Abstract

The local electric fields on a semicontinuous metal film are shown to experience giant fluctuations in the visible and infrared spectral ranges when the dissipation in metallic grains is small. The field fluctuations result in strongly enhanced Raman scattering. The scattered local fields at the Stokes frequency are concentrated in sharp well-separated peaks and are enhanced up to giant values, 1014, that exceed by many orders of magnitude the average enhancement, 106. This opens a fascinating possibility for Raman scattering spectroscopy of single molecules on a semicontinuous metal film. A developed scaling theory for surface-enhanced Raman scattering from a semicontinuous film successfully explains the experimental observations.

© 1998 Optical Society of America

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References

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  1. R. W. Cohen, G. D. Cody, M. D. Coutts, and B. Abeles, Phys. Rev. B 8, 3689 (1973); G. A. Niklasson and C. G. Granqvist, J. Appl. Phys. 55, 3382 (1984); Y. Yagil, P. Gadenne, C. Julien, and G. Deutscher, Phys. Rev. B PRBMDO 46, 2503 (1992); P. Gadenne, A. Beghadi, and J. Lafait, Opt. Commun. OPCOB8 65, 17 (1988).
    [CrossRef]
  2. D. J. Bergman and D. Stroud, Solid State Phys. 46, 147 (1992); D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor & Francis, Philadelphia, 1991).
  3. F. Brouers, D. Rauw, J. P. Clerc, and G. Giraud, Phys. Rev. B 49, 14582 (1994); J. P. Clerc, G. Giraud, and J. M. Luck, Adv. Phys. 39, 191 (1990).
    [CrossRef]
  4. A. K. Sarychev, D. J. Bergman, and Y. Yagil, Phys. Rev. B 51, 5366 (1995).
    [CrossRef]
  5. S. Nie and S. R. Emory, Science 275, 1102 (1997).
    [CrossRef] [PubMed]
  6. K. Kneipp, Y. Wang, H. Kneip, L. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
    [CrossRef]
  7. M. Moskovits, Rev. Mod. Phys. 57, 783 (1985); A. Otto, I. Mrozek, H. Grabhorn, and W. Akemann, J. Phys. C 4, 1143 (1992); R. K. Chang and T. E. Furtak, eds., Surface Enhanced Raman Scattering (Plenum, New York, 1982); M. I. Stockman, V. M. Shalaev, M. Moskovits, R. Botet, and T. F. George, Phys. Rev. BPRBMDO 46, 2821 (1992).
    [CrossRef]
  8. V. M. Shalaev, Phys. Rep. 272, 61 (1996).
    [CrossRef]
  9. V. M. Shalaev, R. Botet, J. Mercer, and E. B. Stechel, Phys. Rev. B 54, 8235 (1996); E. Y. Poliakov, V. M. Shalaev, V. A. Markel, and R. Botet, Opt. Lett. 21, 1628 (1996).
    [CrossRef] [PubMed]
  10. V. A. Markel, L. S. Muratov, M. I. Stockman, and T. F. George, Phys. Rev. B 43, 8183 (1991); M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, Phys. Rev. Lett. 72, 2486 (1994).
    [CrossRef] [PubMed]
  11. D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, V. M. Shalaev, J. Suh, and R. Botet, Phys. Rev. Lett. 72, 4149 (1994); V. M. Shalaev and M. Moskovits, Phys. Rev. Lett. 75, 2451 (1995); S. I. Bozhevolnyi, I. I. Smolyaninov, and A. V. Zayats, Phys. Rev. B PRBMDO 51, 17916 (1995).
    [CrossRef] [PubMed]
  12. E. Betzig and J. K. Trautman, Science 257, 189 (1992); T. L. Ferrel, S. L. Sharp, and R. J. Warmack, Ultramicroscopy 42–44, 408 (1992).
    [CrossRef] [PubMed]
  13. W. P. Ambrose, P. M. Goodwin, J. C. Martin, and R. A. Keller, Science 265, 364 (1994); W. E. Moerner, T. Plakhotnik, T. Irngartinger, U. P. Wild, D. W. Pohl, and B. Hecht, Phys. Rev. Lett. 73, 2764 (1994); C. Girard and A. Dereux, Rep. Prog. Phys. RPPHAG 59, 657 (1996).
    [CrossRef] [PubMed]
  14. A. M. Dykhne, Sov. Phys. JETP 32, 348 (1971).
  15. F. Brouers, S. Blacher, and A. K. Sarychev, in Fractals in the Natural and Applied Sciences (Chapman & Hall, London, 1995), Chap. 24; F. Brouers, S. Blacher, A. N. Lagarkov, A. K. Sarychev, P. Gadenne, and V. M. Shalaev, Phys. Rev. B 55, 13234 (1997).
    [CrossRef]
  16. P. J. Reynolds, W. Klein, and H. E. Stanley, J. Phys. C 10, L167 (1977); A. K. Sarychev, Zk. Eksp. Teor. Fiz. 72, 1001 (1977) [Sov. Phys. JETP 45, 524 (1977)].
    [CrossRef]
  17. P. Gadenne, Y. Yagil, and G. Deutscher, J. Appl. Phys. 66, 3019 (1989).
    [CrossRef]
  18. V. L. Schlegel and T. M. Corton, Ann. Chem. 63, 241 (1991).

1997 (2)

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

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

1996 (1)

V. M. Shalaev, Phys. Rep. 272, 61 (1996).
[CrossRef]

1995 (1)

A. K. Sarychev, D. J. Bergman, and Y. Yagil, Phys. Rev. B 51, 5366 (1995).
[CrossRef]

1989 (1)

P. Gadenne, Y. Yagil, and G. Deutscher, J. Appl. Phys. 66, 3019 (1989).
[CrossRef]

1971 (1)

A. M. Dykhne, Sov. Phys. JETP 32, 348 (1971).

Bergman, D. J.

A. K. Sarychev, D. J. Bergman, and Y. Yagil, Phys. Rev. B 51, 5366 (1995).
[CrossRef]

Dasari, R. R.

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

Deutscher, G.

P. Gadenne, Y. Yagil, and G. Deutscher, J. Appl. Phys. 66, 3019 (1989).
[CrossRef]

Dykhne, A. M.

A. M. Dykhne, Sov. Phys. JETP 32, 348 (1971).

Emory, S. R.

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

Feld, M. S.

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

Gadenne, P.

P. Gadenne, Y. Yagil, and G. Deutscher, J. Appl. Phys. 66, 3019 (1989).
[CrossRef]

Itzkan, I.

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

Kneip, H.

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

Kneipp, K.

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

Nie, S.

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

Perelman, L.

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

Sarychev, A. K.

A. K. Sarychev, D. J. Bergman, and Y. Yagil, Phys. Rev. B 51, 5366 (1995).
[CrossRef]

Shalaev, V. M.

V. M. Shalaev, Phys. Rep. 272, 61 (1996).
[CrossRef]

Wang, Y.

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

Yagil, Y.

A. K. Sarychev, D. J. Bergman, and Y. Yagil, Phys. Rev. B 51, 5366 (1995).
[CrossRef]

P. Gadenne, Y. Yagil, and G. Deutscher, J. Appl. Phys. 66, 3019 (1989).
[CrossRef]

J. Appl. Phys. (1)

P. Gadenne, Y. Yagil, and G. Deutscher, J. Appl. Phys. 66, 3019 (1989).
[CrossRef]

Phys. Rep. (1)

V. M. Shalaev, Phys. Rep. 272, 61 (1996).
[CrossRef]

Phys. Rev. B (1)

A. K. Sarychev, D. J. Bergman, and Y. Yagil, Phys. Rev. B 51, 5366 (1995).
[CrossRef]

Phys. Rev. Lett. (1)

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

Science (1)

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

Sov. Phys. JETP (1)

A. M. Dykhne, Sov. Phys. JETP 32, 348 (1971).

Other (12)

F. Brouers, S. Blacher, and A. K. Sarychev, in Fractals in the Natural and Applied Sciences (Chapman & Hall, London, 1995), Chap. 24; F. Brouers, S. Blacher, A. N. Lagarkov, A. K. Sarychev, P. Gadenne, and V. M. Shalaev, Phys. Rev. B 55, 13234 (1997).
[CrossRef]

P. J. Reynolds, W. Klein, and H. E. Stanley, J. Phys. C 10, L167 (1977); A. K. Sarychev, Zk. Eksp. Teor. Fiz. 72, 1001 (1977) [Sov. Phys. JETP 45, 524 (1977)].
[CrossRef]

M. Moskovits, Rev. Mod. Phys. 57, 783 (1985); A. Otto, I. Mrozek, H. Grabhorn, and W. Akemann, J. Phys. C 4, 1143 (1992); R. K. Chang and T. E. Furtak, eds., Surface Enhanced Raman Scattering (Plenum, New York, 1982); M. I. Stockman, V. M. Shalaev, M. Moskovits, R. Botet, and T. F. George, Phys. Rev. BPRBMDO 46, 2821 (1992).
[CrossRef]

V. L. Schlegel and T. M. Corton, Ann. Chem. 63, 241 (1991).

R. W. Cohen, G. D. Cody, M. D. Coutts, and B. Abeles, Phys. Rev. B 8, 3689 (1973); G. A. Niklasson and C. G. Granqvist, J. Appl. Phys. 55, 3382 (1984); Y. Yagil, P. Gadenne, C. Julien, and G. Deutscher, Phys. Rev. B PRBMDO 46, 2503 (1992); P. Gadenne, A. Beghadi, and J. Lafait, Opt. Commun. OPCOB8 65, 17 (1988).
[CrossRef]

D. J. Bergman and D. Stroud, Solid State Phys. 46, 147 (1992); D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor & Francis, Philadelphia, 1991).

F. Brouers, D. Rauw, J. P. Clerc, and G. Giraud, Phys. Rev. B 49, 14582 (1994); J. P. Clerc, G. Giraud, and J. M. Luck, Adv. Phys. 39, 191 (1990).
[CrossRef]

V. M. Shalaev, R. Botet, J. Mercer, and E. B. Stechel, Phys. Rev. B 54, 8235 (1996); E. Y. Poliakov, V. M. Shalaev, V. A. Markel, and R. Botet, Opt. Lett. 21, 1628 (1996).
[CrossRef] [PubMed]

V. A. Markel, L. S. Muratov, M. I. Stockman, and T. F. George, Phys. Rev. B 43, 8183 (1991); M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, Phys. Rev. Lett. 72, 2486 (1994).
[CrossRef] [PubMed]

D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, V. M. Shalaev, J. Suh, and R. Botet, Phys. Rev. Lett. 72, 4149 (1994); V. M. Shalaev and M. Moskovits, Phys. Rev. Lett. 75, 2451 (1995); S. I. Bozhevolnyi, I. I. Smolyaninov, and A. V. Zayats, Phys. Rev. B PRBMDO 51, 17916 (1995).
[CrossRef] [PubMed]

E. Betzig and J. K. Trautman, Science 257, 189 (1992); T. L. Ferrel, S. L. Sharp, and R. J. Warmack, Ultramicroscopy 42–44, 408 (1992).
[CrossRef] [PubMed]

W. P. Ambrose, P. M. Goodwin, J. C. Martin, and R. A. Keller, Science 265, 364 (1994); W. E. Moerner, T. Plakhotnik, T. Irngartinger, U. P. Wild, D. W. Pohl, and B. Hecht, Phys. Rev. Lett. 73, 2764 (1994); C. Girard and A. Dereux, Rep. Prog. Phys. RPPHAG 59, 657 (1996).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Distributions of the local enhancements of Raman scattering on a silver semicontinuous film at the percolation threshold for different wavelengths: (a) λ=0.36 μm, (b) λ =0.5 μm, (c) λ=1.5 μm, (d) λ=10 μm, and (e) λ=20 μm.

Fig. 2
Fig. 2

Normalized SERS A¯=A/A0 as a function of the metal concentration, Δp=p-pc, on a silver semicontinuous film. (The curve indicates theoretical calculations; the points indicate experimental data.)

Fig. 3
Fig. 3

SERS scaling function, F(x), as a function of x=(p -pc)/Δ* [see Eq. (4)], for different wavelengths: λ=0.9 μm (#), λ=1.1 μm (+), λ=1.3 μm (*), λ=1.5 μm (@), λ =1.7 μm (x), and λ=1.9 μm (○).

Equations (4)

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

A=|T(p)|2IR(x, y)dxdy/(|E0|4εd2),
A(p=pc)=A0(|εm|/εd)2νp/(t+s)(|εm|/εm).
A0|εm|3/(εdεm2)(ωpτ)2/εd,
A(p, ω)=A0(ω)F(Δp/Δ*).

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