of silver nanoparticles,” Phys. Stat. Solidi C 4, 4118–4126 (2007). [CrossRef]
  44. V. Giannini, R. Rodríguez-Oliveros, and J. A. Sánchez-Gil, “Surface plasmon resonances of metallic nanostars/nanoflowers for surface-enhanced raman scattering,” Plasmonics 5, 99–104 (2010). [CrossRef]
  45. P. Senthil Kumar, I. Pastoriza-Santos, B. Rodríguez-González, F. Javier García de Abajo, and L. M. Liz-Marzán, “High-yield synthesis and optical response of gold nanostars,” Nanotechnology 19, 015606 (2008). [CrossRef] [PubMed]
  46. E. R. Encina and E. A. Coronado, “Plasmon coupling in silver nanosphere pairs,” J Chem. Phys. C 114, 3918–3923 (2010). [CrossRef]
  47. A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, “Strong magnetic response of Silicon nanoparticles in the infrared,” Opt. Express 19, 4815–4826 (2011). [CrossRef] [PubMed]

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