Abstract

We show experimentally that the radiation generated in infrared–visible sum-frequency mixing at an air–silver interface can be greatly enhanced when the visible input beam excites a surface plasmon–polariton at the interface. With either a prism or a grating used to couple the visible radiation with the surface polariton, the sum-frequency-generation yield is observed to be enhanced by a factor of 102 for the prism and 104 for the grating for counterpropagating infrared and visible input beams. The result for the prism configuration can be simply understood in terms of the field enhancement associated with the surface polariton excited by the visible input beam. For the grating configuration there is an additional effect in that the nonlinear polarization at the sum frequency can also couple with a surface polariton. As a result the effective interaction length of the sum-frequency-mixing process is sizably increased. The experimental results are in good agreement with estimates based on this model.

© 1999 Optical Society of America

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References

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    [CrossRef]
  2. J. F. McGilp, D. Weaire, and C. H. Patterson, Epioptics, Linear and Nonlinear Optical Spectroscopy of Surfaces and Interfaces (Springer-Verlag, Berlin, 1995).
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    [CrossRef]
  5. R. Braun, B. D. Casson, C. D. Bain, E. W. M. van der Ham, Q. H. F. Vrehen, E. R. Eliel, A. M. Briggs and P. B. Davies, J. Chem. Phys. 110, 4634 (1999).
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    [CrossRef]
  8. S. R. Hatch, R. S. Polizotti, S. Dougal, and P. Rabinowitz, Chem. Phys. Lett. 196, 97 (1992).
    [CrossRef]
  9. J. C. Conboy, J. L. Daschbach, and G. L. Richmond, J. Phys. Chem. 98, 9688 (1994).
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  10. J. C. Conboy, M. C. Messmer, and G. L. Richmond, J. Phys. Chem. 100, 7617 (1996).
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    [CrossRef]
  18. E. W. M. van der Ham, Q. H. F. Vrehen, and E. R. Eliel, Opt. Lett. 21, 1448 (1996).
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  19. E. W. M. van der Ham, Q. H. F. Vrehen, and E. R. Eliel, Surf. Sci. 398, 96 (1996).
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  20. D. Oepts, A. F. G. van der Meer, and P. W. van Amersfoort, Infrared Phys. 36, 297 (1995).
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  22. W. N. Hansen, J. Opt. Soc. Am. 58, 380 (1968).
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  23. B. Pettinger, A. Tadjeddine, and D. M. Kolb, Chem. Phys. Lett. 66, 544 (1979).
    [CrossRef]
  24. R. A. Watts, T. W. Preist, and J. R. Sambles, Phys. Rev. Lett. 79, 3978 (1997).
    [CrossRef]
  25. I. A. Avrutsky, P. V. Basakutsa, and S. Surov, Waveguide Corrugated Structures in Integrated and Fiber Optics (Nauka, Moscow, 1991).
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    [CrossRef]
  27. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  28. J. Rudnick and E. A. Stern, Phys. Rev. B 4, 4274 (1971).
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    [CrossRef]

1999

R. Braun, B. D. Casson, C. D. Bain, E. W. M. van der Ham, Q. H. F. Vrehen, E. R. Eliel, A. M. Briggs and P. B. Davies, J. Chem. Phys. 110, 4634 (1999).
[CrossRef]

1998

E. V. Alieva, L. Kuzik, and V. A. Yakovlev, Chem. Phys. Lett. 292, 542 (1998).
[CrossRef]

1997

R. A. Watts, T. W. Preist, and J. R. Sambles, Phys. Rev. Lett. 79, 3978 (1997).
[CrossRef]

E. V. Alieva, Y. E. Petrov, V. A. Yakovlev, E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, A. F. G. van der Meer, and V. A. Sychugov, JETP Lett. 66, 609 (1997).
[CrossRef]

J. Löbau and K. Wolfrum, J. Opt. Soc. Am. B 14, 2505 (1997).
[CrossRef]

1996

E. W. M. van der Ham, Q. H. F. Vrehen, and E. R. Eliel, Opt. Lett. 21, 1448 (1996).
[CrossRef] [PubMed]

J. C. Conboy, M. C. Messmer, and G. L. Richmond, J. Phys. Chem. 100, 7617 (1996).
[CrossRef]

E. W. M. van der Ham, Q. H. F. Vrehen, and E. R. Eliel, Surf. Sci. 398, 96 (1996).
[CrossRef]

1995

D. Oepts, A. F. G. van der Meer, and P. W. van Amersfoort, Infrared Phys. 36, 297 (1995).
[CrossRef]

E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, G. W. ’t Hooft, M. Barmentlo, J. M. Auerhammer, A. F. G. van der Meer, and P. W. van Amersfoort, Appl. Phys. A: Solids Surf. 60, 113 (1995).
[CrossRef]

1994

J. C. Conboy, J. L. Daschbach, and G. L. Richmond, J. Phys. Chem. 98, 9688 (1994).
[CrossRef]

1992

S. R. Hatch, R. S. Polizotti, S. Dougal, and P. Rabinowitz, Chem. Phys. Lett. 196, 97 (1992).
[CrossRef]

1990

Y. R. Shen, Phys. Rep. 194, 303 (1990).
[CrossRef]

1989

Y. R. Shen, Nature (London) 337, 519 (1989).
[CrossRef]

1982

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, Phys. Rev. Lett. 48, 478 (1982).
[CrossRef]

1979

B. Pettinger, A. Tadjeddine, and D. M. Kolb, Chem. Phys. Lett. 66, 544 (1979).
[CrossRef]

1974

1972

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

1971

J. Rudnick and E. A. Stern, Phys. Rev. B 4, 4274 (1971).
[CrossRef]

E. Kretschmann, Z. Phys. 241, 313 (1971).
[CrossRef]

1968

1909

A. Sommerfeld, Ann. Phys. (Leipzig) 4, 665 (1909).
[CrossRef]

’t Hooft, G. W.

E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, G. W. ’t Hooft, M. Barmentlo, J. M. Auerhammer, A. F. G. van der Meer, and P. W. van Amersfoort, Appl. Phys. A: Solids Surf. 60, 113 (1995).
[CrossRef]

Alexander, R. W.

Alieva, E. V.

E. V. Alieva, L. Kuzik, and V. A. Yakovlev, Chem. Phys. Lett. 292, 542 (1998).
[CrossRef]

E. V. Alieva, Y. E. Petrov, V. A. Yakovlev, E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, A. F. G. van der Meer, and V. A. Sychugov, JETP Lett. 66, 609 (1997).
[CrossRef]

Auerhammer, J. M.

E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, G. W. ’t Hooft, M. Barmentlo, J. M. Auerhammer, A. F. G. van der Meer, and P. W. van Amersfoort, Appl. Phys. A: Solids Surf. 60, 113 (1995).
[CrossRef]

Bain, C. D.

R. Braun, B. D. Casson, C. D. Bain, E. W. M. van der Ham, Q. H. F. Vrehen, E. R. Eliel, A. M. Briggs and P. B. Davies, J. Chem. Phys. 110, 4634 (1999).
[CrossRef]

Barmentlo, M.

E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, G. W. ’t Hooft, M. Barmentlo, J. M. Auerhammer, A. F. G. van der Meer, and P. W. van Amersfoort, Appl. Phys. A: Solids Surf. 60, 113 (1995).
[CrossRef]

Bell, R. J.

Braun, R.

R. Braun, B. D. Casson, C. D. Bain, E. W. M. van der Ham, Q. H. F. Vrehen, E. R. Eliel, A. M. Briggs and P. B. Davies, J. Chem. Phys. 110, 4634 (1999).
[CrossRef]

Briggs, A. M.

R. Braun, B. D. Casson, C. D. Bain, E. W. M. van der Ham, Q. H. F. Vrehen, E. R. Eliel, A. M. Briggs and P. B. Davies, J. Chem. Phys. 110, 4634 (1999).
[CrossRef]

Casson, B. D.

R. Braun, B. D. Casson, C. D. Bain, E. W. M. van der Ham, Q. H. F. Vrehen, E. R. Eliel, A. M. Briggs and P. B. Davies, J. Chem. Phys. 110, 4634 (1999).
[CrossRef]

Chen, C. K.

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, Phys. Rev. Lett. 48, 478 (1982).
[CrossRef]

Christy, R. W.

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

Conboy, J. C.

J. C. Conboy, M. C. Messmer, and G. L. Richmond, J. Phys. Chem. 100, 7617 (1996).
[CrossRef]

J. C. Conboy, J. L. Daschbach, and G. L. Richmond, J. Phys. Chem. 98, 9688 (1994).
[CrossRef]

Daschbach, J. L.

J. C. Conboy, J. L. Daschbach, and G. L. Richmond, J. Phys. Chem. 98, 9688 (1994).
[CrossRef]

Davies, P. B.

R. Braun, B. D. Casson, C. D. Bain, E. W. M. van der Ham, Q. H. F. Vrehen, E. R. Eliel, A. M. Briggs and P. B. Davies, J. Chem. Phys. 110, 4634 (1999).
[CrossRef]

Dougal, S.

S. R. Hatch, R. S. Polizotti, S. Dougal, and P. Rabinowitz, Chem. Phys. Lett. 196, 97 (1992).
[CrossRef]

Eliel, E. R.

R. Braun, B. D. Casson, C. D. Bain, E. W. M. van der Ham, Q. H. F. Vrehen, E. R. Eliel, A. M. Briggs and P. B. Davies, J. Chem. Phys. 110, 4634 (1999).
[CrossRef]

E. V. Alieva, Y. E. Petrov, V. A. Yakovlev, E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, A. F. G. van der Meer, and V. A. Sychugov, JETP Lett. 66, 609 (1997).
[CrossRef]

E. W. M. van der Ham, Q. H. F. Vrehen, and E. R. Eliel, Opt. Lett. 21, 1448 (1996).
[CrossRef] [PubMed]

E. W. M. van der Ham, Q. H. F. Vrehen, and E. R. Eliel, Surf. Sci. 398, 96 (1996).
[CrossRef]

E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, G. W. ’t Hooft, M. Barmentlo, J. M. Auerhammer, A. F. G. van der Meer, and P. W. van Amersfoort, Appl. Phys. A: Solids Surf. 60, 113 (1995).
[CrossRef]

Hansen, W. N.

Hatch, S. R.

S. R. Hatch, R. S. Polizotti, S. Dougal, and P. Rabinowitz, Chem. Phys. Lett. 196, 97 (1992).
[CrossRef]

Heinz, T. F.

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, Phys. Rev. Lett. 48, 478 (1982).
[CrossRef]

Johnson, P. B.

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

Kolb, D. M.

B. Pettinger, A. Tadjeddine, and D. M. Kolb, Chem. Phys. Lett. 66, 544 (1979).
[CrossRef]

Kovener, G. S.

Kretschmann, E.

E. Kretschmann, Z. Phys. 241, 313 (1971).
[CrossRef]

Kuzik, L.

E. V. Alieva, L. Kuzik, and V. A. Yakovlev, Chem. Phys. Lett. 292, 542 (1998).
[CrossRef]

Löbau, J.

Messmer, M. C.

J. C. Conboy, M. C. Messmer, and G. L. Richmond, J. Phys. Chem. 100, 7617 (1996).
[CrossRef]

Oepts, D.

D. Oepts, A. F. G. van der Meer, and P. W. van Amersfoort, Infrared Phys. 36, 297 (1995).
[CrossRef]

Petrov, Y. E.

E. V. Alieva, Y. E. Petrov, V. A. Yakovlev, E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, A. F. G. van der Meer, and V. A. Sychugov, JETP Lett. 66, 609 (1997).
[CrossRef]

Pettinger, B.

B. Pettinger, A. Tadjeddine, and D. M. Kolb, Chem. Phys. Lett. 66, 544 (1979).
[CrossRef]

Polizotti, R. S.

S. R. Hatch, R. S. Polizotti, S. Dougal, and P. Rabinowitz, Chem. Phys. Lett. 196, 97 (1992).
[CrossRef]

Preist, T. W.

R. A. Watts, T. W. Preist, and J. R. Sambles, Phys. Rev. Lett. 79, 3978 (1997).
[CrossRef]

Rabinowitz, P.

S. R. Hatch, R. S. Polizotti, S. Dougal, and P. Rabinowitz, Chem. Phys. Lett. 196, 97 (1992).
[CrossRef]

Ricard, D.

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, Phys. Rev. Lett. 48, 478 (1982).
[CrossRef]

Richmond, G. L.

J. C. Conboy, M. C. Messmer, and G. L. Richmond, J. Phys. Chem. 100, 7617 (1996).
[CrossRef]

J. C. Conboy, J. L. Daschbach, and G. L. Richmond, J. Phys. Chem. 98, 9688 (1994).
[CrossRef]

Rudnick, J.

J. Rudnick and E. A. Stern, Phys. Rev. B 4, 4274 (1971).
[CrossRef]

Sambles, J. R.

R. A. Watts, T. W. Preist, and J. R. Sambles, Phys. Rev. Lett. 79, 3978 (1997).
[CrossRef]

Shen, Y. R.

Y. R. Shen, Phys. Rep. 194, 303 (1990).
[CrossRef]

Y. R. Shen, Nature (London) 337, 519 (1989).
[CrossRef]

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, Phys. Rev. Lett. 48, 478 (1982).
[CrossRef]

Sommerfeld, A.

A. Sommerfeld, Ann. Phys. (Leipzig) 4, 665 (1909).
[CrossRef]

Stern, E. A.

J. Rudnick and E. A. Stern, Phys. Rev. B 4, 4274 (1971).
[CrossRef]

Sychugov, V. A.

E. V. Alieva, Y. E. Petrov, V. A. Yakovlev, E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, A. F. G. van der Meer, and V. A. Sychugov, JETP Lett. 66, 609 (1997).
[CrossRef]

Tadjeddine, A.

B. Pettinger, A. Tadjeddine, and D. M. Kolb, Chem. Phys. Lett. 66, 544 (1979).
[CrossRef]

Tyler, I.

van Amersfoort, P. W.

E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, G. W. ’t Hooft, M. Barmentlo, J. M. Auerhammer, A. F. G. van der Meer, and P. W. van Amersfoort, Appl. Phys. A: Solids Surf. 60, 113 (1995).
[CrossRef]

D. Oepts, A. F. G. van der Meer, and P. W. van Amersfoort, Infrared Phys. 36, 297 (1995).
[CrossRef]

van der Ham, E. W. M.

R. Braun, B. D. Casson, C. D. Bain, E. W. M. van der Ham, Q. H. F. Vrehen, E. R. Eliel, A. M. Briggs and P. B. Davies, J. Chem. Phys. 110, 4634 (1999).
[CrossRef]

E. V. Alieva, Y. E. Petrov, V. A. Yakovlev, E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, A. F. G. van der Meer, and V. A. Sychugov, JETP Lett. 66, 609 (1997).
[CrossRef]

E. W. M. van der Ham, Q. H. F. Vrehen, and E. R. Eliel, Opt. Lett. 21, 1448 (1996).
[CrossRef] [PubMed]

E. W. M. van der Ham, Q. H. F. Vrehen, and E. R. Eliel, Surf. Sci. 398, 96 (1996).
[CrossRef]

E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, G. W. ’t Hooft, M. Barmentlo, J. M. Auerhammer, A. F. G. van der Meer, and P. W. van Amersfoort, Appl. Phys. A: Solids Surf. 60, 113 (1995).
[CrossRef]

van der Meer, A. F. G.

E. V. Alieva, Y. E. Petrov, V. A. Yakovlev, E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, A. F. G. van der Meer, and V. A. Sychugov, JETP Lett. 66, 609 (1997).
[CrossRef]

E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, G. W. ’t Hooft, M. Barmentlo, J. M. Auerhammer, A. F. G. van der Meer, and P. W. van Amersfoort, Appl. Phys. A: Solids Surf. 60, 113 (1995).
[CrossRef]

D. Oepts, A. F. G. van der Meer, and P. W. van Amersfoort, Infrared Phys. 36, 297 (1995).
[CrossRef]

Vrehen, Q. H. F.

R. Braun, B. D. Casson, C. D. Bain, E. W. M. van der Ham, Q. H. F. Vrehen, E. R. Eliel, A. M. Briggs and P. B. Davies, J. Chem. Phys. 110, 4634 (1999).
[CrossRef]

E. V. Alieva, Y. E. Petrov, V. A. Yakovlev, E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, A. F. G. van der Meer, and V. A. Sychugov, JETP Lett. 66, 609 (1997).
[CrossRef]

E. W. M. van der Ham, Q. H. F. Vrehen, and E. R. Eliel, Opt. Lett. 21, 1448 (1996).
[CrossRef] [PubMed]

E. W. M. van der Ham, Q. H. F. Vrehen, and E. R. Eliel, Surf. Sci. 398, 96 (1996).
[CrossRef]

E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, G. W. ’t Hooft, M. Barmentlo, J. M. Auerhammer, A. F. G. van der Meer, and P. W. van Amersfoort, Appl. Phys. A: Solids Surf. 60, 113 (1995).
[CrossRef]

Ward, C. A.

Watts, R. A.

R. A. Watts, T. W. Preist, and J. R. Sambles, Phys. Rev. Lett. 79, 3978 (1997).
[CrossRef]

Wolfrum, K.

Yakovlev, V. A.

E. V. Alieva, L. Kuzik, and V. A. Yakovlev, Chem. Phys. Lett. 292, 542 (1998).
[CrossRef]

E. V. Alieva, Y. E. Petrov, V. A. Yakovlev, E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, A. F. G. van der Meer, and V. A. Sychugov, JETP Lett. 66, 609 (1997).
[CrossRef]

Ann. Phys. (Leipzig)

A. Sommerfeld, Ann. Phys. (Leipzig) 4, 665 (1909).
[CrossRef]

Appl. Opt.

Appl. Phys. A: Solids Surf.

E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, G. W. ’t Hooft, M. Barmentlo, J. M. Auerhammer, A. F. G. van der Meer, and P. W. van Amersfoort, Appl. Phys. A: Solids Surf. 60, 113 (1995).
[CrossRef]

Chem. Phys. Lett.

E. V. Alieva, L. Kuzik, and V. A. Yakovlev, Chem. Phys. Lett. 292, 542 (1998).
[CrossRef]

B. Pettinger, A. Tadjeddine, and D. M. Kolb, Chem. Phys. Lett. 66, 544 (1979).
[CrossRef]

S. R. Hatch, R. S. Polizotti, S. Dougal, and P. Rabinowitz, Chem. Phys. Lett. 196, 97 (1992).
[CrossRef]

Infrared Phys.

D. Oepts, A. F. G. van der Meer, and P. W. van Amersfoort, Infrared Phys. 36, 297 (1995).
[CrossRef]

J. Chem. Phys.

R. Braun, B. D. Casson, C. D. Bain, E. W. M. van der Ham, Q. H. F. Vrehen, E. R. Eliel, A. M. Briggs and P. B. Davies, J. Chem. Phys. 110, 4634 (1999).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

J. Phys. Chem.

J. C. Conboy, J. L. Daschbach, and G. L. Richmond, J. Phys. Chem. 98, 9688 (1994).
[CrossRef]

J. C. Conboy, M. C. Messmer, and G. L. Richmond, J. Phys. Chem. 100, 7617 (1996).
[CrossRef]

JETP Lett.

E. V. Alieva, Y. E. Petrov, V. A. Yakovlev, E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, A. F. G. van der Meer, and V. A. Sychugov, JETP Lett. 66, 609 (1997).
[CrossRef]

Nature (London)

Y. R. Shen, Nature (London) 337, 519 (1989).
[CrossRef]

Opt. Lett.

Phys. Rep.

Y. R. Shen, Phys. Rep. 194, 303 (1990).
[CrossRef]

Phys. Rev. B

J. Rudnick and E. A. Stern, Phys. Rev. B 4, 4274 (1971).
[CrossRef]

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

Phys. Rev. Lett.

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, Phys. Rev. Lett. 48, 478 (1982).
[CrossRef]

R. A. Watts, T. W. Preist, and J. R. Sambles, Phys. Rev. Lett. 79, 3978 (1997).
[CrossRef]

Surf. Sci.

E. W. M. van der Ham, Q. H. F. Vrehen, and E. R. Eliel, Surf. Sci. 398, 96 (1996).
[CrossRef]

Z. Phys.

E. Kretschmann, Z. Phys. 241, 313 (1971).
[CrossRef]

Other

I. A. Avrutsky, P. V. Basakutsa, and S. Surov, Waveguide Corrugated Structures in Integrated and Fiber Optics (Nauka, Moscow, 1991).

J. F. McGilp, D. Weaire, and C. H. Patterson, Epioptics, Linear and Nonlinear Optical Spectroscopy of Surfaces and Interfaces (Springer-Verlag, Berlin, 1995).

P.-F. Brevet, Surface Second Harmonic Generation (Presses Polytechniques et Universitaires Romande, Lausanne, 1997).

G. N. Zhizhin, M. A. Moskalova, E. V. Shomina, and V. A. Yakovlev, in Surface Polaritons, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), Chap. 3.

D. N. Mirlin, in Surface Polaritons, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), Chap. 1.

Y. R. Shen and F. de Martini, in Surface Polaritons, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), Chap. 14.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

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Figures (5)

Fig. 1
Fig. 1

Dispersion relation of a SPP propagating along the interface between vacuum and a metal (solid curve). The dashed line shows the dispersion relation of free-space electromagnetic radiation.

Fig. 2
Fig. 2

Configurations for SFG with a SPP at the visible input wavelength. Left, configuration of input beams used with the prism; the SPP travels to the right, counterdirectional to the IR input beam. Right, configuration used with the grating; the SPP at the visible input wavelength is codirectional with the IR input beam.

Fig. 3
Fig. 3

Experimental results for the sum-frequency yield obtained with the prism coupler (filled symbols, scale at left). The open symbols show the fraction of the visible input power that is coupled into a polariton (scale at right).

Fig. 4
Fig. 4

Experimental results (filled symbols) for the sum-frequency yield on top of the visible grating as a function of the angle of incidence of the visible input radiation. The dotted–dashed curve shows the excitation efficiency of the polariton at the visible input wavelength (input coupling), and the dashed curve displays the phase matching between the nonlinear polarization and the polariton at the sum frequency. The solid curve gives the product of these two factors scaled to the experimental results.

Fig. 5
Fig. 5

Wave-vector components parallel to the interface for the grating coupler for (right) counterpropagating and (left) copropagating configurations of the input beams. The bottom arrows indicate the wave-vector mismatch for the respective cases.

Equations (22)

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Ea(ω)=[Exa(ω)x+Eza(ω)z]×exp(-αaωz-ιωt+ιKSPPωx),
Eb(ω)=[Exb(ω)x+Ezb(ω)z]×exp(-αbωz-ιωt+ιKSPPωx),
αiω=(KSPPω)2-i(ω)ωc21/2,i(a, b).
KSPPωKω+ικω=ωca(ω)b(ω)a(ω)+b(ω)1/2,
αaωωc-11+b(ω)1/2,
αbω|b(ω)|αaω.
Kωωcb(ω)1+b(ω)+b(ω)2[1+b(ω)]31/2,
κωω2cb(ω){b(ω)[b(ω)+1]3}1/2.
Kvis=n(ωvis)ωviscsin θvis,
|kx(ωsfg)|=n(ωsfg)ωsfgcsin θsfg=n(ωvis)ωviscsin θvis-ωircsin θir,
Kvis=kx(ωvis)±Nkgrating
=ωviscsin θvis±N2πa,
P˜(2)(r, t)=P(2)(ωsfg)δ(z)exp[ιkxNL(ωsfg)x-ιωsfgt],
kxNL(ωsfg)=Kvis+kx(ωir),
kx(ωsfg)=kxNL(ωsfg)+kgrating
=kx(ωvis)+kx(ωir)
=ωviscsin θvis-ωircsin θir,
γvis=ESPP(ωvis)E0(ωvis),
γvis2=ESPP(ωvis)E0(ωvis)2=η cos θvisαavisκvis.
KSPPsfg=Ksfg+ικsfg,
lc{[Δk(ωsfg)]2+(κsfg)2}-1/2,
G=γvis2(lc/Δ)2(αasfgΔ)2=γvis2(lcαasfg)22.5×104.

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