Abstract

We report a semi-analytical model for calculating the coupling effects between the dipolar surface plasmon nanoparticles of a periodic structure. This model involves real-valued frequencies only and is therefore applicable to periodic structures with arbitrary dipolar units and environments.

© 2008 Optical Society of America

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  1. M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, "Electromagnetic energy transport via linear chains of silver nanoparticles," Opt. Lett. 23, 1331-1333 (1998).
    [CrossRef]
  2. M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B 62, R16356-16359 (2000).
    [CrossRef]
  3. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nature Mater. 2, 229-232 (2003).
    [CrossRef]
  4. N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, "Optimized surface-enhanced Raman scattering on gold nanoparticle arrays," Appl. Phys. Lett. 82, 3095-3097 (2003).
    [CrossRef]
  5. J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, and J. P. Goudonnet, "Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles," Phys. Rev. Lett. 82, 2590-2593 (1999).
    [CrossRef]
  6. B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, "Metal Nanoparticle Gratings: Influence of Dipolar Particle Interaction on the Plasmon Resonance," Phys. Rev. Lett. 84, 4721-4724 (2000).
    [CrossRef] [PubMed]
  7. S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, "Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy," Phys. Rev. B 65, 193408 (2002).
    [CrossRef]
  8. S. A. Maier, P. G. Kik, and H. A. Atwater, "Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss," Appl. Phys. Lett. 81, 1714-1716 (2002).
    [CrossRef]
  9. Q.-H. Wei, K.-H. Su, S. Durant, and X. Zhang, "Plasmon Resonance of Finite One-Dimensional Au Nanoparticle Chains," Nano Lett. 4, 1067-1071 (2004).
    [CrossRef]
  10. C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. J. Kall, "Nanoparticle Optics: The Importance of Radiative Dipole Coupling in Two-Dimensional Nanoparticle Arrays," Phys. Chem. B 107, 7337-7342 (2003).
    [CrossRef]
  11. S. Zou, N. Janel, and G. C. Schatz, "Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes," J. Chem. Phys. 120, 10871-10875 (2004).
    [CrossRef] [PubMed]
  12. E. M. Hicks, S. Zou, G. C. Schatz; K. G. Spears, R. P. V. Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, "Controlling Plasmon Line Shapes through Diffractive Coupling in Linear Arrays of Cylindrical Nanoparticles Fabricated by Electron Beam Lithography," Nano Lett. 5, 1065-1070 (2005).
    [CrossRef] [PubMed]
  13. F. J. García de Abajo, "Colloquium: Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007).
    [CrossRef]
  14. W. H. Weber, and G. W. Ford, "Propagation of optical excitations by dipolar interactions in metal nanoparticle chains," Phys. Rev. B 70, 125429 (2004).
    [CrossRef]
  15. S. Y. Park, and D. Stroud, "Surface-plasmon dispersion relations in chains of metallic nanoparticles: An exact quasistatic calculation," Phys. Rev. B 69, 125418 (2004).
    [CrossRef]
  16. A. F. Koenderink, and A. Polman, "Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains," Phys. Rev. B 74, 033402 (2006).
    [CrossRef]
  17. A. F. Koenderink, R. de Waele, J. C. Prangsma, and A. Polman, "Experimental evidence for large dynamic effects on the plasmon dispersion of subwavelength metal nanoparticle waveguides," Phys. Rev. B 76, 201403 (R) (2007).
    [CrossRef]
  18. T. Yang, and K. B. Crozier, "Dispersion and Extinction of Surface Plasmons in Gold Nanoparticle Chains: Influence of the Air/Glass Interface," Opt. Express 16, 8570-8580.
    [PubMed]
  19. K. B. Crozier, E. Togan, E. Simsek, and T. Yang, "Experimental measurement of the dispersion relations of the surface plasmon modes of metal nanoparticle chains," Opt. Express 15, 17482-17493 (2007).
    [CrossRef] [PubMed]
  20. Think of a plane wave propagating in z direction. It has an infinite d�?/dkx value.

2007 (3)

F. J. García de Abajo, "Colloquium: Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007).
[CrossRef]

A. F. Koenderink, R. de Waele, J. C. Prangsma, and A. Polman, "Experimental evidence for large dynamic effects on the plasmon dispersion of subwavelength metal nanoparticle waveguides," Phys. Rev. B 76, 201403 (R) (2007).
[CrossRef]

K. B. Crozier, E. Togan, E. Simsek, and T. Yang, "Experimental measurement of the dispersion relations of the surface plasmon modes of metal nanoparticle chains," Opt. Express 15, 17482-17493 (2007).
[CrossRef] [PubMed]

2006 (1)

A. F. Koenderink, and A. Polman, "Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains," Phys. Rev. B 74, 033402 (2006).
[CrossRef]

2005 (1)

E. M. Hicks, S. Zou, G. C. Schatz; K. G. Spears, R. P. V. Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, "Controlling Plasmon Line Shapes through Diffractive Coupling in Linear Arrays of Cylindrical Nanoparticles Fabricated by Electron Beam Lithography," Nano Lett. 5, 1065-1070 (2005).
[CrossRef] [PubMed]

2004 (4)

S. Zou, N. Janel, and G. C. Schatz, "Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes," J. Chem. Phys. 120, 10871-10875 (2004).
[CrossRef] [PubMed]

W. H. Weber, and G. W. Ford, "Propagation of optical excitations by dipolar interactions in metal nanoparticle chains," Phys. Rev. B 70, 125429 (2004).
[CrossRef]

S. Y. Park, and D. Stroud, "Surface-plasmon dispersion relations in chains of metallic nanoparticles: An exact quasistatic calculation," Phys. Rev. B 69, 125418 (2004).
[CrossRef]

Q.-H. Wei, K.-H. Su, S. Durant, and X. Zhang, "Plasmon Resonance of Finite One-Dimensional Au Nanoparticle Chains," Nano Lett. 4, 1067-1071 (2004).
[CrossRef]

2003 (3)

C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. J. Kall, "Nanoparticle Optics: The Importance of Radiative Dipole Coupling in Two-Dimensional Nanoparticle Arrays," Phys. Chem. B 107, 7337-7342 (2003).
[CrossRef]

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nature Mater. 2, 229-232 (2003).
[CrossRef]

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, "Optimized surface-enhanced Raman scattering on gold nanoparticle arrays," Appl. Phys. Lett. 82, 3095-3097 (2003).
[CrossRef]

2002 (2)

S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, "Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy," Phys. Rev. B 65, 193408 (2002).
[CrossRef]

S. A. Maier, P. G. Kik, and H. A. Atwater, "Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss," Appl. Phys. Lett. 81, 1714-1716 (2002).
[CrossRef]

2000 (2)

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B 62, R16356-16359 (2000).
[CrossRef]

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, "Metal Nanoparticle Gratings: Influence of Dipolar Particle Interaction on the Plasmon Resonance," Phys. Rev. Lett. 84, 4721-4724 (2000).
[CrossRef] [PubMed]

1999 (1)

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, and J. P. Goudonnet, "Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles," Phys. Rev. Lett. 82, 2590-2593 (1999).
[CrossRef]

1998 (1)

Atwater, H. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nature Mater. 2, 229-232 (2003).
[CrossRef]

S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, "Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy," Phys. Rev. B 65, 193408 (2002).
[CrossRef]

S. A. Maier, P. G. Kik, and H. A. Atwater, "Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss," Appl. Phys. Lett. 81, 1714-1716 (2002).
[CrossRef]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B 62, R16356-16359 (2000).
[CrossRef]

Aubard, J.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, "Optimized surface-enhanced Raman scattering on gold nanoparticle arrays," Appl. Phys. Lett. 82, 3095-3097 (2003).
[CrossRef]

Aussenegg, F. R.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, "Optimized surface-enhanced Raman scattering on gold nanoparticle arrays," Appl. Phys. Lett. 82, 3095-3097 (2003).
[CrossRef]

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, "Metal Nanoparticle Gratings: Influence of Dipolar Particle Interaction on the Plasmon Resonance," Phys. Rev. Lett. 84, 4721-4724 (2000).
[CrossRef] [PubMed]

M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, "Electromagnetic energy transport via linear chains of silver nanoparticles," Opt. Lett. 23, 1331-1333 (1998).
[CrossRef]

Bourillot, E.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, and J. P. Goudonnet, "Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles," Phys. Rev. Lett. 82, 2590-2593 (1999).
[CrossRef]

Brongersma, M. L.

S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, "Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy," Phys. Rev. B 65, 193408 (2002).
[CrossRef]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B 62, R16356-16359 (2000).
[CrossRef]

Crozier, K. B.

de Waele, R.

A. F. Koenderink, R. de Waele, J. C. Prangsma, and A. Polman, "Experimental evidence for large dynamic effects on the plasmon dispersion of subwavelength metal nanoparticle waveguides," Phys. Rev. B 76, 201403 (R) (2007).
[CrossRef]

Dereux, A.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, and J. P. Goudonnet, "Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles," Phys. Rev. Lett. 82, 2590-2593 (1999).
[CrossRef]

Ditlbacher, H.

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, "Metal Nanoparticle Gratings: Influence of Dipolar Particle Interaction on the Plasmon Resonance," Phys. Rev. Lett. 84, 4721-4724 (2000).
[CrossRef] [PubMed]

Durant, S.

Q.-H. Wei, K.-H. Su, S. Durant, and X. Zhang, "Plasmon Resonance of Finite One-Dimensional Au Nanoparticle Chains," Nano Lett. 4, 1067-1071 (2004).
[CrossRef]

Duyne, R. P. V.

E. M. Hicks, S. Zou, G. C. Schatz; K. G. Spears, R. P. V. Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, "Controlling Plasmon Line Shapes through Diffractive Coupling in Linear Arrays of Cylindrical Nanoparticles Fabricated by Electron Beam Lithography," Nano Lett. 5, 1065-1070 (2005).
[CrossRef] [PubMed]

Félidj, N.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, "Optimized surface-enhanced Raman scattering on gold nanoparticle arrays," Appl. Phys. Lett. 82, 3095-3097 (2003).
[CrossRef]

Ford, G. W.

W. H. Weber, and G. W. Ford, "Propagation of optical excitations by dipolar interactions in metal nanoparticle chains," Phys. Rev. B 70, 125429 (2004).
[CrossRef]

García de Abajo, F. J.

F. J. García de Abajo, "Colloquium: Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007).
[CrossRef]

Goudonnet, J. P.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, and J. P. Goudonnet, "Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles," Phys. Rev. Lett. 82, 2590-2593 (1999).
[CrossRef]

Gunnarsson, L.

E. M. Hicks, S. Zou, G. C. Schatz; K. G. Spears, R. P. V. Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, "Controlling Plasmon Line Shapes through Diffractive Coupling in Linear Arrays of Cylindrical Nanoparticles Fabricated by Electron Beam Lithography," Nano Lett. 5, 1065-1070 (2005).
[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. J. Kall, "Nanoparticle Optics: The Importance of Radiative Dipole Coupling in Two-Dimensional Nanoparticle Arrays," Phys. Chem. B 107, 7337-7342 (2003).
[CrossRef]

Harel, E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nature Mater. 2, 229-232 (2003).
[CrossRef]

Hartman, J. W.

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B 62, R16356-16359 (2000).
[CrossRef]

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. J. Kall, "Nanoparticle Optics: The Importance of Radiative Dipole Coupling in Two-Dimensional Nanoparticle Arrays," Phys. Chem. B 107, 7337-7342 (2003).
[CrossRef]

Hicks, E. M.

E. M. Hicks, S. Zou, G. C. Schatz; K. G. Spears, R. P. V. Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, "Controlling Plasmon Line Shapes through Diffractive Coupling in Linear Arrays of Cylindrical Nanoparticles Fabricated by Electron Beam Lithography," Nano Lett. 5, 1065-1070 (2005).
[CrossRef] [PubMed]

Hohenau, A.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, "Optimized surface-enhanced Raman scattering on gold nanoparticle arrays," Appl. Phys. Lett. 82, 3095-3097 (2003).
[CrossRef]

Janel, N.

S. Zou, N. Janel, and G. C. Schatz, "Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes," J. Chem. Phys. 120, 10871-10875 (2004).
[CrossRef] [PubMed]

Kall, M.

E. M. Hicks, S. Zou, G. C. Schatz; K. G. Spears, R. P. V. Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, "Controlling Plasmon Line Shapes through Diffractive Coupling in Linear Arrays of Cylindrical Nanoparticles Fabricated by Electron Beam Lithography," Nano Lett. 5, 1065-1070 (2005).
[CrossRef] [PubMed]

Kall, M. J.

C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. J. Kall, "Nanoparticle Optics: The Importance of Radiative Dipole Coupling in Two-Dimensional Nanoparticle Arrays," Phys. Chem. B 107, 7337-7342 (2003).
[CrossRef]

Kasemo, B.

E. M. Hicks, S. Zou, G. C. Schatz; K. G. Spears, R. P. V. Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, "Controlling Plasmon Line Shapes through Diffractive Coupling in Linear Arrays of Cylindrical Nanoparticles Fabricated by Electron Beam Lithography," Nano Lett. 5, 1065-1070 (2005).
[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. J. Kall, "Nanoparticle Optics: The Importance of Radiative Dipole Coupling in Two-Dimensional Nanoparticle Arrays," Phys. Chem. B 107, 7337-7342 (2003).
[CrossRef]

Kik, P. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nature Mater. 2, 229-232 (2003).
[CrossRef]

S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, "Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy," Phys. Rev. B 65, 193408 (2002).
[CrossRef]

S. A. Maier, P. G. Kik, and H. A. Atwater, "Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss," Appl. Phys. Lett. 81, 1714-1716 (2002).
[CrossRef]

Koel, B. E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nature Mater. 2, 229-232 (2003).
[CrossRef]

Koenderink, A. F.

A. F. Koenderink, R. de Waele, J. C. Prangsma, and A. Polman, "Experimental evidence for large dynamic effects on the plasmon dispersion of subwavelength metal nanoparticle waveguides," Phys. Rev. B 76, 201403 (R) (2007).
[CrossRef]

A. F. Koenderink, and A. Polman, "Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains," Phys. Rev. B 74, 033402 (2006).
[CrossRef]

Krenn, J. R.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, "Optimized surface-enhanced Raman scattering on gold nanoparticle arrays," Appl. Phys. Lett. 82, 3095-3097 (2003).
[CrossRef]

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, "Metal Nanoparticle Gratings: Influence of Dipolar Particle Interaction on the Plasmon Resonance," Phys. Rev. Lett. 84, 4721-4724 (2000).
[CrossRef] [PubMed]

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, and J. P. Goudonnet, "Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles," Phys. Rev. Lett. 82, 2590-2593 (1999).
[CrossRef]

M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, "Electromagnetic energy transport via linear chains of silver nanoparticles," Opt. Lett. 23, 1331-1333 (1998).
[CrossRef]

Lacroute, Y.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, and J. P. Goudonnet, "Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles," Phys. Rev. Lett. 82, 2590-2593 (1999).
[CrossRef]

Lamprecht, B.

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, "Metal Nanoparticle Gratings: Influence of Dipolar Particle Interaction on the Plasmon Resonance," Phys. Rev. Lett. 84, 4721-4724 (2000).
[CrossRef] [PubMed]

Lechner, R. T.

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, "Metal Nanoparticle Gratings: Influence of Dipolar Particle Interaction on the Plasmon Resonance," Phys. Rev. Lett. 84, 4721-4724 (2000).
[CrossRef] [PubMed]

Leitner, A.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, "Optimized surface-enhanced Raman scattering on gold nanoparticle arrays," Appl. Phys. Lett. 82, 3095-3097 (2003).
[CrossRef]

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, "Metal Nanoparticle Gratings: Influence of Dipolar Particle Interaction on the Plasmon Resonance," Phys. Rev. Lett. 84, 4721-4724 (2000).
[CrossRef] [PubMed]

M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, "Electromagnetic energy transport via linear chains of silver nanoparticles," Opt. Lett. 23, 1331-1333 (1998).
[CrossRef]

Lévi, G.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, "Optimized surface-enhanced Raman scattering on gold nanoparticle arrays," Appl. Phys. Lett. 82, 3095-3097 (2003).
[CrossRef]

Maier, S. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nature Mater. 2, 229-232 (2003).
[CrossRef]

S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, "Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy," Phys. Rev. B 65, 193408 (2002).
[CrossRef]

S. A. Maier, P. G. Kik, and H. A. Atwater, "Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss," Appl. Phys. Lett. 81, 1714-1716 (2002).
[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. J. Kall, "Nanoparticle Optics: The Importance of Radiative Dipole Coupling in Two-Dimensional Nanoparticle Arrays," Phys. Chem. B 107, 7337-7342 (2003).
[CrossRef]

Meltzer, S.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nature Mater. 2, 229-232 (2003).
[CrossRef]

Park, S. Y.

S. Y. Park, and D. Stroud, "Surface-plasmon dispersion relations in chains of metallic nanoparticles: An exact quasistatic calculation," Phys. Rev. B 69, 125418 (2004).
[CrossRef]

Polman, A.

A. F. Koenderink, R. de Waele, J. C. Prangsma, and A. Polman, "Experimental evidence for large dynamic effects on the plasmon dispersion of subwavelength metal nanoparticle waveguides," Phys. Rev. B 76, 201403 (R) (2007).
[CrossRef]

A. F. Koenderink, and A. Polman, "Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains," Phys. Rev. B 74, 033402 (2006).
[CrossRef]

Prangsma, J. C.

A. F. Koenderink, R. de Waele, J. C. Prangsma, and A. Polman, "Experimental evidence for large dynamic effects on the plasmon dispersion of subwavelength metal nanoparticle waveguides," Phys. Rev. B 76, 201403 (R) (2007).
[CrossRef]

Prikulis, J.

C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. J. Kall, "Nanoparticle Optics: The Importance of Radiative Dipole Coupling in Two-Dimensional Nanoparticle Arrays," Phys. Chem. B 107, 7337-7342 (2003).
[CrossRef]

Quinten, M.

Requicha, A. A. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nature Mater. 2, 229-232 (2003).
[CrossRef]

Rindzevicius, T.

E. M. Hicks, S. Zou, G. C. Schatz; K. G. Spears, R. P. V. Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, "Controlling Plasmon Line Shapes through Diffractive Coupling in Linear Arrays of Cylindrical Nanoparticles Fabricated by Electron Beam Lithography," Nano Lett. 5, 1065-1070 (2005).
[CrossRef] [PubMed]

Schatz, G. C.

E. M. Hicks, S. Zou, G. C. Schatz; K. G. Spears, R. P. V. Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, "Controlling Plasmon Line Shapes through Diffractive Coupling in Linear Arrays of Cylindrical Nanoparticles Fabricated by Electron Beam Lithography," Nano Lett. 5, 1065-1070 (2005).
[CrossRef] [PubMed]

S. Zou, N. Janel, and G. C. Schatz, "Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes," J. Chem. Phys. 120, 10871-10875 (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. J. Kall, "Nanoparticle Optics: The Importance of Radiative Dipole Coupling in Two-Dimensional Nanoparticle Arrays," Phys. Chem. B 107, 7337-7342 (2003).
[CrossRef]

Schider, G.

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, "Optimized surface-enhanced Raman scattering on gold nanoparticle arrays," Appl. Phys. Lett. 82, 3095-3097 (2003).
[CrossRef]

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, "Metal Nanoparticle Gratings: Influence of Dipolar Particle Interaction on the Plasmon Resonance," Phys. Rev. Lett. 84, 4721-4724 (2000).
[CrossRef] [PubMed]

Simsek, E.

Spears, K. G.

E. M. Hicks, S. Zou, G. C. Schatz; K. G. Spears, R. P. V. Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, "Controlling Plasmon Line Shapes through Diffractive Coupling in Linear Arrays of Cylindrical Nanoparticles Fabricated by Electron Beam Lithography," Nano Lett. 5, 1065-1070 (2005).
[CrossRef] [PubMed]

Stroud, D.

S. Y. Park, and D. Stroud, "Surface-plasmon dispersion relations in chains of metallic nanoparticles: An exact quasistatic calculation," Phys. Rev. B 69, 125418 (2004).
[CrossRef]

Su, K.-H.

Q.-H. Wei, K.-H. Su, S. Durant, and X. Zhang, "Plasmon Resonance of Finite One-Dimensional Au Nanoparticle Chains," Nano Lett. 4, 1067-1071 (2004).
[CrossRef]

Togan, E.

Van Duyne, R. P.

C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. J. Kall, "Nanoparticle Optics: The Importance of Radiative Dipole Coupling in Two-Dimensional Nanoparticle Arrays," Phys. Chem. B 107, 7337-7342 (2003).
[CrossRef]

Weber, W. H.

W. H. Weber, and G. W. Ford, "Propagation of optical excitations by dipolar interactions in metal nanoparticle chains," Phys. Rev. B 70, 125429 (2004).
[CrossRef]

Weeber, J. C.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, and J. P. Goudonnet, "Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles," Phys. Rev. Lett. 82, 2590-2593 (1999).
[CrossRef]

Wei, Q.-H.

Q.-H. Wei, K.-H. Su, S. Durant, and X. Zhang, "Plasmon Resonance of Finite One-Dimensional Au Nanoparticle Chains," Nano Lett. 4, 1067-1071 (2004).
[CrossRef]

Yang, T.

Zhang, X.

Q.-H. Wei, K.-H. Su, S. Durant, and X. Zhang, "Plasmon Resonance of Finite One-Dimensional Au Nanoparticle Chains," Nano Lett. 4, 1067-1071 (2004).
[CrossRef]

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. J. Kall, "Nanoparticle Optics: The Importance of Radiative Dipole Coupling in Two-Dimensional Nanoparticle Arrays," Phys. Chem. B 107, 7337-7342 (2003).
[CrossRef]

Zou, S.

E. M. Hicks, S. Zou, G. C. Schatz; K. G. Spears, R. P. V. Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, "Controlling Plasmon Line Shapes through Diffractive Coupling in Linear Arrays of Cylindrical Nanoparticles Fabricated by Electron Beam Lithography," Nano Lett. 5, 1065-1070 (2005).
[CrossRef] [PubMed]

S. Zou, N. Janel, and G. C. Schatz, "Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes," J. Chem. Phys. 120, 10871-10875 (2004).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, "Optimized surface-enhanced Raman scattering on gold nanoparticle arrays," Appl. Phys. Lett. 82, 3095-3097 (2003).
[CrossRef]

S. A. Maier, P. G. Kik, and H. A. Atwater, "Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss," Appl. Phys. Lett. 81, 1714-1716 (2002).
[CrossRef]

J. Chem. Phys. (1)

S. Zou, N. Janel, and G. C. Schatz, "Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes," J. Chem. Phys. 120, 10871-10875 (2004).
[CrossRef] [PubMed]

Nano Lett. (2)

E. M. Hicks, S. Zou, G. C. Schatz; K. G. Spears, R. P. V. Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, "Controlling Plasmon Line Shapes through Diffractive Coupling in Linear Arrays of Cylindrical Nanoparticles Fabricated by Electron Beam Lithography," Nano Lett. 5, 1065-1070 (2005).
[CrossRef] [PubMed]

Q.-H. Wei, K.-H. Su, S. Durant, and X. Zhang, "Plasmon Resonance of Finite One-Dimensional Au Nanoparticle Chains," Nano Lett. 4, 1067-1071 (2004).
[CrossRef]

Nature Mater. (1)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nature Mater. 2, 229-232 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Chem. B (1)

C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. J. Kall, "Nanoparticle Optics: The Importance of Radiative Dipole Coupling in Two-Dimensional Nanoparticle Arrays," Phys. Chem. B 107, 7337-7342 (2003).
[CrossRef]

Phys. Rev. B (6)

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B 62, R16356-16359 (2000).
[CrossRef]

S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, "Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy," Phys. Rev. B 65, 193408 (2002).
[CrossRef]

W. H. Weber, and G. W. Ford, "Propagation of optical excitations by dipolar interactions in metal nanoparticle chains," Phys. Rev. B 70, 125429 (2004).
[CrossRef]

S. Y. Park, and D. Stroud, "Surface-plasmon dispersion relations in chains of metallic nanoparticles: An exact quasistatic calculation," Phys. Rev. B 69, 125418 (2004).
[CrossRef]

A. F. Koenderink, and A. Polman, "Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains," Phys. Rev. B 74, 033402 (2006).
[CrossRef]

A. F. Koenderink, R. de Waele, J. C. Prangsma, and A. Polman, "Experimental evidence for large dynamic effects on the plasmon dispersion of subwavelength metal nanoparticle waveguides," Phys. Rev. B 76, 201403 (R) (2007).
[CrossRef]

Phys. Rev. Lett. (2)

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, and J. P. Goudonnet, "Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles," Phys. Rev. Lett. 82, 2590-2593 (1999).
[CrossRef]

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, "Metal Nanoparticle Gratings: Influence of Dipolar Particle Interaction on the Plasmon Resonance," Phys. Rev. Lett. 84, 4721-4724 (2000).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

F. J. García de Abajo, "Colloquium: Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007).
[CrossRef]

Other (1)

Think of a plane wave propagating in z direction. It has an infinite d�?/dkx value.

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Figures (8)

Fig. 1.
Fig. 1.

Scanning electron micrograph of an array of gold nanoparticle chains on a glass substrate.

Fig. 2.
Fig. 2.

Schematic explanation of the equivalent dipole modeling. (a) a normally incident field, including incoming, reflected and transmitted fields; (b) scattered field from a metallic nanoparticle in addition to the incident field; and (c) field generated by a point dipole. The metallic nanoparticle is modeled as a point dipole whose polarizability is chosen so that the field it generates is equal to the field scattered by the nanoparticle.

Fig. 3.
Fig. 3.

Polarizability of a nanoparticle unit cell, consisting of a line of gold nanocylinders at an air/glass interface, obtained by FDTD. f/c is the frequency divided by the speed of light.

Fig. 4.
Fig. 4.

Comparison of the profile of the transversely polarized scattered field from a chain of nanoparticles and the profile of the transversely polarized field generated by a chain of point dipoles. Nanoparticles and point dipoles are located near an air/glass interface. Red: scattered field value at (140 nm, 0, 0)/value at (0, 0, 1 µm)×1/3; magenta: point dipole field value at (140 nm, 0, 0)/value at (0, 0, 1 µm)×1/3; blue: scattered field value at (980nm, 0, 0)/value at (0, 0, 1 µm)×5; green: point dipole field value at (980nm, 0, 0)/value at (0, 0, 1 µm)×5. (a) amplitude ratio; (b) phase difference. f/c is the frequency divided by the speed of light.

Fig. 5.
Fig. 5.

K1 (a.u.) of an array of point dipole chains at an air/glass interface, at the oscillation frequency of f/c=1.6 µm-1 . c is speed of light. The point dipoles are polarized in y direction and spaced by d=140 nm in the chain direction x. kx spans the first Brillouin Zone from 0 to π/d at a fixed interval.

Fig. 6.
Fig. 6.

Surface plasmon behaviors in an array of gold nanoparticle chains at an air/glass interface. (a) Magnitude of real part of the external electric field divided by excited equivalent point dipole moment in one particle of the array. (b) Resonance frequency versus wave vector along the chain direction, kx ; and corresponding threshold gain at resonance. The two straight lines in each figure are the light lines of air and glass. f/c is frequency divided by the speed of light.

Fig. 7.
Fig. 7.

Extinction ratio of an array of gold nanoparticle chains at an air/glass interface. Plane waves illuminate the particles from the glass side at different angles to the chain direction x. ky =0. (a) Semi-Analytical modeling result; (b) FDTD-only simulation result. The two straight lines in each figure are the light lines of air and glass. f/c is the frequency divided by the speed of light.

Fig. 8.
Fig. 8.

Surface plasmon behaviors in a single chain of gold nanoparticles at an air/glass interface. The equivalent point dipoles are polarized in y direction and spaced by d=140 nm in the chain direction x. (a) K1 (a.u.) at the oscillation frequency of f/c=1.6 µm-1. kx spans the first Brillouin Zone from 0 to π/d at a fixed interval. (b) Resonance frequency versus wave vector along the chain direction, kx; and corresponding threshold gain at resonance. f/c is the frequency divided by the speed of light.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

M d 2 P dt 2 = K 0 P + E i ( ω , k x ) Q 2 v dP dt + E o Q 2 + MG dP dt
[ ( ω 0 2 ω 2 ) M Re ( K 1 Q 2 ) ] + i [ ω v Im ( K 1 Q 2 ) + ω MG ] = Q 2 E o 0 P 0
{ ( ω 0 2 ω 2 ) M [ Re ( K 1 Q 2 ) + ( v M s ) sM ] } + i { ω v Im ( K 1 Q 2 ) + 2 ω Ms } = 0

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