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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 27, Iss. 9 — Sep. 1, 2010
  • pp: 1819–1827

Metallic nanorod arrays: negative refraction and optical properties explained by retarded dipolar interactions

René Kullock, Stefan Grafström, Paul R. Evans, Robert J. Pollard, and Lukas M. Eng  »View Author Affiliations

JOSA B, Vol. 27, Issue 9, pp. 1819-1827 (2010)

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We show that the optical properties of arrays of parallel-aligned metallic nanorods can be understood by means of a retarded dipolar interaction model. Exemplarily, arrays of gold nanorods having various lengths and diameters are investigated experimentally. A strong diameter dependence of the long-axis surface plasmon resonance (LSPR) as well as a lower energy limit of this mode for varying length was found. The model also shows that, for small nanorod distances ( d < λ / 2 ) , the optical properties are independent of the azimuthal angle of the incoming plane wave and of the detailed arrangement of the nanorods. Furthermore, the model was used to explain the dependence of the LSPR on the angle of incidence and to find the conditions for which negative and extraordinary positive refractions occur in these structures.

© 2010 Optical Society of America

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(260.3910) Physical optics : Metal optics
(290.2200) Scattering : Extinction
(160.3918) Materials : Metamaterials

ToC Category:
Physical Optics

Original Manuscript: May 5, 2010
Manuscript Accepted: June 27, 2010
Published: August 13, 2010

Virtual Issues
Vol. 5, Iss. 13 Virtual Journal for Biomedical Optics

René Kullock, Stefan Grafström, Paul R. Evans, Robert J. Pollard, and Lukas M. Eng, "Metallic nanorod arrays: negative refraction and optical properties explained by retarded dipolar interactions," J. Opt. Soc. Am. B 27, 1819-1827 (2010)

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  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]
  2. C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007). [CrossRef] [PubMed]
  3. T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313, 1595 (2006). [CrossRef] [PubMed]
  4. K. A. Willets and R. P. van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Annu. Rev. Phys. Chem. 58, 267–297 (2007). [CrossRef]
  5. T. Rindzevicius, Y. Alaverdyan, M. Käll, W. A. Murray, and W. L. Barnes, “Long-Range refractive index sensing using plasmonic nanostructures,” J. Phys. Chem. C 111, 11806–11810 (2007). [CrossRef]
  6. R. Atkinson, W. Hendren, G. Wurtz, W. Dickson, A. Zayats, P. Evans, and R. Pollard, “Anisotropic optical properties of arrays of gold nanorods embedded in alumina,” Phys. Rev. B 73, 235402 (2006). [CrossRef]
  7. P. Evans, R. Kullock, W. Hendren, R. Atkinson, R. Pollard, and L. M. Eng, “Optical transmission properties and electric field distribution of interacting 2D silver nanorod arrays,” Adv. Funct. Mater. 18, 1075–1079 (2008). [CrossRef]
  8. G. A. Wurtz, W. Dickson, D. O’Connor, R. Atkinson, W. Hendren, P. Evans, R. Pollard, and A. V. Zayats, “Guided plasmonic modes in nanorod assemblies: strong electromagnetic coupling regime,” Opt. Express 16, 7460–7470 (2008). [CrossRef] [PubMed]
  9. R. Kullock, W. R. Hendren, A. Hille, S. Grafström, P. R. Evans, R. J. Pollard, R. Atkinson, and L. M. Eng, “Polarization conversion through collective surface plasmons in metallic nanorod arrays,” Opt. Express 16, 21671–21681 (2008). [CrossRef] [PubMed]
  10. D. P. Lyvers, J. Moon, A. V. Kildishev, V. M. Shalaev, and A. Wei, “Gold nanorod arrays as plasmonic cavity resonators,” ACS Nano 2, 2569–2576 (2008). [CrossRef]
  11. S. J. Lee, Z. Guan, H. Xu, and M. Moskovits, “Surface-enhanced Raman spectroscopy and nanogeometry: the plasmonic origin of SERS,” J. Phys. Chem. C 111, 17985–17988 (2007). [CrossRef]
  12. G. A. Wurtz, P. R. Evans, W. Hendren, R. Atkinson, W. Dickson, R. J. Pollard, A. V. Zayats, W. Harrison, and C. Bower, “Molecular plasmonics with tunable exciton-plasmon coupling strength in J-aggregate hybridized Au nanorod assemblies,” Nano Lett. 7, 1297–1303 (2007). [CrossRef] [PubMed]
  13. A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nature Mater. 8, 867–871 (2009). [CrossRef]
  14. P. R. Evans, G. A. Wurtz, W. R. Hendren, R. Atkinson, W. Dickson, A. V. Zayats, and R. J. Pollard, “Electrically switchable nonreciprocal transmission of plasmonic nanorods with liquid crystal,” Appl. Phys. Lett. 91, 043101 (2007). [CrossRef]
  15. J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321, 930 (2008). [CrossRef] [PubMed]
  16. C. Tserkezis, N. Papanikolaou, E. Almpanis, and N. Stefanou, “Tailoring plasmons with metallic nanorod arrays,” Phys. Rev. B 80, 125124 (2009). [CrossRef]
  17. R. C. McPhedran and D. R. McKenzie, “Electrostatic and optical resonances of arrays of cylinders,” Appl. Phys. A 23, 223–235 (1980).
  18. A. Pokrovsky and A. Efros, “Nonlocal electrodynamics of two-dimensional wire mesh photonic crystals,” Phys. Rev. B 65, 045110 (2002). [CrossRef]
  19. J. Pitarke, J. Inglesfield, and N. Giannakis, “Surface-plasmon polaritons in a lattice of metal cylinders,” Phys. Rev. B 75, 165415 (2007). [CrossRef]
  20. A. Andersson, O. Hunderi, and C. G. Granqvist, “Nickel pigmented anodic aluminum oxide for selective absorption of solar energy,” J. Appl. Phys. 51, 754–764 (1980). [CrossRef]
  21. C. A. Foss, G. L. Hornyak, J. A. Stockert, and C. R. Martin, “Template-synthesized nanoscopic gold particles: optical spectra and the effects of particle size and shape,” J. Phys. Chem. 98, 2963–2971 (1994). [CrossRef]
  22. Y. Liu, G. Bartal, and X. Zhang, “All-angle negative refraction and imaging in a bulk medium made of metallic nanowires in the visible region,” Opt. Express 16, 15439–15448 (2008). [CrossRef] [PubMed]
  23. W. Lu and S. Sridhar, “Superlens imaging theory for anisotropic nanostructured metamaterials with broadband all-angle negative refraction,” Phys. Rev. B 77, 233101 (2008). [CrossRef]
  24. A. I. Rahachou and I. V. Zozoulenko, “Light propagation in nanorod arrays,” J. Opt. A, Pure Appl. Opt. 9, 265–270 (2007). [CrossRef]
  25. T. Yamaguchi, S. Yoshida, and A. Kinbara, “Optical effect of the substrate on the anomalous absorption of aggregated silver films,” Thin Solid Films 21, 173–187 (1974). [CrossRef]
  26. A. Wokaun, “Surface enhancement of optical fields,” Mol. Phys. 56, 1–33 (1985). [CrossRef]
  27. M. Meier, A. Wokaun, and P. F. Liao, “Enhanced fields on rough surfaces: dipolar interactions among particles of sizes exceeding the Rayleigh limit,” J. Opt. Soc. Am. B 2, 931–949 (1985). [CrossRef]
  28. S. Camelio, D. Babonneau, D. Lantiat, L. Simonot, and F. Pailloux, “Anisotropic optical properties of silver nanoparticle arrays on rippled dielectric surfaces produced by low-energy ion erosion,” Phys. Rev. B 80, 155434 (2009). [CrossRef]
  29. 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. B 107, 7343–7350 (2003). [CrossRef]
  30. B. N. Khlebtsov, V. A. Khanadeyev, and N. G. Khlebtsov, “Collective plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Opt. Spectrosc. 104, 282–294 (2008). [CrossRef]
  31. B. Auguié and W. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101, 143902 (2008). [CrossRef] [PubMed]
  32. S. Biring, H. H. Wang, J. K. Wang, and Y. L. Wang, “Light scattering from 2D arrays of monodispersed Ag-nanoparticles separated by tunable nano-gaps: spectral evolution and analytical analysis of plasmonic coupling,” Opt. Express 16, 15312–15324 (2008). [CrossRef] [PubMed]
  33. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998). [CrossRef]
  34. P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]
  35. A. Vial, A. Grimault, D. Macías, D. Barchiesi, and M. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005). [CrossRef]
  36. P. Evans, W. R. Hendren, R. Atkinson, G. A. Wurtz, W. Dickson, A. V. Zayats, and R. J. Pollard, “Growth and properties of gold and nickel nanorods in thin film alumina,” Nanotechnology 17, 5746–5753 (2006). [CrossRef]
  37. H. Kuwata, H. Tamaru, K. Esumi, and K. Miyano, “Resonant light scattering from metal nanoparticles: practical analysis beyond Rayleigh approximation,” Appl. Phys. Lett. 83, 4625–4627 (2003). [CrossRef]
  38. M. Meier and A. Wokaun, “Enhanced fields on large metal particles: dynamic depolarization,” Opt. Lett. 8, 581–583 (1983). [CrossRef] [PubMed]
  39. A. Moroz, “Depolarization field of spheroidal particles,” J. Opt. Soc. Am. B 26, 517–527 (2009). [CrossRef]
  40. B. N. Khlebtsov, A. Melnikov, and N. G. Khlebtsov, “On the extinction multipole plasmons in gold nanorods,” J. Quant. Spectrosc. Radiat. Transf. 107, 306–314 (2007). [CrossRef]

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