Abstract

We report a theoretical and experimental study of enhanced optical second-harmonic generation due to excitation of coupled surface plasmons from a thin silver grating bounded by two quartz crystals. With incident radiation from a Nd:YAG laser, diffracted second-harmonic generation in the n = 1, 0, and −1 modes is observed for the coupled surface plasmon fundamental modes. Nonlinear reflectance ratios calculated by using the reduced Rayleigh equations are in good agreement with the experimental results. Enhancement of the second-harmonic generation is limited by the scattering of the long-range surface plasmon mode in the thinnest silver films studied.

© 1988 Optical Society of America

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  1. D. Sarid, Phys. Rev. Lett. 47, 1927 (1981).
    [CrossRef]
  2. J. C. Quail, J. G. Rako, H. J. Simon, Opt. Lett. 8, 377 (1983).
    [CrossRef] [PubMed]
  3. T. Inagaki, M. Motosuga, E. T. Arakawa, J. P. Goudonnet, Phys. Rev. B 32, 6238 (1985).
    [CrossRef]
  4. R. W. Gruhlke, W. R. Holland, D. G. Hall, Opt. Lett. 12, 364 (1987).
    [CrossRef] [PubMed]
  5. Z. Chen, H. J. Simon, J. Opt. Soc. Am. B 5, 1396 (1988).
    [CrossRef]
  6. J. C. Quail, J. G. Rako, H. J. Simon, R. T. Deck, Phys. Rev. Lett. 50, 1987 (1983).
    [CrossRef]
  7. J. L. Coutaz, M. Nevière, E. Pic, R. Reinisch, Phys. Rev. B 32, 2227 (1985), and references therein.
    [CrossRef]
  8. C. Zhenghao, C. Dafu, L. Huibin, Z. Yueliang, Y. Guozhen, G. Shijie, Opt. Lett. 8, 563 (1983); Appl. Phys. Lett. 51, 1301 (1987).
    [CrossRef] [PubMed]
  9. H. J. Simon, C. Huang, J. C. Quail, Z. Chen, Phys. Rev. B (to be published).
  10. S. Dutta Gupta, G. V. Varada, G. S. Agarwal, Phys. Rev. B 36, 6331 (1987).
    [CrossRef]
  11. Z. Chen, H. J. Simon, “Optical second-harmonic generation with grating-coupled surface plasmons from a quartz–silver–quartz grating structure,” submitted to Phys. Rev. B.
  12. M. C. Hutley, Diffraction Gratings (Academic, London, 1982).

1988 (1)

1987 (2)

R. W. Gruhlke, W. R. Holland, D. G. Hall, Opt. Lett. 12, 364 (1987).
[CrossRef] [PubMed]

S. Dutta Gupta, G. V. Varada, G. S. Agarwal, Phys. Rev. B 36, 6331 (1987).
[CrossRef]

1985 (2)

T. Inagaki, M. Motosuga, E. T. Arakawa, J. P. Goudonnet, Phys. Rev. B 32, 6238 (1985).
[CrossRef]

J. L. Coutaz, M. Nevière, E. Pic, R. Reinisch, Phys. Rev. B 32, 2227 (1985), and references therein.
[CrossRef]

1983 (3)

1981 (1)

D. Sarid, Phys. Rev. Lett. 47, 1927 (1981).
[CrossRef]

Agarwal, G. S.

S. Dutta Gupta, G. V. Varada, G. S. Agarwal, Phys. Rev. B 36, 6331 (1987).
[CrossRef]

Arakawa, E. T.

T. Inagaki, M. Motosuga, E. T. Arakawa, J. P. Goudonnet, Phys. Rev. B 32, 6238 (1985).
[CrossRef]

Chen, Z.

Z. Chen, H. J. Simon, J. Opt. Soc. Am. B 5, 1396 (1988).
[CrossRef]

Z. Chen, H. J. Simon, “Optical second-harmonic generation with grating-coupled surface plasmons from a quartz–silver–quartz grating structure,” submitted to Phys. Rev. B.

H. J. Simon, C. Huang, J. C. Quail, Z. Chen, Phys. Rev. B (to be published).

Coutaz, J. L.

J. L. Coutaz, M. Nevière, E. Pic, R. Reinisch, Phys. Rev. B 32, 2227 (1985), and references therein.
[CrossRef]

Dafu, C.

Deck, R. T.

J. C. Quail, J. G. Rako, H. J. Simon, R. T. Deck, Phys. Rev. Lett. 50, 1987 (1983).
[CrossRef]

Dutta Gupta, S.

S. Dutta Gupta, G. V. Varada, G. S. Agarwal, Phys. Rev. B 36, 6331 (1987).
[CrossRef]

Goudonnet, J. P.

T. Inagaki, M. Motosuga, E. T. Arakawa, J. P. Goudonnet, Phys. Rev. B 32, 6238 (1985).
[CrossRef]

Gruhlke, R. W.

Guozhen, Y.

Hall, D. G.

Holland, W. R.

Huang, C.

H. J. Simon, C. Huang, J. C. Quail, Z. Chen, Phys. Rev. B (to be published).

Huibin, L.

Hutley, M. C.

M. C. Hutley, Diffraction Gratings (Academic, London, 1982).

Inagaki, T.

T. Inagaki, M. Motosuga, E. T. Arakawa, J. P. Goudonnet, Phys. Rev. B 32, 6238 (1985).
[CrossRef]

Motosuga, M.

T. Inagaki, M. Motosuga, E. T. Arakawa, J. P. Goudonnet, Phys. Rev. B 32, 6238 (1985).
[CrossRef]

Nevière, M.

J. L. Coutaz, M. Nevière, E. Pic, R. Reinisch, Phys. Rev. B 32, 2227 (1985), and references therein.
[CrossRef]

Pic, E.

J. L. Coutaz, M. Nevière, E. Pic, R. Reinisch, Phys. Rev. B 32, 2227 (1985), and references therein.
[CrossRef]

Quail, J. C.

J. C. Quail, J. G. Rako, H. J. Simon, R. T. Deck, Phys. Rev. Lett. 50, 1987 (1983).
[CrossRef]

J. C. Quail, J. G. Rako, H. J. Simon, Opt. Lett. 8, 377 (1983).
[CrossRef] [PubMed]

H. J. Simon, C. Huang, J. C. Quail, Z. Chen, Phys. Rev. B (to be published).

Rako, J. G.

J. C. Quail, J. G. Rako, H. J. Simon, R. T. Deck, Phys. Rev. Lett. 50, 1987 (1983).
[CrossRef]

J. C. Quail, J. G. Rako, H. J. Simon, Opt. Lett. 8, 377 (1983).
[CrossRef] [PubMed]

Reinisch, R.

J. L. Coutaz, M. Nevière, E. Pic, R. Reinisch, Phys. Rev. B 32, 2227 (1985), and references therein.
[CrossRef]

Sarid, D.

D. Sarid, Phys. Rev. Lett. 47, 1927 (1981).
[CrossRef]

Shijie, G.

Simon, H. J.

Z. Chen, H. J. Simon, J. Opt. Soc. Am. B 5, 1396 (1988).
[CrossRef]

J. C. Quail, J. G. Rako, H. J. Simon, Opt. Lett. 8, 377 (1983).
[CrossRef] [PubMed]

J. C. Quail, J. G. Rako, H. J. Simon, R. T. Deck, Phys. Rev. Lett. 50, 1987 (1983).
[CrossRef]

H. J. Simon, C. Huang, J. C. Quail, Z. Chen, Phys. Rev. B (to be published).

Z. Chen, H. J. Simon, “Optical second-harmonic generation with grating-coupled surface plasmons from a quartz–silver–quartz grating structure,” submitted to Phys. Rev. B.

Varada, G. V.

S. Dutta Gupta, G. V. Varada, G. S. Agarwal, Phys. Rev. B 36, 6331 (1987).
[CrossRef]

Yueliang, Z.

Zhenghao, C.

J. Opt. Soc. Am. B (1)

Opt. Lett. (3)

Phys. Rev. B (3)

T. Inagaki, M. Motosuga, E. T. Arakawa, J. P. Goudonnet, Phys. Rev. B 32, 6238 (1985).
[CrossRef]

S. Dutta Gupta, G. V. Varada, G. S. Agarwal, Phys. Rev. B 36, 6331 (1987).
[CrossRef]

J. L. Coutaz, M. Nevière, E. Pic, R. Reinisch, Phys. Rev. B 32, 2227 (1985), and references therein.
[CrossRef]

Phys. Rev. Lett. (2)

D. Sarid, Phys. Rev. Lett. 47, 1927 (1981).
[CrossRef]

J. C. Quail, J. G. Rako, H. J. Simon, R. T. Deck, Phys. Rev. Lett. 50, 1987 (1983).
[CrossRef]

Other (3)

H. J. Simon, C. Huang, J. C. Quail, Z. Chen, Phys. Rev. B (to be published).

Z. Chen, H. J. Simon, “Optical second-harmonic generation with grating-coupled surface plasmons from a quartz–silver–quartz grating structure,” submitted to Phys. Rev. B.

M. C. Hutley, Diffraction Gratings (Academic, London, 1982).

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Figures (2)

Fig. 1
Fig. 1

Nonlinear reflectance for the n = 1 SHG diffracted mode versus the angle of incidence in the region of excitation of coupled fundamental surface plasmon modes for a metal thickness d = 52.0 nm. The ordinate for the LRSP mode is shown to the left, and the ordinate for the short-range surface plasmon mode to the right.

Fig. 2
Fig. 2

Nonlinear reflectance on a logarithmic scale for the diffracted SHG mode with a metal film thickness of 23.0 nm in the region of the angle of incidence for excitation of the fundamental LRSP mode. Circles, squares, and triangles are the experimental points and the solid, dotted, and dashed–dotted lines are the theoretical curves for the n = 1, 0, and −1 modes, respectively.

Equations (6)

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P NLS = p , p = - P p p NLS exp i [ ( k p + k p ) x + ( α p + α p ) z ] ,
P l NLS = exp i [ k l ( 2 ) x ] p = - P p , l - p NLS exp i [ γ p , l - p ( 2 ) z ] .
A l n = 2 π α n ( 2 ) ( 2 ω c ) 2 p = - y ^ · k ^ p , l - p × P p , l - p NLS α n ( 2 ) - γ p , l - p ( 2 ) × exp i [ γ p , l - p ( 2 ) d ] Z n - ( l - p ) .
α g ( 2 ) = { ( 2 ω c ) 2 N 2 - [ k g ( 2 ) ] 2 } 1 / 2 ,
Z n - ( l - p ) = 1 a - a / 2 a / 2 d x exp i { - [ k n ( 2 ) - k l ( 2 ) ] x - [ α n ( 2 ) - γ p , l - p ( 2 ) ] ζ ( x ) } .
R n ( 2 w ) = 2 π ω c 2 ( n 2 N ) 2 α n ( 2 ) ( α 0 ) 2 l l = - A l n A l n * .

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