Abstract

We study the coupling induced by retardation effects when two plasmon-resonant nanoparticles are interacting. This coupling leads to an additional resonance, the strength of which depends on a subtle balance between particle separation and size. The scattering cross section and the near field associated with this coupled resonance are studied for cylindrical particles in air and in water. Implications for surface-enhanced Raman scattering and nano-optics are discussed.

© 2001 Optical Society of America

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  1. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  2. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters, Vol. 25 of Springer Series in Material Science (Springer-Verlag, Berlin, 1995).
    [CrossRef]
  3. H. Metiu, Prog. Surf. Sci. 17, 153 (1984).
  4. M. Moskovits, Rev. Mod. Phys. 57, 783 (1985).
    [CrossRef]
  5. P. K. Aravind, A. Nitzan, and H. Metiu, Surf. Sci. 110, 189 (1981).
    [CrossRef]
  6. Y. Xu, Appl. Opt. 34, 4573 (1995).
    [CrossRef] [PubMed]
  7. M. I. Mischenko, D. W. Mackowski, and L. D. Travis, Appl. Opt. 21, 4589 (1995).
    [CrossRef]
  8. J. P. Kottmann and O. J. F. Martin, IEEE Trans. Antennas Propag. 48, 1719 (2000).
    [CrossRef]
  9. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  10. J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, New J. Phys. 2, 27.1 (2000), http://njp.org .
    [CrossRef]
  11. J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, Opt. Express 6, 213 (2000), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  12. M. Bass, ed., Handbook of Optics, 2nd ed. (McGraw-Hill, New York, 1995), Vol. I, Chap.  43.8.
  13. J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, J. Microsc. 202, 60 (2001).
    [CrossRef] [PubMed]
  14. M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, Opt. Lett. 23, 1331 (1998).
    [CrossRef]
  15. J.-C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J.-P. Goudonnet, Phys. Rev. B 60, 9061 (1999).
    [CrossRef]
  16. H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, Phys. Rev. Lett. 83, 4357 (1999).
    [CrossRef]
  17. K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
    [CrossRef]
  18. S. Nie and S. R. Emory, Science 275, 1102 (1997).
    [CrossRef] [PubMed]

2001

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, J. Microsc. 202, 60 (2001).
[CrossRef] [PubMed]

2000

J. P. Kottmann and O. J. F. Martin, IEEE Trans. Antennas Propag. 48, 1719 (2000).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, Opt. Express 6, 213 (2000), http://www.opticsexpress.org .
[CrossRef] [PubMed]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, New J. Phys. 2, 27.1 (2000), http://njp.org .
[CrossRef]

1999

J.-C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J.-P. Goudonnet, Phys. Rev. B 60, 9061 (1999).
[CrossRef]

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, Phys. Rev. Lett. 83, 4357 (1999).
[CrossRef]

1998

1997

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

S. Nie and S. R. Emory, Science 275, 1102 (1997).
[CrossRef] [PubMed]

1995

M. I. Mischenko, D. W. Mackowski, and L. D. Travis, Appl. Opt. 21, 4589 (1995).
[CrossRef]

Y. Xu, Appl. Opt. 34, 4573 (1995).
[CrossRef] [PubMed]

1985

M. Moskovits, Rev. Mod. Phys. 57, 783 (1985).
[CrossRef]

1984

H. Metiu, Prog. Surf. Sci. 17, 153 (1984).

1981

P. K. Aravind, A. Nitzan, and H. Metiu, Surf. Sci. 110, 189 (1981).
[CrossRef]

1972

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

Aravind, P. K.

P. K. Aravind, A. Nitzan, and H. Metiu, Surf. Sci. 110, 189 (1981).
[CrossRef]

Aussenegg, F. R.

Bjerneld, E. J.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, Phys. Rev. Lett. 83, 4357 (1999).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Börjesson, L.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, Phys. Rev. Lett. 83, 4357 (1999).
[CrossRef]

Christy, R. W.

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

Dasari, R. R.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Dereux, A.

J.-C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J.-P. Goudonnet, Phys. Rev. B 60, 9061 (1999).
[CrossRef]

Emory, S. R.

S. Nie and S. R. Emory, Science 275, 1102 (1997).
[CrossRef] [PubMed]

Feld, M. S.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Girard, C.

J.-C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J.-P. Goudonnet, Phys. Rev. B 60, 9061 (1999).
[CrossRef]

Goudonnet, J.-P.

J.-C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J.-P. Goudonnet, Phys. Rev. B 60, 9061 (1999).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Itzkan, I.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Johnson, P. B.

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

Käll, M.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, Phys. Rev. Lett. 83, 4357 (1999).
[CrossRef]

Kneipp, H.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Kneipp, K.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Kottmann, J. P.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, J. Microsc. 202, 60 (2001).
[CrossRef] [PubMed]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, New J. Phys. 2, 27.1 (2000), http://njp.org .
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, Opt. Express 6, 213 (2000), http://www.opticsexpress.org .
[CrossRef] [PubMed]

J. P. Kottmann and O. J. F. Martin, IEEE Trans. Antennas Propag. 48, 1719 (2000).
[CrossRef]

Kreibig, U.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters, Vol. 25 of Springer Series in Material Science (Springer-Verlag, Berlin, 1995).
[CrossRef]

Krenn, J. R.

J.-C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J.-P. Goudonnet, Phys. Rev. B 60, 9061 (1999).
[CrossRef]

M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, Opt. Lett. 23, 1331 (1998).
[CrossRef]

Leitner, A.

Mackowski, D. W.

M. I. Mischenko, D. W. Mackowski, and L. D. Travis, Appl. Opt. 21, 4589 (1995).
[CrossRef]

Martin, O. J. F.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, J. Microsc. 202, 60 (2001).
[CrossRef] [PubMed]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, New J. Phys. 2, 27.1 (2000), http://njp.org .
[CrossRef]

J. P. Kottmann and O. J. F. Martin, IEEE Trans. Antennas Propag. 48, 1719 (2000).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, Opt. Express 6, 213 (2000), http://www.opticsexpress.org .
[CrossRef] [PubMed]

Metiu, H.

H. Metiu, Prog. Surf. Sci. 17, 153 (1984).

P. K. Aravind, A. Nitzan, and H. Metiu, Surf. Sci. 110, 189 (1981).
[CrossRef]

Mischenko, M. I.

M. I. Mischenko, D. W. Mackowski, and L. D. Travis, Appl. Opt. 21, 4589 (1995).
[CrossRef]

Moskovits, M.

M. Moskovits, Rev. Mod. Phys. 57, 783 (1985).
[CrossRef]

Nie, S.

S. Nie and S. R. Emory, Science 275, 1102 (1997).
[CrossRef] [PubMed]

Nitzan, A.

P. K. Aravind, A. Nitzan, and H. Metiu, Surf. Sci. 110, 189 (1981).
[CrossRef]

Perelman, L. T.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Quinten, M.

Schultz, S.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, J. Microsc. 202, 60 (2001).
[CrossRef] [PubMed]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, New J. Phys. 2, 27.1 (2000), http://njp.org .
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, Opt. Express 6, 213 (2000), http://www.opticsexpress.org .
[CrossRef] [PubMed]

Smith, D. R.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, J. Microsc. 202, 60 (2001).
[CrossRef] [PubMed]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, New J. Phys. 2, 27.1 (2000), http://njp.org .
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, Opt. Express 6, 213 (2000), http://www.opticsexpress.org .
[CrossRef] [PubMed]

Travis, L. D.

M. I. Mischenko, D. W. Mackowski, and L. D. Travis, Appl. Opt. 21, 4589 (1995).
[CrossRef]

Vollmer, M.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters, Vol. 25 of Springer Series in Material Science (Springer-Verlag, Berlin, 1995).
[CrossRef]

Wang, Y.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Weeber, J.-C.

J.-C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J.-P. Goudonnet, Phys. Rev. B 60, 9061 (1999).
[CrossRef]

Xu, H.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, Phys. Rev. Lett. 83, 4357 (1999).
[CrossRef]

Xu, Y.

Appl. Opt.

M. I. Mischenko, D. W. Mackowski, and L. D. Travis, Appl. Opt. 21, 4589 (1995).
[CrossRef]

Y. Xu, Appl. Opt. 34, 4573 (1995).
[CrossRef] [PubMed]

IEEE Trans. Antennas Propag.

J. P. Kottmann and O. J. F. Martin, IEEE Trans. Antennas Propag. 48, 1719 (2000).
[CrossRef]

J. Microsc.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, J. Microsc. 202, 60 (2001).
[CrossRef] [PubMed]

New J. Phys.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, New J. Phys. 2, 27.1 (2000), http://njp.org .
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

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

J.-C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J.-P. Goudonnet, Phys. Rev. B 60, 9061 (1999).
[CrossRef]

Phys. Rev. Lett.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, Phys. Rev. Lett. 83, 4357 (1999).
[CrossRef]

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Prog. Surf. Sci.

H. Metiu, Prog. Surf. Sci. 17, 153 (1984).

Rev. Mod. Phys.

M. Moskovits, Rev. Mod. Phys. 57, 783 (1985).
[CrossRef]

Science

S. Nie and S. R. Emory, Science 275, 1102 (1997).
[CrossRef] [PubMed]

Surf. Sci.

P. K. Aravind, A. Nitzan, and H. Metiu, Surf. Sci. 110, 189 (1981).
[CrossRef]

Other

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters, Vol. 25 of Springer Series in Material Science (Springer-Verlag, Berlin, 1995).
[CrossRef]

M. Bass, ed., Handbook of Optics, 2nd ed. (McGraw-Hill, New York, 1995), Vol. I, Chap.  43.8.

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Figures (4)

Fig. 1
Fig. 1

Two silver cylinders with the same diameter d and a separation distance a are illuminated with a plane wave propagating in the k direction with incident electric field E0. The distributions of the positive and negative polarization charges corresponding to the two coupled modes visible in Fig.  2 are also shown: (a) When the external field E0 is parallel to the line joining the particles, the charges oscillate in phase and the positive and negative charges accumulate on the sides of the gap. (b) For the other illumination direction, when the particles are large enough that their driving fields are out of phase, another mode can be excited.

Fig. 2
Fig. 2

SCS for two interacting cylinders as a function of the diameter d. The separation a is scaled with d, such that the ratio d/a=5 remains constant. Two incident polarizations are considered: (a) E0ex [corresponding to Fig.  1(a)] and (b) E0ey [Fig.  1(b)].

Fig. 3
Fig. 3

Same situation as in Fig.  2(b) but with a water background ϵw=1.78.

Fig. 4
Fig. 4

Amplitude enhancement as a function of the observation position in the gap between the two particles (dashed line in Fig.  1). Same geometry as in Fig.  2. Two incident polarizations are considered: (a) E0ex [corresponding to Fig.  2(a)] and (b) E0ey [Fig.  2(b)].

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