Abstract

Two-dimensional arrays of gold nanoparticles with a periodicity commensurate with the wavelength of resonant excitation of localized plasmons have been shown to exhibit a strong long-range interaction between particles. We investigate experimentally the effect of varying the degree of disorder in the geometrical arrangement from a periodic to a disordered lattice with constant occupancy. We also investigate the effect of disorder arising from variations in particle size for a regular lattice, and the effect this has on the broadening of the spectral line shape is discussed. A coupled dipole model is used to describe the observed spectral features.

© 2009 Optical Society of America

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  1. U. Kreibig and L. Genzel, Surf. Sci. 156, 678 (1985).
    [CrossRef]
  2. S. Link and M. El-Sayed, Int. Rev. Phys. Chem. 19, 409 (2000).
    [CrossRef]
  3. V. A. Markel and A. Sarychev, Phys. Rev. B 75, 085426 (2007).
    [CrossRef]
  4. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, Nature Mater. 2, 229 (2003).
    [CrossRef]
  5. A. Grigorenko, H. Gleeson, Y. Zhang, N. Roberts, A. Sidorov, and A. Panteleev, Appl. Phys. Lett. 88, 124103 (2006).
    [CrossRef]
  6. Z. V. Vardeny and A. Nahata, Nat. Photonics 2, 75 (2008).
    [CrossRef]
  7. A. A. Govyadinov and V. A. Markel, Phys. Rev. B 78, 035403 (2008).
    [CrossRef]
  8. V. G. Kravets, F. Schedin, and A. N. Grigorenko, Phys. Rev. Lett. 101, 087403 (2008).
    [CrossRef] [PubMed]
  9. B. Auguié and W. L. Barnes, Phys. Rev. Lett. 101, 143902 (2008).
    [CrossRef] [PubMed]
  10. Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, Appl. Phys. Lett. 93, 181108 (2008).
    [CrossRef]
  11. D. Nau, A. Schoenhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, M. W. Klein, and H. Giessen, Phys. Rev. Lett. 98, 133902 (2007).
    [CrossRef] [PubMed]
  12. A. Baddeley and R. Turner, J. Stat. Software 12, 1 (2005).
  13. D. Strauss, Biometrika 62, 467 (1975).
    [CrossRef]
  14. H. Kuwata-Gonokami, H. Tamaru, K. Esumi, and K. Miyano, Appl. Phys. Lett. 83, 4625 (2003).
    [CrossRef]
  15. G. C. Schatz and R. P. Van Duyne, J. Chem. Phys. 103, 869 (1995).
    [CrossRef]
  16. C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, Phys. Rev. Lett. 88, 077402 (2002).
    [CrossRef] [PubMed]

2008 (5)

Z. V. Vardeny and A. Nahata, Nat. Photonics 2, 75 (2008).
[CrossRef]

A. A. Govyadinov and V. A. Markel, Phys. Rev. B 78, 035403 (2008).
[CrossRef]

V. G. Kravets, F. Schedin, and A. N. Grigorenko, Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef] [PubMed]

B. Auguié and W. L. Barnes, Phys. Rev. Lett. 101, 143902 (2008).
[CrossRef] [PubMed]

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, Appl. Phys. Lett. 93, 181108 (2008).
[CrossRef]

2007 (2)

D. Nau, A. Schoenhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, M. W. Klein, and H. Giessen, Phys. Rev. Lett. 98, 133902 (2007).
[CrossRef] [PubMed]

V. A. Markel and A. Sarychev, Phys. Rev. B 75, 085426 (2007).
[CrossRef]

2006 (1)

A. Grigorenko, H. Gleeson, Y. Zhang, N. Roberts, A. Sidorov, and A. Panteleev, Appl. Phys. Lett. 88, 124103 (2006).
[CrossRef]

2005 (1)

A. Baddeley and R. Turner, J. Stat. Software 12, 1 (2005).

2003 (2)

H. Kuwata-Gonokami, H. Tamaru, K. Esumi, and K. Miyano, Appl. Phys. Lett. 83, 4625 (2003).
[CrossRef]

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, Nature Mater. 2, 229 (2003).
[CrossRef]

2002 (1)

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, Phys. Rev. Lett. 88, 077402 (2002).
[CrossRef] [PubMed]

2000 (1)

S. Link and M. El-Sayed, Int. Rev. Phys. Chem. 19, 409 (2000).
[CrossRef]

1995 (1)

G. C. Schatz and R. P. Van Duyne, J. Chem. Phys. 103, 869 (1995).
[CrossRef]

1985 (1)

U. Kreibig and L. Genzel, Surf. Sci. 156, 678 (1985).
[CrossRef]

1975 (1)

D. Strauss, Biometrika 62, 467 (1975).
[CrossRef]

Atwater, H. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, Nature Mater. 2, 229 (2003).
[CrossRef]

Auguié, B.

B. Auguié and W. L. Barnes, Phys. Rev. Lett. 101, 143902 (2008).
[CrossRef] [PubMed]

Baddeley, A.

A. Baddeley and R. Turner, J. Stat. Software 12, 1 (2005).

Barnes, W. L.

B. Auguié and W. L. Barnes, Phys. Rev. Lett. 101, 143902 (2008).
[CrossRef] [PubMed]

Bauer, C.

D. Nau, A. Schoenhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, M. W. Klein, and H. Giessen, Phys. Rev. Lett. 98, 133902 (2007).
[CrossRef] [PubMed]

Christ, A.

D. Nau, A. Schoenhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, M. W. Klein, and H. Giessen, Phys. Rev. Lett. 98, 133902 (2007).
[CrossRef] [PubMed]

Chu, Y.

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, Appl. Phys. Lett. 93, 181108 (2008).
[CrossRef]

Crozier, K. B.

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, Appl. Phys. Lett. 93, 181108 (2008).
[CrossRef]

El-Sayed, M.

S. Link and M. El-Sayed, Int. Rev. Phys. Chem. 19, 409 (2000).
[CrossRef]

Esumi, K.

H. Kuwata-Gonokami, H. Tamaru, K. Esumi, and K. Miyano, Appl. Phys. Lett. 83, 4625 (2003).
[CrossRef]

Feldmann, J.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, Phys. Rev. Lett. 88, 077402 (2002).
[CrossRef] [PubMed]

Franzl, T.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, Phys. Rev. Lett. 88, 077402 (2002).
[CrossRef] [PubMed]

Genzel, L.

U. Kreibig and L. Genzel, Surf. Sci. 156, 678 (1985).
[CrossRef]

Giessen, H.

D. Nau, A. Schoenhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, M. W. Klein, and H. Giessen, Phys. Rev. Lett. 98, 133902 (2007).
[CrossRef] [PubMed]

Gleeson, H.

A. Grigorenko, H. Gleeson, Y. Zhang, N. Roberts, A. Sidorov, and A. Panteleev, Appl. Phys. Lett. 88, 124103 (2006).
[CrossRef]

Govyadinov, A. A.

A. A. Govyadinov and V. A. Markel, Phys. Rev. B 78, 035403 (2008).
[CrossRef]

Grigorenko, A.

A. Grigorenko, H. Gleeson, Y. Zhang, N. Roberts, A. Sidorov, and A. Panteleev, Appl. Phys. Lett. 88, 124103 (2006).
[CrossRef]

Grigorenko, A. N.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef] [PubMed]

Harel, E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, Nature Mater. 2, 229 (2003).
[CrossRef]

Kik, P. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, Nature Mater. 2, 229 (2003).
[CrossRef]

Klein, M. W.

D. Nau, A. Schoenhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, M. W. Klein, and H. Giessen, Phys. Rev. Lett. 98, 133902 (2007).
[CrossRef] [PubMed]

Koel, B. E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, Nature Mater. 2, 229 (2003).
[CrossRef]

Kravets, V. G.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef] [PubMed]

Kreibig, U.

U. Kreibig and L. Genzel, Surf. Sci. 156, 678 (1985).
[CrossRef]

Kuhl, J.

D. Nau, A. Schoenhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, M. W. Klein, and H. Giessen, Phys. Rev. Lett. 98, 133902 (2007).
[CrossRef] [PubMed]

Kuwata-Gonokami, H.

H. Kuwata-Gonokami, H. Tamaru, K. Esumi, and K. Miyano, Appl. Phys. Lett. 83, 4625 (2003).
[CrossRef]

Link, S.

S. Link and M. El-Sayed, Int. Rev. Phys. Chem. 19, 409 (2000).
[CrossRef]

Maier, S. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, Nature Mater. 2, 229 (2003).
[CrossRef]

Markel, V. A.

A. A. Govyadinov and V. A. Markel, Phys. Rev. B 78, 035403 (2008).
[CrossRef]

V. A. Markel and A. Sarychev, Phys. Rev. B 75, 085426 (2007).
[CrossRef]

Meltzer, S.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, Nature Mater. 2, 229 (2003).
[CrossRef]

Miyano, K.

H. Kuwata-Gonokami, H. Tamaru, K. Esumi, and K. Miyano, Appl. Phys. Lett. 83, 4625 (2003).
[CrossRef]

Mulvaney, P.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, Phys. Rev. Lett. 88, 077402 (2002).
[CrossRef] [PubMed]

Nahata, A.

Z. V. Vardeny and A. Nahata, Nat. Photonics 2, 75 (2008).
[CrossRef]

Nau, D.

D. Nau, A. Schoenhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, M. W. Klein, and H. Giessen, Phys. Rev. Lett. 98, 133902 (2007).
[CrossRef] [PubMed]

Panteleev, A.

A. Grigorenko, H. Gleeson, Y. Zhang, N. Roberts, A. Sidorov, and A. Panteleev, Appl. Phys. Lett. 88, 124103 (2006).
[CrossRef]

Requicha, A. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, Nature Mater. 2, 229 (2003).
[CrossRef]

Roberts, N.

A. Grigorenko, H. Gleeson, Y. Zhang, N. Roberts, A. Sidorov, and A. Panteleev, Appl. Phys. Lett. 88, 124103 (2006).
[CrossRef]

Sarychev, A.

V. A. Markel and A. Sarychev, Phys. Rev. B 75, 085426 (2007).
[CrossRef]

Schatz, G. C.

G. C. Schatz and R. P. Van Duyne, J. Chem. Phys. 103, 869 (1995).
[CrossRef]

Schedin, F.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef] [PubMed]

Schoenhardt, A.

D. Nau, A. Schoenhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, M. W. Klein, and H. Giessen, Phys. Rev. Lett. 98, 133902 (2007).
[CrossRef] [PubMed]

Schonbrun, E.

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, Appl. Phys. Lett. 93, 181108 (2008).
[CrossRef]

Sidorov, A.

A. Grigorenko, H. Gleeson, Y. Zhang, N. Roberts, A. Sidorov, and A. Panteleev, Appl. Phys. Lett. 88, 124103 (2006).
[CrossRef]

Sönnichsen, C.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, Phys. Rev. Lett. 88, 077402 (2002).
[CrossRef] [PubMed]

Strauss, D.

D. Strauss, Biometrika 62, 467 (1975).
[CrossRef]

Tamaru, H.

H. Kuwata-Gonokami, H. Tamaru, K. Esumi, and K. Miyano, Appl. Phys. Lett. 83, 4625 (2003).
[CrossRef]

Turner, R.

A. Baddeley and R. Turner, J. Stat. Software 12, 1 (2005).

Van Duyne, R. P.

G. C. Schatz and R. P. Van Duyne, J. Chem. Phys. 103, 869 (1995).
[CrossRef]

Vardeny, Z. V.

Z. V. Vardeny and A. Nahata, Nat. Photonics 2, 75 (2008).
[CrossRef]

von Plessen, G.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, Phys. Rev. Lett. 88, 077402 (2002).
[CrossRef] [PubMed]

Wilk, T.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, Phys. Rev. Lett. 88, 077402 (2002).
[CrossRef] [PubMed]

Wilson, O.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, Phys. Rev. Lett. 88, 077402 (2002).
[CrossRef] [PubMed]

Yang, T.

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, Appl. Phys. Lett. 93, 181108 (2008).
[CrossRef]

Zentgraf, T.

D. Nau, A. Schoenhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, M. W. Klein, and H. Giessen, Phys. Rev. Lett. 98, 133902 (2007).
[CrossRef] [PubMed]

Zhang, Y.

A. Grigorenko, H. Gleeson, Y. Zhang, N. Roberts, A. Sidorov, and A. Panteleev, Appl. Phys. Lett. 88, 124103 (2006).
[CrossRef]

Appl. Phys. Lett. (3)

A. Grigorenko, H. Gleeson, Y. Zhang, N. Roberts, A. Sidorov, and A. Panteleev, Appl. Phys. Lett. 88, 124103 (2006).
[CrossRef]

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, Appl. Phys. Lett. 93, 181108 (2008).
[CrossRef]

H. Kuwata-Gonokami, H. Tamaru, K. Esumi, and K. Miyano, Appl. Phys. Lett. 83, 4625 (2003).
[CrossRef]

Biometrika (1)

D. Strauss, Biometrika 62, 467 (1975).
[CrossRef]

Int. Rev. Phys. Chem. (1)

S. Link and M. El-Sayed, Int. Rev. Phys. Chem. 19, 409 (2000).
[CrossRef]

J. Chem. Phys. (1)

G. C. Schatz and R. P. Van Duyne, J. Chem. Phys. 103, 869 (1995).
[CrossRef]

J. Stat. Software (1)

A. Baddeley and R. Turner, J. Stat. Software 12, 1 (2005).

Nat. Photonics (1)

Z. V. Vardeny and A. Nahata, Nat. Photonics 2, 75 (2008).
[CrossRef]

Nature Mater. (1)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, Nature Mater. 2, 229 (2003).
[CrossRef]

Phys. Rev. B (2)

V. A. Markel and A. Sarychev, Phys. Rev. B 75, 085426 (2007).
[CrossRef]

A. A. Govyadinov and V. A. Markel, Phys. Rev. B 78, 035403 (2008).
[CrossRef]

Phys. Rev. Lett. (4)

V. G. Kravets, F. Schedin, and A. N. Grigorenko, Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef] [PubMed]

B. Auguié and W. L. Barnes, Phys. Rev. Lett. 101, 143902 (2008).
[CrossRef] [PubMed]

D. Nau, A. Schoenhardt, C. Bauer, A. Christ, T. Zentgraf, J. Kuhl, M. W. Klein, and H. Giessen, Phys. Rev. Lett. 98, 133902 (2007).
[CrossRef] [PubMed]

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, Phys. Rev. Lett. 88, 077402 (2002).
[CrossRef] [PubMed]

Surf. Sci. (1)

U. Kreibig and L. Genzel, Surf. Sci. 156, 678 (1985).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Scanning electron micrographs of particle arrays. (a) Ordered array, i.e., no added disorder; (b) 10% disorder in particle positions. (c) Pseudo-random positions; (d) 10% variation in the length of the long-axis of the particles; (e) 100% variation in the length of the long-axis of the particles.

Fig. 2
Fig. 2

(a) Extinction spectra from five different arrays of nanoparticles of varying positional disorder but with constant average occupancy. The deviation from the ordered array is indicated in the legend as a percentage of the nominal regular particle separation ( 550 nm ) . The vertical dashed curves indicate the ⟨1,0⟩ and ⟨1,1⟩ diffraction edges for the periodic array in a homogeneous environment (refractive index 1.46). The nominal particle sizes were 120 nm × 80 nm × 35 nm . (b) Calculated extinction spectra using a coupled dipole model with the same parameters.

Fig. 3
Fig. 3

(a) Extinction spectra from arrays of nanoparticles with regular positions but a variation in particle sizes. The legend indicates the level of disorder introduced in the length of the long-axis of the nanorods. The vertical dashed curves indicate the ⟨1,0⟩ and ⟨1,1⟩ diffraction edges for the 550 nm periodic array in a 1.46 refractive index homogeneous environment. The nominal particle sizes were 120 nm × 80 nm × 35 nm . (b) Calculated average spectra for five distributions of 441 ellipsoids. (c) Calculated spectra for a regular array of dipoles (pitch 550 nm ) using the distribution of individual LSPR frequencies shown in (d).

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