Abstract

Surface-enhanced Raman scattering (SERS) from a self-affine surface is shown to be very large. A theory is developed expressing this SERS in terms of the eigenmodes of a self-affine surface; the theory successfully explains the observed SERS from cold-deposited thin films that are known to have a self-affine structure. Spatial distributions of local fields at the fundamental and Stokes frequencies are strongly inhomogeneous and contain hot zones (high-field areas) localized in nanometer-sized regions that can be spatially separated for the two waves.

© 1996 Optical Society of America

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References

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  1. R. K. Chang, T. E. Furtak, eds., Surface Enhanced Raman Scattering (Plenum, New York, 1982).
    [CrossRef]
  2. R. Chiarello, V. Panella, J. Krim, C. Thompson, Phys. Rev. Lett. 67, 3408 (1991); C. Douketis, Z. Wang, T. L. Haslett, M. Moskovits, Phys. Rev. B 51, 11022 (1995).
    [CrossRef] [PubMed]
  3. A.-L. Barabasi, H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]
  4. V. M. Shalaev, R. Botet, J. Mercer, E. B. Stechel, “Optical properties of self-affine thin films,” Phys. Rev. B (in press).
  5. E. Betzig, J. K. Trautman, Science 257, 189 (1992).
    [CrossRef] [PubMed]
  6. J. M. Kim, J. M. Kosterlitz, Phys. Rev. Lett. 62, 2289 (1989).
    [CrossRef] [PubMed]
  7. E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1993); B. T. Draine, Astrophys. J. 333, 848 (1988).
    [CrossRef]
  8. V. M. Shalaev, Phys. Rep. 272, 62 (1996); V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, R. L. Armstrong, Phys. Rev. B 53, 2425 (1996); V. M. Shalaev, E. Y. Poliakov, V. A. Markel, Phys. Rev. B 53, 2437 (1996); M. I. Stockman, V. M. Shalaev, M. Moskovits, R. Botet, T. F. George, Phys. Rev. B 46, 2821 (1992).
    [CrossRef]
  9. P. B. Johnson, R. W. Christy, Phys. Rev. B 6, 3470 (1972).

1996 (1)

V. M. Shalaev, Phys. Rep. 272, 62 (1996); V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, R. L. Armstrong, Phys. Rev. B 53, 2425 (1996); V. M. Shalaev, E. Y. Poliakov, V. A. Markel, Phys. Rev. B 53, 2437 (1996); M. I. Stockman, V. M. Shalaev, M. Moskovits, R. Botet, T. F. George, Phys. Rev. B 46, 2821 (1992).
[CrossRef]

1993 (1)

E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1993); B. T. Draine, Astrophys. J. 333, 848 (1988).
[CrossRef]

1992 (1)

E. Betzig, J. K. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

1991 (1)

R. Chiarello, V. Panella, J. Krim, C. Thompson, Phys. Rev. Lett. 67, 3408 (1991); C. Douketis, Z. Wang, T. L. Haslett, M. Moskovits, Phys. Rev. B 51, 11022 (1995).
[CrossRef] [PubMed]

1989 (1)

J. M. Kim, J. M. Kosterlitz, Phys. Rev. Lett. 62, 2289 (1989).
[CrossRef] [PubMed]

1972 (1)

P. B. Johnson, R. W. Christy, Phys. Rev. B 6, 3470 (1972).

Barabasi, A.-L.

A.-L. Barabasi, H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Betzig, E.

E. Betzig, J. K. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

Botet, R.

V. M. Shalaev, R. Botet, J. Mercer, E. B. Stechel, “Optical properties of self-affine thin films,” Phys. Rev. B (in press).

Chiarello, R.

R. Chiarello, V. Panella, J. Krim, C. Thompson, Phys. Rev. Lett. 67, 3408 (1991); C. Douketis, Z. Wang, T. L. Haslett, M. Moskovits, Phys. Rev. B 51, 11022 (1995).
[CrossRef] [PubMed]

Christy, R. W.

P. B. Johnson, R. W. Christy, Phys. Rev. B 6, 3470 (1972).

Johnson, P. B.

P. B. Johnson, R. W. Christy, Phys. Rev. B 6, 3470 (1972).

Kim, J. M.

J. M. Kim, J. M. Kosterlitz, Phys. Rev. Lett. 62, 2289 (1989).
[CrossRef] [PubMed]

Kosterlitz, J. M.

J. M. Kim, J. M. Kosterlitz, Phys. Rev. Lett. 62, 2289 (1989).
[CrossRef] [PubMed]

Krim, J.

R. Chiarello, V. Panella, J. Krim, C. Thompson, Phys. Rev. Lett. 67, 3408 (1991); C. Douketis, Z. Wang, T. L. Haslett, M. Moskovits, Phys. Rev. B 51, 11022 (1995).
[CrossRef] [PubMed]

Mercer, J.

V. M. Shalaev, R. Botet, J. Mercer, E. B. Stechel, “Optical properties of self-affine thin films,” Phys. Rev. B (in press).

Panella, V.

R. Chiarello, V. Panella, J. Krim, C. Thompson, Phys. Rev. Lett. 67, 3408 (1991); C. Douketis, Z. Wang, T. L. Haslett, M. Moskovits, Phys. Rev. B 51, 11022 (1995).
[CrossRef] [PubMed]

Pennypacker, C. R.

E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1993); B. T. Draine, Astrophys. J. 333, 848 (1988).
[CrossRef]

Purcell, E. M.

E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1993); B. T. Draine, Astrophys. J. 333, 848 (1988).
[CrossRef]

Shalaev, V. M.

V. M. Shalaev, Phys. Rep. 272, 62 (1996); V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, R. L. Armstrong, Phys. Rev. B 53, 2425 (1996); V. M. Shalaev, E. Y. Poliakov, V. A. Markel, Phys. Rev. B 53, 2437 (1996); M. I. Stockman, V. M. Shalaev, M. Moskovits, R. Botet, T. F. George, Phys. Rev. B 46, 2821 (1992).
[CrossRef]

V. M. Shalaev, R. Botet, J. Mercer, E. B. Stechel, “Optical properties of self-affine thin films,” Phys. Rev. B (in press).

Stanley, H. E.

A.-L. Barabasi, H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Stechel, E. B.

V. M. Shalaev, R. Botet, J. Mercer, E. B. Stechel, “Optical properties of self-affine thin films,” Phys. Rev. B (in press).

Thompson, C.

R. Chiarello, V. Panella, J. Krim, C. Thompson, Phys. Rev. Lett. 67, 3408 (1991); C. Douketis, Z. Wang, T. L. Haslett, M. Moskovits, Phys. Rev. B 51, 11022 (1995).
[CrossRef] [PubMed]

Trautman, J. K.

E. Betzig, J. K. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

Astrophys. J. (1)

E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1993); B. T. Draine, Astrophys. J. 333, 848 (1988).
[CrossRef]

Phys. Rep. (1)

V. M. Shalaev, Phys. Rep. 272, 62 (1996); V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, R. L. Armstrong, Phys. Rev. B 53, 2425 (1996); V. M. Shalaev, E. Y. Poliakov, V. A. Markel, Phys. Rev. B 53, 2437 (1996); M. I. Stockman, V. M. Shalaev, M. Moskovits, R. Botet, T. F. George, Phys. Rev. B 46, 2821 (1992).
[CrossRef]

Phys. Rev. B (1)

P. B. Johnson, R. W. Christy, Phys. Rev. B 6, 3470 (1972).

Phys. Rev. Lett. (2)

J. M. Kim, J. M. Kosterlitz, Phys. Rev. Lett. 62, 2289 (1989).
[CrossRef] [PubMed]

R. Chiarello, V. Panella, J. Krim, C. Thompson, Phys. Rev. Lett. 67, 3408 (1991); C. Douketis, Z. Wang, T. L. Haslett, M. Moskovits, Phys. Rev. B 51, 11022 (1995).
[CrossRef] [PubMed]

Science (1)

E. Betzig, J. K. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

Other (3)

R. K. Chang, T. E. Furtak, eds., Surface Enhanced Raman Scattering (Plenum, New York, 1982).
[CrossRef]

A.-L. Barabasi, H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

V. M. Shalaev, R. Botet, J. Mercer, E. B. Stechel, “Optical properties of self-affine thin films,” Phys. Rev. B (in press).

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Figures (2)

Fig. 1
Fig. 1

(a) Self-affine film obtained in the RSS model (D = 2.6). (b) The enhancement of Raman scattering, GRS,∥ = (GRS,x + GRS,y)/2 and GRS,⊥ = GRS,z, on silver self-affine films for small and large Stokes shifts [see Eqs. (5) and (6)].

Fig. 2
Fig. 2

(a) Spatial distributions for the local fields at the fundamental frequency, λ = 550 nm (bottom plot; the field distribution is magnified by 3), and for the Stokes fields, λs = 600 nm (top plot). (The applied field is linearly polarized in the plane of the Ag film.) (b), (c) The contour plots for the field distributions shown in (a).

Equations (7)

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d i , α = α 0 [ E α ( 0 ) + j W ij , αβ d j , β ] ,
E i , α = α 0 1 d i , α = Z j α ij , αβ E β ( 0 ) , α ij , αβ α ij , αβ ( ω ) = n | n n | ( Z w n ) .
d i , α s = κ i E i , α + α 0 s j W ij , αβ d j , β s ,
G RS = | Z s Z | 2 | E ( 0 ) | 2 α j , β α s [ α j , βγ E γ ( 0 ) ] α j , δα s * [ α j , δ δ * E δ ( 0 ) * ] S ,
G RS , η = | Z | 4 α | ( α j 2 ) αη | 2 S ,
G RS , η = | Z | 2 α | α j , αη | 2 S .
I i s = | Z s | 4 | κ | 2 α j∊S | α ij , αβ s E j , β | 2 ,

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