Abstract

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

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [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).
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    [CrossRef]

2009 (4)

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]

C. Tserkezis, N. Papanikolaou, E. Almpanis, and N. Stefanou, “Tailoring plasmons with metallic nanorod arrays,” Phys. Rev. B 80, 125124 (2009).
[CrossRef]

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]

A. Moroz, “Depolarization field of spheroidal particles,” J. Opt. Soc. Am. B 26, 517–527 (2009).
[CrossRef]

2008 (10)

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]

B. Auguié and W. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101, 143902 (2008).
[CrossRef] [PubMed]

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]

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]

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]

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]

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]

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]

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]

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]

2007 (9)

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]

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]

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007).
[CrossRef] [PubMed]

K. A. Willets and R. P. van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Annu. Rev. Phys. Chem. 58, 267–297 (2007).
[CrossRef]

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]

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]

J. Pitarke, J. Inglesfield, and N. Giannakis, “Surface-plasmon polaritons in a lattice of metal cylinders,” Phys. Rev. B 75, 165415 (2007).
[CrossRef]

A. I. Rahachou and I. V. Zozoulenko, “Light propagation in nanorod arrays,” J. Opt. A, Pure Appl. Opt. 9, 265–270 (2007).
[CrossRef]

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]

2006 (3)

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]

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]

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313, 1595 (2006).
[CrossRef] [PubMed]

2005 (1)

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]

2003 (2)

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]

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]

2002 (1)

A. Pokrovsky and A. Efros, “Nonlocal electrodynamics of two-dimensional wire mesh photonic crystals,” Phys. Rev. B 65, 045110 (2002).
[CrossRef]

1998 (2)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

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]

1994 (1)

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]

1985 (2)

1983 (1)

1980 (2)

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]

R. C. McPhedran and D. R. McKenzie, “Electrostatic and optical resonances of arrays of cylinders,” Appl. Phys. A 23, 223–235 (1980).

1974 (1)

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]

1972 (1)

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Alaverdyan, Y.

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]

Almpanis, E.

C. Tserkezis, N. Papanikolaou, E. Almpanis, and N. Stefanou, “Tailoring plasmons with metallic nanorod arrays,” Phys. Rev. B 80, 125124 (2009).
[CrossRef]

Andersson, A.

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]

Atkinson, R.

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]

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]

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]

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]

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]

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]

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]

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]

Auguié, B.

B. Auguié and W. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101, 143902 (2008).
[CrossRef] [PubMed]

Babonneau, D.

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]

Barchiesi, D.

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]

Barnes, W.

B. Auguié and W. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101, 143902 (2008).
[CrossRef] [PubMed]

Barnes, W. L.

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]

Bartal, G.

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]

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]

Biring, S.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

Bower, C.

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]

Camelio, S.

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]

Christy, R.

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

de la Chapelle, M.

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]

Dickson, W.

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]

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]

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]

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]

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]

Ebbesen, T. W.

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]

Efros, A.

A. Pokrovsky and A. Efros, “Nonlocal electrodynamics of two-dimensional wire mesh photonic crystals,” Phys. Rev. B 65, 045110 (2002).
[CrossRef]

Eng, L. M.

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]

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]

Esumi, K.

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]

Evans, P.

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]

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).
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[CrossRef]

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]

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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).
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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).
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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).
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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).
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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).
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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]

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]

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).
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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).
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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).
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T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313, 1595 (2006).
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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).
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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).
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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).
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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).
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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).
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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).
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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).
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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).
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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).
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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).
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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).
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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).
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Pailloux, F.

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).
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C. Tserkezis, N. Papanikolaou, E. Almpanis, and N. Stefanou, “Tailoring plasmons with metallic nanorod arrays,” Phys. Rev. B 80, 125124 (2009).
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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).
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J. Pitarke, J. Inglesfield, and N. Giannakis, “Surface-plasmon polaritons in a lattice of metal cylinders,” Phys. Rev. B 75, 165415 (2007).
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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).
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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).
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[CrossRef]

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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).
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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]

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).
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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]

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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).
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T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313, 1595 (2006).
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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).
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C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007).
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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]

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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).
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C. Tserkezis, N. Papanikolaou, E. Almpanis, and N. Stefanou, “Tailoring plasmons with metallic nanorod arrays,” Phys. Rev. B 80, 125124 (2009).
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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).
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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]

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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]

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T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313, 1595 (2006).
[CrossRef] [PubMed]

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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]

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C. Tserkezis, N. Papanikolaou, E. Almpanis, and N. Stefanou, “Tailoring plasmons with metallic nanorod arrays,” Phys. Rev. B 80, 125124 (2009).
[CrossRef]

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T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313, 1595 (2006).
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Wang, J. K.

Wang, Y.

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).
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C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007).
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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).
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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]

Wurtz, G.

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]

Wurtz, G. A.

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]

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]

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Figures (9)

Fig. 1
Fig. 1

Perspective and top views of a quadratic spheroid array having a radius of three particles. Note that the center particle is omitted here.

Fig. 2
Fig. 2

Comparison of the extinction between (a) MMP and (b) DIM for a gold spheroid array ( h = 100   nm , 2 R = 20   nm , β = 45 ° , air). The interparticle distance is varied from 200 to 50 nm as indicated.

Fig. 3
Fig. 3

Visualization of the geometrical factor: The resonance condition [Eq. (6)] is fulfilled where the arrow hits the dielectric function of the metal. Hence, the smaller L, the larger the resonance wavelength. Inset: Comparison of C ̂ z to L z ( β = 45 ° in percent). From C ̂ z > 0 follows L eff , z > L z such that the resonance wavelength blueshifts. Parameters: d = 60   nm , 2 R = 20   nm , and h = 100   nm ( L z = 0.055 821 ) .

Fig. 4
Fig. 4

Influence of the diameter 2 R on the resonance wavelength. (a) Resonance spectra depending on the diameter for different distances, calculated with the analytical model (AAO, n = 1.5 ). (b) Extinction measurements of nanorod structures in AAO with diameters ranging from 24 to 40 nm as indicated ( d = 70   nm , h 300   nm , β = 40 ° ). The resulting resonance wavelengths are marked as crosses in (a) and agree qualitatively with the calculations despite the different geometries.

Fig. 5
Fig. 5

Influence of the length on the LSPR wavelength. (a) Resonance shift versus length for different distances, calculated with the analytical model ( n = 1.0 ) . (b) Measured extinction spectra of structures with lengths ranging from 240 to 400 nm ( β = 30 ° ) .

Fig. 6
Fig. 6

AOI dependence of the extinction peak shown for an array of Au spheroids ( h = 100   nm , 2 R = 20   nm , d = 60   nm , air). As indicated, β is varied between 0° and 75° and the spectrum of a single particle is plotted for comparison (at β = 90 ° ; not to scale).

Fig. 7
Fig. 7

The complex sum C z plotted for (a) β = 20 ° and (b),(c) 60°. The influence of the arrangement (hexagonal or quadratic) and of the azimuthal angle [small deviations in (c)] are shown. Note that for λ / d > 2.5 the azimuthal angle has a negligible influence, and only for large β or small λ / d the imaginary part becomes significant.

Fig. 8
Fig. 8

MMP results of nanorod arrays showing negative flux. (a) A plane wave hits the nanorod array under an angle of β = 25 ° . The phase-resolved field plot of the Poynting vector S shows wave fronts inside the array that have a negative slope. (b) Map of S x normalized with respect to the free-space flux ( S x 0 = 1 ) for various AOIs and wavelengths. Values of S x < 0 indicate negative and values > 1 indicate extraordinary positive flux.

Fig. 9
Fig. 9

Negative refraction in a Au spheroid array ( h = 100   nm , 2 R = 20   nm , d = 60   nm , n = 1.5 ). Top row: Extinction of the array and of an isolated particle (not to scale) for different β’s (5°, 20°, and 60°). Bottom row: The angle of the Poynting vector inside the structure, β S , indicates regions of negative and extraordinary positive refraction. For comparison, the incident angle β is plotted as well as the phase of f z .

Equations (30)

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α array , x = α x y 1 C x α x y ,     α array , z = α z 1 C z α z ,
C x = 1 d 3 j 0 e i ( k ̃ r ̃ j + ϕ ̃ j ) r ̃ j 3 { k ̃ 2 [ r ̃ j 2 x ̃ j 2 ] + 1 i k ̃ r ̃ j r ̃ j 2 [ 3 x ̃ j 2 r ̃ j 2 ] } ,
C z = 1 d 3 j 0 e i ( k ̃ r ̃ j + ϕ ̃ j ) r ̃ j 3 { k ̃ 2 r ̃ j 2 + i k ̃ r ̃ j 1 } ,
σ ext = 4 π k [ cos   β α array , x ] 2 + [ sin   β α array , z ] 2 ,
σ ext , single = 4 π k I ( α single , z ) ,
α single , z = R 2 h 2 ϵ m ϵ d 3 ϵ d + 3 L z ( ϵ m ϵ d ) ,
ϵ m = ( 1 1 L z ) ϵ d
α array , z = R 2 h 2 ϵ m ϵ d 3 ϵ d + 3 L eff , z ( ϵ m ϵ d ) ,
L eff , z = L z + R 2 h 6 ( C z ) L z + C ̂ z .
ϵ m = ( 1 1 L eff , z ) ϵ d + L eff , z L eff , z ϵ m ,
L eff , z = 2 R 3 h + R 2 h 6 ( C z ) .
ω res = ω p 2 ϵ c Γ 2 ,     ϵ c ( 1 L eff , z 1 ) ϵ d + ϵ .
σ ext sin   β α array , z ( β ) .
β S = arctan ( Re { f z   sin   β ( ϵ D y α array , z   sin   β ) } Re { f x   cos   β ( ϵ D y α array , z   sin   β ) } ) ,
f x / z = 1 1 C x / z α x y / z = α array , x / z α x y / z .
β S arctan ( f z   sin   β f x   cos   β ) .
α ̂ = ( α x y 0 0 0 α x y 0 0 0 α z ) .
ϕ = 2 π λ sin   β x .
E loc ( r i ) = E 0 e i k r i + j i e i k r i j r i j 3 { k 2 r i j × ( P j × r i j ) + 1 i k r i j r i j 2 [ 3 r i j ( r i j P j ) r i j 2 P j ] } ,
E loc , 0 = E 0 + j 0 e i k r j r j 3 { k 2 [ r j 2 P j r j ( r j P j ) ] + 1 i k r j r j 2 [ 3 r j ( r j P j ) r j 2 P j ] } .
( E loc , 0 , x 0 E loc , 0 , z ) = ( E 0 , x 0 E 0 , z ) + j 0 e i k r j r j 3 { k 2 [ r j 2 Δ Λ ] + 1 i k r j r j 2 [ 3 Λ r j 2 Δ ] } ,
Δ = ( α x y E loc , j , x 0 α z E loc , j , z ) ,     Λ = ( x j y j 0 ) x j α x y E loc , j , x .
( E loc , x 0 E loc , z ) = ( E 0 , x 0 E 0 , z ) + ( C x α x y E loc , x 0 C z α z E loc , z ) ,
P x / z = α x y / z E loc , x / z = α x y / z 1 C x / z α x y / z E x 0 / z 0 α array , x y / z E x 0 / z 0 ,
E x / z = 1 1 C x / z α x y / z E x 0 / z 0 f x / z E x 0 / z 0 .
H = H 0 + H D ,
H 0 = ϵ k ̂ × E 0 = ϵ ( k ̂ z E x 0 k ̂ x E z 0 ) e y = ϵ ( cos 2 β + sin 2 β ) E 0 e y = ϵ E 0 e y
H D = j 0 e i k r j r j 2 k 2 { 1 + i k r j } r j × P j = 1 d 3 j 0 e i ( k ̃ r ̃ j + ϕ ̃ j ) r ̃ j 3 { k ̃ 2 r ̃ j + i k ̃ } x ̃ j α array , z E z 0 e y D y α array , z ( sin   β ) E 0 e y .
S = c 8 π Re { ( f z   sin   β 0 f x   cos   β ) ( ϵ D y α array , z   sin   β ) } | E 0 | 2 ,
β S = arctan ( S x S z ) = arctan ( Re { f z   sin   β ( ϵ D y α array , z   sin   β ) } Re { f x   cos   β ( ϵ D y α array , z   sin   β ) } ) arctan ( Re { f z   sin   β } Re { f x   cos   β } ) ,

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