Abstract

We study how retardation leads to interference effects in radiatively coupled plasmonic nanoparticles. We show that inclined illumination through a glass substrate on two plasmonic particles results in either an enhanced field or an attenuated field localized at the position of the first particle. Periodic intensity blinking of the first particle is observed as a function of the particle separation. This phenomenon is nonsymmetric, and almost no blinking is observed on the second particle. The effect is strongest when the illumination angle is chosen such that the optical retardation path in the substrate coincides with the particle distance. Implications of this plasmonic blinking for near-field measurements are discussed.

© 2009 Optical Society of America

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  1. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, Nature Mater. 2, 229 (2003).
    [CrossRef]
  2. C. Girard and R. Quidant, Opt. Express 12, 6141 (2004).
    [CrossRef] [PubMed]
  3. W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, Opt. Commun. 220, 137 (2003).
    [CrossRef]
  4. K. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. Lett. 91, 227402 (2003).
    [CrossRef] [PubMed]
  5. D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner, Nano Lett. 4, 957 (2004).
    [CrossRef]
  6. P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
    [CrossRef] [PubMed]
  7. P. Ghenuche, R. Quidant, and G. Badenes, Opt. Lett. 30, 1882 (2005).
    [CrossRef] [PubMed]
  8. S. Enoch, R. Quidant, and G. Badenes, Opt. Express 12, 3422 (2004).
    [CrossRef] [PubMed]
  9. S. Zou and G. C. Schatz, J. Chem. Phys. 121, 12,606 (2004).
    [CrossRef]
  10. J. P. Kottmann and O. J. F. Martin, Opt. Lett. 26, 1096 (2001).
    [CrossRef]
  11. A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, Nano Lett. 8, 2171 (2008).
    [CrossRef] [PubMed]
  12. R. deWaele, A. F. Koenderink, and A. Polman, Nano Lett. 7, 2004 (2007).
    [CrossRef]
  13. A. F. Koenderink, J. V. Hernández, F. Robicheaux, L. D. Noordam, and A. Polman, Nano Lett. 7, 745 (2007).
    [CrossRef] [PubMed]
  14. S. Zou, N. Janel, and G. C. Schatz, J. Chem. Phys. 120, 10,871 (2004).
    [CrossRef]
  15. V. A. Markel, J. Chem. Phys. 122, 097101 (2005).
    [CrossRef] [PubMed]
  16. S. Zou and G. C. Schatz, J. Chem. Phys. 122, 097102 (2005).
    [CrossRef]
  17. A. O. Pinchuk and G. C. Schatz, Mater. Sci. Eng., B 149, 251 (2007).
    [CrossRef]
  18. O. J. F. Martin and N. B. Piller, Phys. Rev. E 58, 3909 (1998).
    [CrossRef]
  19. M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, Phys. Rev. E 62, 5797 (2000).
    [CrossRef]
  20. M. Paulus and O. J. F. Martin, Opt. Quantum Electron. 33, 315 (2001).
    [CrossRef]
  21. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
    [CrossRef]

2008 (1)

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, Nano Lett. 8, 2171 (2008).
[CrossRef] [PubMed]

2007 (3)

R. deWaele, A. F. Koenderink, and A. Polman, Nano Lett. 7, 2004 (2007).
[CrossRef]

A. F. Koenderink, J. V. Hernández, F. Robicheaux, L. D. Noordam, and A. Polman, Nano Lett. 7, 745 (2007).
[CrossRef] [PubMed]

A. O. Pinchuk and G. C. Schatz, Mater. Sci. Eng., B 149, 251 (2007).
[CrossRef]

2005 (4)

V. A. Markel, J. Chem. Phys. 122, 097101 (2005).
[CrossRef] [PubMed]

S. Zou and G. C. Schatz, J. Chem. Phys. 122, 097102 (2005).
[CrossRef]

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

P. Ghenuche, R. Quidant, and G. Badenes, Opt. Lett. 30, 1882 (2005).
[CrossRef] [PubMed]

2004 (5)

S. Enoch, R. Quidant, and G. Badenes, Opt. Express 12, 3422 (2004).
[CrossRef] [PubMed]

C. Girard and R. Quidant, Opt. Express 12, 6141 (2004).
[CrossRef] [PubMed]

S. Zou, N. Janel, and G. C. Schatz, J. Chem. Phys. 120, 10,871 (2004).
[CrossRef]

D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner, Nano Lett. 4, 957 (2004).
[CrossRef]

S. Zou and G. C. Schatz, J. Chem. Phys. 121, 12,606 (2004).
[CrossRef]

2003 (3)

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

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, Opt. Commun. 220, 137 (2003).
[CrossRef]

K. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef] [PubMed]

2001 (2)

M. Paulus and O. J. F. Martin, Opt. Quantum Electron. 33, 315 (2001).
[CrossRef]

J. P. Kottmann and O. J. F. Martin, Opt. Lett. 26, 1096 (2001).
[CrossRef]

2000 (1)

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, Phys. Rev. E 62, 5797 (2000).
[CrossRef]

1998 (1)

O. J. F. Martin and N. B. Piller, Phys. Rev. E 58, 3909 (1998).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Atwater, H. A.

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

Aussenegg, F. R.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, Opt. Commun. 220, 137 (2003).
[CrossRef]

Badenes, G.

Bergman, D. J.

K. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef] [PubMed]

Christ, A.

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, Nano Lett. 8, 2171 (2008).
[CrossRef] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

deWaele, R.

R. deWaele, A. F. Koenderink, and A. Polman, Nano Lett. 7, 2004 (2007).
[CrossRef]

Eisler, H. J.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

Ekinci, Y.

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, Nano Lett. 8, 2171 (2008).
[CrossRef] [PubMed]

Enoch, S.

Fromm, D. P.

D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner, Nano Lett. 4, 957 (2004).
[CrossRef]

Gay-Balmaz, P.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, Phys. Rev. E 62, 5797 (2000).
[CrossRef]

Ghenuche, P.

Gippius, N. A.

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, Nano Lett. 8, 2171 (2008).
[CrossRef] [PubMed]

Girard, C.

Harel, E.

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

Hecht, B.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

Hernández, J. V.

A. F. Koenderink, J. V. Hernández, F. Robicheaux, L. D. Noordam, and A. Polman, Nano Lett. 7, 745 (2007).
[CrossRef] [PubMed]

Hohenau, A.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, Opt. Commun. 220, 137 (2003).
[CrossRef]

Janel, N.

S. Zou, N. Janel, and G. C. Schatz, J. Chem. Phys. 120, 10,871 (2004).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[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, Nature Mater. 2, 229 (2003).
[CrossRef]

Kino, G.

D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner, Nano Lett. 4, 957 (2004).
[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, Nature Mater. 2, 229 (2003).
[CrossRef]

Koenderink, A. F.

A. F. Koenderink, J. V. Hernández, F. Robicheaux, L. D. Noordam, and A. Polman, Nano Lett. 7, 745 (2007).
[CrossRef] [PubMed]

R. deWaele, A. F. Koenderink, and A. Polman, Nano Lett. 7, 2004 (2007).
[CrossRef]

Kottmann, J. P.

Krenn, J. R.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, Opt. Commun. 220, 137 (2003).
[CrossRef]

Lamprecht, B.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, Opt. Commun. 220, 137 (2003).
[CrossRef]

Leitner, A.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, Opt. Commun. 220, 137 (2003).
[CrossRef]

Li, K.

K. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef] [PubMed]

Maier, S. A.

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

Markel, V. A.

V. A. Markel, J. Chem. Phys. 122, 097101 (2005).
[CrossRef] [PubMed]

Martin, O. J. F.

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, Nano Lett. 8, 2171 (2008).
[CrossRef] [PubMed]

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

M. Paulus and O. J. F. Martin, Opt. Quantum Electron. 33, 315 (2001).
[CrossRef]

J. P. Kottmann and O. J. F. Martin, Opt. Lett. 26, 1096 (2001).
[CrossRef]

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, Phys. Rev. E 62, 5797 (2000).
[CrossRef]

O. J. F. Martin and N. B. Piller, Phys. Rev. E 58, 3909 (1998).
[CrossRef]

Meltzer, S.

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

Moerner, W. E.

D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner, Nano Lett. 4, 957 (2004).
[CrossRef]

Muhlschlegel, P.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

Noordam, L. D.

A. F. Koenderink, J. V. Hernández, F. Robicheaux, L. D. Noordam, and A. Polman, Nano Lett. 7, 745 (2007).
[CrossRef] [PubMed]

Paulus, M.

M. Paulus and O. J. F. Martin, Opt. Quantum Electron. 33, 315 (2001).
[CrossRef]

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, Phys. Rev. E 62, 5797 (2000).
[CrossRef]

Piller, N. B.

O. J. F. Martin and N. B. Piller, Phys. Rev. E 58, 3909 (1998).
[CrossRef]

Pinchuk, A. O.

A. O. Pinchuk and G. C. Schatz, Mater. Sci. Eng., B 149, 251 (2007).
[CrossRef]

Pohl, D. W.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

Polman, A.

R. deWaele, A. F. Koenderink, and A. Polman, Nano Lett. 7, 2004 (2007).
[CrossRef]

A. F. Koenderink, J. V. Hernández, F. Robicheaux, L. D. Noordam, and A. Polman, Nano Lett. 7, 745 (2007).
[CrossRef] [PubMed]

Quidant, R.

Rechberger, W.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, Opt. Commun. 220, 137 (2003).
[CrossRef]

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, Nature Mater. 2, 229 (2003).
[CrossRef]

Robicheaux, F.

A. F. Koenderink, J. V. Hernández, F. Robicheaux, L. D. Noordam, and A. Polman, Nano Lett. 7, 745 (2007).
[CrossRef] [PubMed]

Schatz, G. C.

A. O. Pinchuk and G. C. Schatz, Mater. Sci. Eng., B 149, 251 (2007).
[CrossRef]

S. Zou and G. C. Schatz, J. Chem. Phys. 122, 097102 (2005).
[CrossRef]

S. Zou, N. Janel, and G. C. Schatz, J. Chem. Phys. 120, 10,871 (2004).
[CrossRef]

S. Zou and G. C. Schatz, J. Chem. Phys. 121, 12,606 (2004).
[CrossRef]

Schuck, P. J.

D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner, Nano Lett. 4, 957 (2004).
[CrossRef]

Stockman, M. I.

K. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef] [PubMed]

Sundaramurthy, A.

D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner, Nano Lett. 4, 957 (2004).
[CrossRef]

Tikhodeev, S. G.

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, Nano Lett. 8, 2171 (2008).
[CrossRef] [PubMed]

Zou, S.

S. Zou and G. C. Schatz, J. Chem. Phys. 122, 097102 (2005).
[CrossRef]

S. Zou, N. Janel, and G. C. Schatz, J. Chem. Phys. 120, 10,871 (2004).
[CrossRef]

S. Zou and G. C. Schatz, J. Chem. Phys. 121, 12,606 (2004).
[CrossRef]

J. Chem. Phys. (4)

S. Zou and G. C. Schatz, J. Chem. Phys. 121, 12,606 (2004).
[CrossRef]

S. Zou, N. Janel, and G. C. Schatz, J. Chem. Phys. 120, 10,871 (2004).
[CrossRef]

V. A. Markel, J. Chem. Phys. 122, 097101 (2005).
[CrossRef] [PubMed]

S. Zou and G. C. Schatz, J. Chem. Phys. 122, 097102 (2005).
[CrossRef]

Mater. Sci. Eng., B (1)

A. O. Pinchuk and G. C. Schatz, Mater. Sci. Eng., B 149, 251 (2007).
[CrossRef]

Nano Lett. (4)

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, Nano Lett. 8, 2171 (2008).
[CrossRef] [PubMed]

R. deWaele, A. F. Koenderink, and A. Polman, Nano Lett. 7, 2004 (2007).
[CrossRef]

A. F. Koenderink, J. V. Hernández, F. Robicheaux, L. D. Noordam, and A. Polman, Nano Lett. 7, 745 (2007).
[CrossRef] [PubMed]

D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner, Nano Lett. 4, 957 (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, Nature Mater. 2, 229 (2003).
[CrossRef]

Opt. Commun. (1)

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, Opt. Commun. 220, 137 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

M. Paulus and O. J. F. Martin, Opt. Quantum Electron. 33, 315 (2001).
[CrossRef]

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Phys. Rev. E (2)

O. J. F. Martin and N. B. Piller, Phys. Rev. E 58, 3909 (1998).
[CrossRef]

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, Phys. Rev. E 62, 5797 (2000).
[CrossRef]

Phys. Rev. Lett. (1)

K. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef] [PubMed]

Science (1)

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Particles are illuminated through the glass substrate at an angle α. The resulting retardation distance r and the particle separation distance d are indicated in the figure.

Fig. 2
Fig. 2

Relative field intensity at the edges of particle 1 and of particle 2 plotted as a function of the incident angle α and of the particle distance d at the plasmon resonance λ = 635 nm for n s = 1.5 . The intensity of particle 1 is subject to strong oscillations as a function of the particle separation for all incident angles. The strongest field and the strongest oscillation contrast are observed at α = 42 ° , where the optical path length of the retardation distance r coincides with the distance d of the particles.  

Fig. 3
Fig. 3

(a) Field intensity at particle 1 (dashed curve) and at particle 2 (dotted curve) for n s = 2 and α = 30 ° at the plasmon resonance λ = 700 nm . (b) Phase of the scattered field from particle 2 and of the illumination field, at the position of particle 1 as a function of the separation distance. At the distances where intensity maxima are observed in (a), the phases of the scattered field from particle 2 and the phase of the direct illumination coincide. (c), (d) x components of the real part of the scattered complex amplitude A between both particles at the particle separation distance d 1 = 1200 nm and d 2 = 1400 nm , respectively. The two counterpropagating waves are in phase at the intensity maxima in particle 2 and out of phase at the intensity minima in particle 2.

Fig. 4
Fig. 4

Relative field intensity at particle 1 (dashed curve) and at particle 2 (dotted curve) as a function of the particle separation at the plasmon resonance ( λ = 700 nm ) and α = 30 ° .

Equations (1)

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1 n s = sin ( α ) .

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