Abstract

We explore the optical response of two-dimensional (2D) arrays of silver nanoparticles, focussing our attention on structures for which the individual particles in isolation support both dipolar and quadrupolar localised surface plasmon modes. For individual spheres we show that when dipolar and quadrupolar modes are excited simultaneously, interference leads to most of the scattered light being radiated in the forward direction. This is in contrast to what happens when each mode is excited on its own. We further show, using finite-element modelling that when such particles are assembled into square 2D arrays, the dipolar and quadrupolar modes can combine to produce a single peak in the optical density of the array. By simulating the field distributions associated with these modes we are able to illustrate the dual-mode character of this feature in the optical density. We have extended our examination of this effect by considering how the optical density of these arrays changes with incident angle for two polarisations (s and p).

© 2010 OSA

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2009

G. Vecchi, V. Giannini, and J. Gómez Rivas, “Shaping the Fluorescent Emission by Lattice Resonances in Plasmonic Crystals of Nanoantennas,” Phys. Rev. Lett. 102(14), 146807 (2009).
[CrossRef] [PubMed]

2008

Y. Z. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93(18), 181108 (2008).
[CrossRef]

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
[CrossRef]

F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry Breaking in Plasmonic Nanocavities: Subradiant LSPR Sensing and a Tunable Fano Resonance,” Nano Lett. 8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77(3), 035440 (2008).
[CrossRef]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[CrossRef] [PubMed]

2007

W. A. Murray and W. L. Barnes, “Plasmonic materials,” Adv. Mater. 19(22), 3771–3782 (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(5), 1297–1303 (2007).
[CrossRef] [PubMed]

F. J. G. de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
[CrossRef]

2005

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
[CrossRef] [PubMed]

D. V. Vezenov, B. T. Mayers, D. B. Wolfe, and G. M. Whitesides, “Integrated fluorescent light source for optofluidic applications,” Appl. Phys. Lett. 86(4), 041104 (2005).
[CrossRef]

2004

K. Lindfors, T. Kalkbrenner, P. Stoller, and V. Sandoghdar, “Detection and spectroscopy of gold nanoparticles using supercontinuum white light confocal microscopy,” Phys. Rev. Lett. 93(3), 037401 (2004).
[CrossRef] [PubMed]

E. Hutter and J. H. Fendler, “Exploitation of localized surface plasmon resonance,” Adv. Mater. 16(19), 1685–1706 (2004).
[CrossRef]

S. L. 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]

2003

C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: The importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107(30), 7337–7342 (2003).
[CrossRef]

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

S. Malynych and G. Chumanov, “Light-induced coherent interactions between silver nanoparticles in two-dimensional arrays,” J. Am. Chem. Soc. 125(10), 2896–2898 (2003).
[CrossRef] [PubMed]

1999

S. J. Oldenburg, G. D. Hale, J. B. Jackson, and N. J. Halas, “Light scattering from dipole and quadrupole nanoshell antennas,” Appl. Phys. Lett. 75(8), 1063–1065 (1999).
[CrossRef]

1980

1908

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 330(3), 377–445 (1908).
[CrossRef]

Atkinson, R.

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(5), 1297–1303 (2007).
[CrossRef] [PubMed]

Aussenegg, F. R.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

Barnes, W. L.

W. A. Murray and W. L. Barnes, “Plasmonic materials,” Adv. Mater. 19(22), 3771–3782 (2007).
[CrossRef]

Borghs, G.

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77(3), 035440 (2008).
[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(5), 1297–1303 (2007).
[CrossRef] [PubMed]

Chu, Y. Z.

Y. Z. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93(18), 181108 (2008).
[CrossRef]

Chumanov, G.

S. Malynych and G. Chumanov, “Light-induced coherent interactions between silver nanoparticles in two-dimensional arrays,” J. Am. Chem. Soc. 125(10), 2896–2898 (2003).
[CrossRef] [PubMed]

Crozier, K. B.

Y. Z. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93(18), 181108 (2008).
[CrossRef]

de Abajo, F. J. G.

F. J. G. de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
[CrossRef]

Dickson, W.

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(5), 1297–1303 (2007).
[CrossRef] [PubMed]

Evans, P. R.

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(5), 1297–1303 (2007).
[CrossRef] [PubMed]

Fedotov, V. A.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
[CrossRef]

Fendler, J. H.

E. Hutter and J. H. Fendler, “Exploitation of localized surface plasmon resonance,” Adv. Mater. 16(19), 1685–1706 (2004).
[CrossRef]

Firsov, A. A.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Geim, A. K.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Genov, D. A.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[CrossRef] [PubMed]

Giannini, V.

G. Vecchi, V. Giannini, and J. Gómez Rivas, “Shaping the Fluorescent Emission by Lattice Resonances in Plasmonic Crystals of Nanoantennas,” Phys. Rev. Lett. 102(14), 146807 (2009).
[CrossRef] [PubMed]

Gleeson, H. F.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Gómez Rivas, J.

G. Vecchi, V. Giannini, and J. Gómez Rivas, “Shaping the Fluorescent Emission by Lattice Resonances in Plasmonic Crystals of Nanoantennas,” Phys. Rev. Lett. 102(14), 146807 (2009).
[CrossRef] [PubMed]

Grigorenko, A. N.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Gunnarsson, L.

C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: The importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107(30), 7337–7342 (2003).
[CrossRef]

Halas, N. J.

F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry Breaking in Plasmonic Nanocavities: Subradiant LSPR Sensing and a Tunable Fano Resonance,” Nano Lett. 8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

S. J. Oldenburg, G. D. Hale, J. B. Jackson, and N. J. Halas, “Light scattering from dipole and quadrupole nanoshell antennas,” Appl. Phys. Lett. 75(8), 1063–1065 (1999).
[CrossRef]

Hale, G. D.

S. J. Oldenburg, G. D. Hale, J. B. Jackson, and N. J. Halas, “Light scattering from dipole and quadrupole nanoshell antennas,” Appl. Phys. Lett. 75(8), 1063–1065 (1999).
[CrossRef]

Hao, F.

F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry Breaking in Plasmonic Nanocavities: Subradiant LSPR Sensing and a Tunable Fano Resonance,” Nano Lett. 8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

Harrison, W.

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(5), 1297–1303 (2007).
[CrossRef] [PubMed]

Haynes, C. L.

C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: The importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107(30), 7337–7342 (2003).
[CrossRef]

Hendren, W.

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(5), 1297–1303 (2007).
[CrossRef] [PubMed]

Hohenau, A.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

Hutter, E.

E. Hutter and J. H. Fendler, “Exploitation of localized surface plasmon resonance,” Adv. Mater. 16(19), 1685–1706 (2004).
[CrossRef]

Jackson, J. B.

S. J. Oldenburg, G. D. Hale, J. B. Jackson, and N. J. Halas, “Light scattering from dipole and quadrupole nanoshell antennas,” Appl. Phys. Lett. 75(8), 1063–1065 (1999).
[CrossRef]

Kalkbrenner, T.

K. Lindfors, T. Kalkbrenner, P. Stoller, and V. Sandoghdar, “Detection and spectroscopy of gold nanoparticles using supercontinuum white light confocal microscopy,” Phys. Rev. Lett. 93(3), 037401 (2004).
[CrossRef] [PubMed]

Kall, M.

C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: The importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107(30), 7337–7342 (2003).
[CrossRef]

Kasemo, B.

C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: The importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107(30), 7337–7342 (2003).
[CrossRef]

Khanadeyev, V. A.

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77(3), 035440 (2008).
[CrossRef]

Khlebtsov, B. N.

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77(3), 035440 (2008).
[CrossRef]

Khlebtsov, N. G.

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77(3), 035440 (2008).
[CrossRef]

Khrushchev, I. Y.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Krenn, J. R.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

Lamprecht, B.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

Leitner, A.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

Lindfors, K.

K. Lindfors, T. Kalkbrenner, P. Stoller, and V. Sandoghdar, “Detection and spectroscopy of gold nanoparticles using supercontinuum white light confocal microscopy,” Phys. Rev. Lett. 93(3), 037401 (2004).
[CrossRef] [PubMed]

Liu, M.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[CrossRef] [PubMed]

Mackowski, D. W.

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77(3), 035440 (2008).
[CrossRef]

Maier, S. A.

F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry Breaking in Plasmonic Nanocavities: Subradiant LSPR Sensing and a Tunable Fano Resonance,” Nano Lett. 8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

Malynych, S.

S. Malynych and G. Chumanov, “Light-induced coherent interactions between silver nanoparticles in two-dimensional arrays,” J. Am. Chem. Soc. 125(10), 2896–2898 (2003).
[CrossRef] [PubMed]

Mayers, B. T.

D. V. Vezenov, B. T. Mayers, D. B. Wolfe, and G. M. Whitesides, “Integrated fluorescent light source for optofluidic applications,” Appl. Phys. Lett. 86(4), 041104 (2005).
[CrossRef]

McFarland, A. D.

C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: The importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107(30), 7337–7342 (2003).
[CrossRef]

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 330(3), 377–445 (1908).
[CrossRef]

Murray, W. A.

W. A. Murray and W. L. Barnes, “Plasmonic materials,” Adv. Mater. 19(22), 3771–3782 (2007).
[CrossRef]

Nordlander, P.

F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry Breaking in Plasmonic Nanocavities: Subradiant LSPR Sensing and a Tunable Fano Resonance,” Nano Lett. 8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

Oldenburg, S. J.

S. J. Oldenburg, G. D. Hale, J. B. Jackson, and N. J. Halas, “Light scattering from dipole and quadrupole nanoshell antennas,” Appl. Phys. Lett. 75(8), 1063–1065 (1999).
[CrossRef]

Papasimakis, N.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
[CrossRef]

Petrovic, J.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Pollard, R. J.

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(5), 1297–1303 (2007).
[CrossRef] [PubMed]

Prikulis, J.

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N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
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[CrossRef]

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K. Lindfors, T. Kalkbrenner, P. Stoller, and V. Sandoghdar, “Detection and spectroscopy of gold nanoparticles using supercontinuum white light confocal microscopy,” Phys. Rev. Lett. 93(3), 037401 (2004).
[CrossRef] [PubMed]

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S. L. 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]

C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: The importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107(30), 7337–7342 (2003).
[CrossRef]

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F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry Breaking in Plasmonic Nanocavities: Subradiant LSPR Sensing and a Tunable Fano Resonance,” Nano Lett. 8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

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K. Lindfors, T. Kalkbrenner, P. Stoller, and V. Sandoghdar, “Detection and spectroscopy of gold nanoparticles using supercontinuum white light confocal microscopy,” Phys. Rev. Lett. 93(3), 037401 (2004).
[CrossRef] [PubMed]

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F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry Breaking in Plasmonic Nanocavities: Subradiant LSPR Sensing and a Tunable Fano Resonance,” Nano Lett. 8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

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C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: The importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107(30), 7337–7342 (2003).
[CrossRef]

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G. Vecchi, V. Giannini, and J. Gómez Rivas, “Shaping the Fluorescent Emission by Lattice Resonances in Plasmonic Crystals of Nanoantennas,” Phys. Rev. Lett. 102(14), 146807 (2009).
[CrossRef] [PubMed]

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D. V. Vezenov, B. T. Mayers, D. B. Wolfe, and G. M. Whitesides, “Integrated fluorescent light source for optofluidic applications,” Appl. Phys. Lett. 86(4), 041104 (2005).
[CrossRef]

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S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[CrossRef] [PubMed]

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D. V. Vezenov, B. T. Mayers, D. B. Wolfe, and G. M. Whitesides, “Integrated fluorescent light source for optofluidic applications,” Appl. Phys. Lett. 86(4), 041104 (2005).
[CrossRef]

Wiscombe, W. J.

Wolfe, D. B.

D. V. Vezenov, B. T. Mayers, D. B. Wolfe, and G. M. Whitesides, “Integrated fluorescent light source for optofluidic applications,” Appl. Phys. Lett. 86(4), 041104 (2005).
[CrossRef]

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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(5), 1297–1303 (2007).
[CrossRef] [PubMed]

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Y. Z. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93(18), 181108 (2008).
[CrossRef]

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B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77(3), 035440 (2008).
[CrossRef]

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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(5), 1297–1303 (2007).
[CrossRef] [PubMed]

Zhang, S.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[CrossRef] [PubMed]

Zhang, X.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[CrossRef] [PubMed]

Zhang, Y.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Zhao, L. L.

C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: The importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107(30), 7337–7342 (2003).
[CrossRef]

Zheludev, N. I.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
[CrossRef]

Zou, S. L.

S. L. 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]

Adv. Mater.

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D. V. Vezenov, B. T. Mayers, D. B. Wolfe, and G. M. Whitesides, “Integrated fluorescent light source for optofluidic applications,” Appl. Phys. Lett. 86(4), 041104 (2005).
[CrossRef]

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[CrossRef]

J. Am. Chem. Soc.

S. Malynych and G. Chumanov, “Light-induced coherent interactions between silver nanoparticles in two-dimensional arrays,” J. Am. Chem. Soc. 125(10), 2896–2898 (2003).
[CrossRef] [PubMed]

J. Chem. Phys.

S. L. 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]

J. Phys. Chem. B

C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Kall, “Nanoparticle optics: The importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107(30), 7337–7342 (2003).
[CrossRef]

Nano Lett.

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(5), 1297–1303 (2007).
[CrossRef] [PubMed]

F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry Breaking in Plasmonic Nanocavities: Subradiant LSPR Sensing and a Tunable Fano Resonance,” Nano Lett. 8(11), 3983–3988 (2008).
[CrossRef] [PubMed]

Nat. Photonics

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
[CrossRef]

Nature

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Opt. Commun.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

Phys. Rev. B

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77(3), 035440 (2008).
[CrossRef]

Phys. Rev. Lett.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[CrossRef] [PubMed]

G. Vecchi, V. Giannini, and J. Gómez Rivas, “Shaping the Fluorescent Emission by Lattice Resonances in Plasmonic Crystals of Nanoantennas,” Phys. Rev. Lett. 102(14), 146807 (2009).
[CrossRef] [PubMed]

K. Lindfors, T. Kalkbrenner, P. Stoller, and V. Sandoghdar, “Detection and spectroscopy of gold nanoparticles using supercontinuum white light confocal microscopy,” Phys. Rev. Lett. 93(3), 037401 (2004).
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Supplementary Material (4)

» Media 1: AVI (1745 KB)     
» Media 2: AVI (1818 KB)     
» Media 3: AVI (1749 KB)     
» Media 4: AVI (1720 KB)     

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Figures (7)

Fig. 1
Fig. 1

Spectra calculated using Mie theory showing the extinction and scattering efficiencies of a 100 nm diameter silver sphere surrounded by glass (n=1.5). Permittivity values for silver were taken from the literature [15] and interpolated with a spline fit. The spectral features of the dipolar and quadrupolar modes are at 548 nm and 427 nm respectively. Also shown are the sets of spectra obtained when the calculation is carried out but only considering single modes – the dipole in red or the quadrupole in blue. Additional features in the spectra below 400 nm arise from fluctuations in the permittivity values and are not plasmonic effects.

Fig. 2
Fig. 2

Far-field scattered intensity profiles calculated from Mie theory for a 100 nm diameter silver sphere surrounded by glass. The relative scattering intensity is shown for (a) a pure dipolar mode, (b) a pure quadrupolar mode and (c) the quadrupole frequency with contributions from all modes included. The colour-scale of each plot is normalised so that the maximum scattered intensity is unity for each.

Fig. 3
Fig. 3

A schematic showing a small portion of an infinite square array of metal nanoparticles such as those considered in this study. The directions associated with normally incident light are indicated (left), as well as the directions for p-polarised light at oblique incidence to the array (right).

Fig. 4
Fig. 4

Optical density spectra of infinite square arrays of silver nanospheres (100 nm diameter) surrounded by glass for a range of array periods as calculated using a finite-element method (see Appendix 2). The arrays with the largest periods show two clear features, those of the dipolar and the quadrupolar modes. Closer separations show just one peak corresponding to the dual-mode resonance. The features below 375 nm are mainly due to diffraction effects.

Fig. 5
Fig. 5

Simulated electric field profiles for infinite square arrays of 100 nm diameter silver spheres in glass. Shown in each plot is the magnitude of the real part of the total electric field in the glass surrounding the sphere at a single phase in the x-z plane, and arrows showing the direction and strength of the total electric field inside the sphere. These plots are for (a) a 255 nm period array calculated at a wavelength of 500 nm, corresponding to the dipolar mode (Media 1), (b) 255 nm period at a wavelength of 428 nm, corresponding to the quadrupolar mode (Media 2), and (c) a 185 nm period at a wavelength of 436 nm, corresponding to the single spectral feature of the short-period system (Media 3). (c) shows the instantaneous electric field profile for two different phases separated by 180°.

Fig. 6
Fig. 6

Simulated electric field profiles for infinite square arrays of 100 nm diameter silver spheres in glass. Shown in each plot is the magnitude of the real part of the total electric field in the glass surrounding the sphere out to the limits of the unit cell, and arrows showing the direction and strength of the total electric field inside the sphere in the x-y plane. These plots are for a 185 nm period at a wavelength of 436 nm, corresponding to the single spectral feature of the short-period system at two different phases of the optical cycle separated by 180° ((a) and (b)). An animation of the complete optical cycle is shown in Media 4.

Fig. 7
Fig. 7

Optical density of a square array of 100 nm diameter silver nanospheres embedded in PDMS (n=1.41) for a range of incident angles as calculated by finite element modelling for both p- and s-polarised light ((a) and (b) repectively). When the light is p-polarised, there is significant radiative coupling between neighbouring particles which keeps the frequency of the dipolar mode blue-shifted relative to the single-particle case. For s-polarised light, there is significantly less interparticle coupling due to the phase retardation of incident light across the array. This effect is more significant at higher angles, and the two peaks corresponding to the dipole and quadrupolar modes are recovered.

Equations (2)

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E θ E 0 e i k r i k r cos φ n 2 n + 1 n ( n + 1 ) ( a n d P n 1 d θ + b n P n 1 sin θ )
E φ E 0 e i k r i k r sin φ n 2 n + 1 n ( n + 1 ) ( a n P n 1 sin θ + b n d P n 1 d θ )

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