Abstract

Surface plasmons can be excited on a metal by an external plane-wave beam through the use of prism or grating couplers or by introducing roughness. This can enhance the electric field at the surface compared with that in the incident beam, and it has been suggested that this effect is an important aspect of surface-enhanced Raman scattering. A general upper limit for this field enhancement is derived on the basis of energy conservation. Numerical results are given for Ag, Au, and Cu. With a perfect coupler on a Ag surface, the maximum increase of the square of the electric field in the 2–3-eV range is ≅300. On randomly roughened surfaces, the estimated enhancements are of the order of unity.

© 1981 Optical Society of America

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  1. R. M. Hexter, M. G. Albrecht, Spectrochim. Acta 35A, 233 (1979).
  2. J. C. Tsang, J. R. Kirtley, J. A. Bradley, Phys. Rev. Lett. 43, 772 (1979).
    [CrossRef]
  3. E. Burstein, J. Chen, C. Y. Chen, S. Lundquist, E. Tosatti, Solid State Commun. 29, 567 (1979).
    [CrossRef]
  4. A. Otto, Z. Phys. 216, 398 (1968).
    [CrossRef]
  5. E. Kretschmann, H. Raether, Z. Naturforsch. Teil A 23, 2135 (1968).
  6. W. H. Weber, S. L. McCarthy, Appl. Phys. Lett. 25, 396 (1974).
    [CrossRef]
  7. H. J. Simon, D. E. Mitchell, J. G. Watson, Phys. Rev. Lett. 33, 1531 (1974).
    [CrossRef]
  8. Y. J. Chen, W. P. Chen, E. Burstein, Phys. Rev. Lett. 36, 1207 (1976).
    [CrossRef]
  9. R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
    [CrossRef]
  10. I. Pockrand, J. Phys. D. 9, 2423 (1976).
    [CrossRef]
  11. D. Heitmann, Opt. Commun. 20, 292 (1977).
    [CrossRef]
  12. S. S. Jha, J. R. Kirtley, J. C. Tsang, Phys. Rev. B 22, 3973 (1980).
    [CrossRef]
  13. P. B. Johnson, R. W. Christy, Phys. Rev. B 12, 4370 (1972).
    [CrossRef]
  14. A. Girlando, M. R. Philpott, D. Heitmann, J. D. Swalen, R. Santo, J. Chem. Phys. 72, 5187 (1980).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  18. B. Pettinger, V. Wenning, D. M. Kolb, Ber. Bunsenges. Phys. Chem. 82, 1236 (1978).
  19. W. H. Weber, C. F. Eagen, Opt. Lett. 4, 236 (1979).
    [CrossRef] [PubMed]
  20. C. F. Eagen, W. H. Weber, S. L. McCarthy, R. W. Terhune, Chem. Phys. Lett. 75, 274 (1980).
    [CrossRef]
  21. W. H. Weber, G. W. Ford, Phys. Rev. Lett. 44, 1774 (1980).
    [CrossRef]

1980 (6)

S. S. Jha, J. R. Kirtley, J. C. Tsang, Phys. Rev. B 22, 3973 (1980).
[CrossRef]

A. Girlando, M. R. Philpott, D. Heitmann, J. D. Swalen, R. Santo, J. Chem. Phys. 72, 5187 (1980).
[CrossRef]

P. N. Sanda, J. M. Warlaumont, J. E. Demuth, J. C. Tsang, K. Christmann, J. A. Bradley, Phys. Rev. Lett. 45, 1519 (1980).
[CrossRef]

S. O. Sari, D. K. Cohen, K. D. Scherkoske, Phys. Rev. B 21, 2162 (1980).
[CrossRef]

C. F. Eagen, W. H. Weber, S. L. McCarthy, R. W. Terhune, Chem. Phys. Lett. 75, 274 (1980).
[CrossRef]

W. H. Weber, G. W. Ford, Phys. Rev. Lett. 44, 1774 (1980).
[CrossRef]

1979 (4)

W. H. Weber, C. F. Eagen, Opt. Lett. 4, 236 (1979).
[CrossRef] [PubMed]

R. M. Hexter, M. G. Albrecht, Spectrochim. Acta 35A, 233 (1979).

J. C. Tsang, J. R. Kirtley, J. A. Bradley, Phys. Rev. Lett. 43, 772 (1979).
[CrossRef]

E. Burstein, J. Chen, C. Y. Chen, S. Lundquist, E. Tosatti, Solid State Commun. 29, 567 (1979).
[CrossRef]

1978 (1)

B. Pettinger, V. Wenning, D. M. Kolb, Ber. Bunsenges. Phys. Chem. 82, 1236 (1978).

1977 (1)

D. Heitmann, Opt. Commun. 20, 292 (1977).
[CrossRef]

1976 (2)

I. Pockrand, J. Phys. D. 9, 2423 (1976).
[CrossRef]

Y. J. Chen, W. P. Chen, E. Burstein, Phys. Rev. Lett. 36, 1207 (1976).
[CrossRef]

1974 (2)

W. H. Weber, S. L. McCarthy, Appl. Phys. Lett. 25, 396 (1974).
[CrossRef]

H. J. Simon, D. E. Mitchell, J. G. Watson, Phys. Rev. Lett. 33, 1531 (1974).
[CrossRef]

1972 (1)

P. B. Johnson, R. W. Christy, Phys. Rev. B 12, 4370 (1972).
[CrossRef]

1970 (1)

1968 (3)

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
[CrossRef]

A. Otto, Z. Phys. 216, 398 (1968).
[CrossRef]

E. Kretschmann, H. Raether, Z. Naturforsch. Teil A 23, 2135 (1968).

Albrecht, M. G.

R. M. Hexter, M. G. Albrecht, Spectrochim. Acta 35A, 233 (1979).

Arakawa, E. T.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
[CrossRef]

Bradley, J. A.

P. N. Sanda, J. M. Warlaumont, J. E. Demuth, J. C. Tsang, K. Christmann, J. A. Bradley, Phys. Rev. Lett. 45, 1519 (1980).
[CrossRef]

J. C. Tsang, J. R. Kirtley, J. A. Bradley, Phys. Rev. Lett. 43, 772 (1979).
[CrossRef]

Burstein, E.

E. Burstein, J. Chen, C. Y. Chen, S. Lundquist, E. Tosatti, Solid State Commun. 29, 567 (1979).
[CrossRef]

Y. J. Chen, W. P. Chen, E. Burstein, Phys. Rev. Lett. 36, 1207 (1976).
[CrossRef]

Chen, C. Y.

E. Burstein, J. Chen, C. Y. Chen, S. Lundquist, E. Tosatti, Solid State Commun. 29, 567 (1979).
[CrossRef]

Chen, J.

E. Burstein, J. Chen, C. Y. Chen, S. Lundquist, E. Tosatti, Solid State Commun. 29, 567 (1979).
[CrossRef]

Chen, W. P.

Y. J. Chen, W. P. Chen, E. Burstein, Phys. Rev. Lett. 36, 1207 (1976).
[CrossRef]

Chen, Y. J.

Y. J. Chen, W. P. Chen, E. Burstein, Phys. Rev. Lett. 36, 1207 (1976).
[CrossRef]

Christmann, K.

P. N. Sanda, J. M. Warlaumont, J. E. Demuth, J. C. Tsang, K. Christmann, J. A. Bradley, Phys. Rev. Lett. 45, 1519 (1980).
[CrossRef]

Christy, R. W.

P. B. Johnson, R. W. Christy, Phys. Rev. B 12, 4370 (1972).
[CrossRef]

Cohen, D. K.

S. O. Sari, D. K. Cohen, K. D. Scherkoske, Phys. Rev. B 21, 2162 (1980).
[CrossRef]

Cowan, J. J.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
[CrossRef]

Demuth, J. E.

P. N. Sanda, J. M. Warlaumont, J. E. Demuth, J. C. Tsang, K. Christmann, J. A. Bradley, Phys. Rev. Lett. 45, 1519 (1980).
[CrossRef]

Eagen, C. F.

C. F. Eagen, W. H. Weber, S. L. McCarthy, R. W. Terhune, Chem. Phys. Lett. 75, 274 (1980).
[CrossRef]

W. H. Weber, C. F. Eagen, Opt. Lett. 4, 236 (1979).
[CrossRef] [PubMed]

Ford, G. W.

W. H. Weber, G. W. Ford, Phys. Rev. Lett. 44, 1774 (1980).
[CrossRef]

Girlando, A.

A. Girlando, M. R. Philpott, D. Heitmann, J. D. Swalen, R. Santo, J. Chem. Phys. 72, 5187 (1980).
[CrossRef]

Hamm, R. N.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
[CrossRef]

Heitmann, D.

A. Girlando, M. R. Philpott, D. Heitmann, J. D. Swalen, R. Santo, J. Chem. Phys. 72, 5187 (1980).
[CrossRef]

D. Heitmann, Opt. Commun. 20, 292 (1977).
[CrossRef]

Hexter, R. M.

R. M. Hexter, M. G. Albrecht, Spectrochim. Acta 35A, 233 (1979).

Jha, S. S.

S. S. Jha, J. R. Kirtley, J. C. Tsang, Phys. Rev. B 22, 3973 (1980).
[CrossRef]

Johnson, P. B.

P. B. Johnson, R. W. Christy, Phys. Rev. B 12, 4370 (1972).
[CrossRef]

Kirtley, J. R.

S. S. Jha, J. R. Kirtley, J. C. Tsang, Phys. Rev. B 22, 3973 (1980).
[CrossRef]

J. C. Tsang, J. R. Kirtley, J. A. Bradley, Phys. Rev. Lett. 43, 772 (1979).
[CrossRef]

Kolb, D. M.

B. Pettinger, V. Wenning, D. M. Kolb, Ber. Bunsenges. Phys. Chem. 82, 1236 (1978).

Kretschmann, E.

E. Kretschmann, H. Raether, Z. Naturforsch. Teil A 23, 2135 (1968).

Lundquist, S.

E. Burstein, J. Chen, C. Y. Chen, S. Lundquist, E. Tosatti, Solid State Commun. 29, 567 (1979).
[CrossRef]

McCarthy, S. L.

C. F. Eagen, W. H. Weber, S. L. McCarthy, R. W. Terhune, Chem. Phys. Lett. 75, 274 (1980).
[CrossRef]

W. H. Weber, S. L. McCarthy, Appl. Phys. Lett. 25, 396 (1974).
[CrossRef]

Mitchell, D. E.

H. J. Simon, D. E. Mitchell, J. G. Watson, Phys. Rev. Lett. 33, 1531 (1974).
[CrossRef]

Otto, A.

A. Otto, Z. Phys. 216, 398 (1968).
[CrossRef]

Pettinger, B.

B. Pettinger, V. Wenning, D. M. Kolb, Ber. Bunsenges. Phys. Chem. 82, 1236 (1978).

Philpott, M. R.

A. Girlando, M. R. Philpott, D. Heitmann, J. D. Swalen, R. Santo, J. Chem. Phys. 72, 5187 (1980).
[CrossRef]

Pockrand, I.

I. Pockrand, J. Phys. D. 9, 2423 (1976).
[CrossRef]

Raether, H.

E. Kretschmann, H. Raether, Z. Naturforsch. Teil A 23, 2135 (1968).

Ritchie, R. H.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
[CrossRef]

Sanda, P. N.

P. N. Sanda, J. M. Warlaumont, J. E. Demuth, J. C. Tsang, K. Christmann, J. A. Bradley, Phys. Rev. Lett. 45, 1519 (1980).
[CrossRef]

Santo, R.

A. Girlando, M. R. Philpott, D. Heitmann, J. D. Swalen, R. Santo, J. Chem. Phys. 72, 5187 (1980).
[CrossRef]

Sari, S. O.

S. O. Sari, D. K. Cohen, K. D. Scherkoske, Phys. Rev. B 21, 2162 (1980).
[CrossRef]

Scherkoske, K. D.

S. O. Sari, D. K. Cohen, K. D. Scherkoske, Phys. Rev. B 21, 2162 (1980).
[CrossRef]

Simon, H. J.

H. J. Simon, D. E. Mitchell, J. G. Watson, Phys. Rev. Lett. 33, 1531 (1974).
[CrossRef]

Stanford, J. L.

Swalen, J. D.

A. Girlando, M. R. Philpott, D. Heitmann, J. D. Swalen, R. Santo, J. Chem. Phys. 72, 5187 (1980).
[CrossRef]

Terhune, R. W.

C. F. Eagen, W. H. Weber, S. L. McCarthy, R. W. Terhune, Chem. Phys. Lett. 75, 274 (1980).
[CrossRef]

Tosatti, E.

E. Burstein, J. Chen, C. Y. Chen, S. Lundquist, E. Tosatti, Solid State Commun. 29, 567 (1979).
[CrossRef]

Tsang, J. C.

S. S. Jha, J. R. Kirtley, J. C. Tsang, Phys. Rev. B 22, 3973 (1980).
[CrossRef]

P. N. Sanda, J. M. Warlaumont, J. E. Demuth, J. C. Tsang, K. Christmann, J. A. Bradley, Phys. Rev. Lett. 45, 1519 (1980).
[CrossRef]

J. C. Tsang, J. R. Kirtley, J. A. Bradley, Phys. Rev. Lett. 43, 772 (1979).
[CrossRef]

Warlaumont, J. M.

P. N. Sanda, J. M. Warlaumont, J. E. Demuth, J. C. Tsang, K. Christmann, J. A. Bradley, Phys. Rev. Lett. 45, 1519 (1980).
[CrossRef]

Watson, J. G.

H. J. Simon, D. E. Mitchell, J. G. Watson, Phys. Rev. Lett. 33, 1531 (1974).
[CrossRef]

Weber, W. H.

W. H. Weber, G. W. Ford, Phys. Rev. Lett. 44, 1774 (1980).
[CrossRef]

C. F. Eagen, W. H. Weber, S. L. McCarthy, R. W. Terhune, Chem. Phys. Lett. 75, 274 (1980).
[CrossRef]

W. H. Weber, C. F. Eagen, Opt. Lett. 4, 236 (1979).
[CrossRef] [PubMed]

W. H. Weber, S. L. McCarthy, Appl. Phys. Lett. 25, 396 (1974).
[CrossRef]

Wenning, V.

B. Pettinger, V. Wenning, D. M. Kolb, Ber. Bunsenges. Phys. Chem. 82, 1236 (1978).

Appl. Phys. Lett. (1)

W. H. Weber, S. L. McCarthy, Appl. Phys. Lett. 25, 396 (1974).
[CrossRef]

Ber. Bunsenges. Phys. Chem. (1)

B. Pettinger, V. Wenning, D. M. Kolb, Ber. Bunsenges. Phys. Chem. 82, 1236 (1978).

Chem. Phys. Lett. (1)

C. F. Eagen, W. H. Weber, S. L. McCarthy, R. W. Terhune, Chem. Phys. Lett. 75, 274 (1980).
[CrossRef]

J. Chem. Phys. (1)

A. Girlando, M. R. Philpott, D. Heitmann, J. D. Swalen, R. Santo, J. Chem. Phys. 72, 5187 (1980).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. D. (1)

I. Pockrand, J. Phys. D. 9, 2423 (1976).
[CrossRef]

Opt. Commun. (1)

D. Heitmann, Opt. Commun. 20, 292 (1977).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (3)

S. S. Jha, J. R. Kirtley, J. C. Tsang, Phys. Rev. B 22, 3973 (1980).
[CrossRef]

P. B. Johnson, R. W. Christy, Phys. Rev. B 12, 4370 (1972).
[CrossRef]

S. O. Sari, D. K. Cohen, K. D. Scherkoske, Phys. Rev. B 21, 2162 (1980).
[CrossRef]

Phys. Rev. Lett. (6)

P. N. Sanda, J. M. Warlaumont, J. E. Demuth, J. C. Tsang, K. Christmann, J. A. Bradley, Phys. Rev. Lett. 45, 1519 (1980).
[CrossRef]

H. J. Simon, D. E. Mitchell, J. G. Watson, Phys. Rev. Lett. 33, 1531 (1974).
[CrossRef]

Y. J. Chen, W. P. Chen, E. Burstein, Phys. Rev. Lett. 36, 1207 (1976).
[CrossRef]

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
[CrossRef]

J. C. Tsang, J. R. Kirtley, J. A. Bradley, Phys. Rev. Lett. 43, 772 (1979).
[CrossRef]

W. H. Weber, G. W. Ford, Phys. Rev. Lett. 44, 1774 (1980).
[CrossRef]

Solid State Commun. (1)

E. Burstein, J. Chen, C. Y. Chen, S. Lundquist, E. Tosatti, Solid State Commun. 29, 567 (1979).
[CrossRef]

Spectrochim. Acta (1)

R. M. Hexter, M. G. Albrecht, Spectrochim. Acta 35A, 233 (1979).

Z. Naturforsch. Teil A (1)

E. Kretschmann, H. Raether, Z. Naturforsch. Teil A 23, 2135 (1968).

Z. Phys. (1)

A. Otto, Z. Phys. 216, 398 (1968).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Schematic drawing of the excitation of a surface-plasmon wave with a plane-wave coupler, which is represented by the dashed lines. The coupler can be a prism, a grating, or random roughness.

Fig. 2
Fig. 2

Calculated upper limit for the electric-field enhancements achievable with a perfect grating coupler of d = 800 nm on Ag, Au, and Cu surfaces.

Equations (10)

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

H S P = H y y ˆ exp [ i ( k S P x ω t ) ] { exp ( q 1 z ) z > 0 exp ( + q 2 z ) z < 0 ,
E SP = c H y ω exp [ i ( k S P x ω t ) ] { ( i q 1 x ˆ k S P z ˆ ) exp ( q 1 z ) / 1 z > 0 ( i q 2 x ˆ k S P z ˆ ) exp ( + q 2 z ) / 2 z < 0 ,
k SP = ω c ( 1 2 1 + 2 ) 1 / 2 , q i = ω c ( i 2 1 + 2 ) 1 / 2 , R l ( k S P ) , R l ( q i ) > 0 .
P S P = c 8 π d z R l { E S P × H S P * } · x ˆ .
P S P = ω 1 16 π | E S P ( 0 + ) | 2 | q 1 | 2 + | k S P | 2 R l { k S P ( 1 q 1 + 2 q 2 ) 2 q 1 q 2 } ,
d P S P d x = α P S P ,
I = c 8 π 1 1 / 2 cos θ | E 0 | 2 ( 1 R ) ,
α P S P = c 8 π 1 1 / 2 cos θ | E 0 | 2 ( 1 R ) .
| E S P ( 0 + ) | 2 | E 0 | 2 = 2 cos θ 2 2 ( 1 R ) 1 1 / 2 2 ( 2 1 ) 1 / 2 .
| E S P ( 0 + ) | 2 | E 0 | 2 q 1 k S P 2 ( 2 ) 1 / 2 ( 2 1 ) 1 1 / 2 2 ,

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