Abstract

Second-harmonic radiation is generated at a gold surface by use of a laser pulse that is varied in duration from 14 to 29 fs and in intensity from 109 to 1011 W/cm2. At laser intensities below 1010 W/cm2, the second-harmonic signal has the expected quadratic dependence on pump-laser intensity; however, at higher intensities, the dependence is supraquadratic. This difference arises because the leading edge of the laser pulse interacts significantly with the gold electrons to create a nonequilibrium, photoexcited distribution. The second-harmonic generation process occurs before electron–electron or electron–phonon collisions can equilibrate the distribution and therefore serves as a probe of the nonequilibrium distribution.

© 1999 Optical Society of America

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  1. C. K. Sun, F. Vallee, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, Phys. Rev. B 50, 15337 (1994).
    [CrossRef]
  2. W. S. Fann, R. Storz, H. W. K. Tom, and J. Bokor, Phys. Rev. B 46, 13592 (1992).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. J. Hohlfeld, U. Conrad, and E. Matthias, Appl. Phys. B 63, 541 (1996).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. M. Theye, Phys. Rev. B 2, 3060 (1970).
    [CrossRef]
  20. S. D. Brorson, J. G. Fujimoto, and E. P. Ippen, Phys. Rev. Lett. 59, 1962 (1987).
    [CrossRef] [PubMed]
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    [CrossRef]
  22. A. T. Georges, Phys. Rev. B 51, 13735 (1995).
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  23. A. T. Georges, Phys. Rev. A 54, 2412 (1996).
    [CrossRef] [PubMed]
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  26. S. M. Sze, J. L. Moll, and T. Sugano, Solid State Electron. 7, 509 (1964).
    [CrossRef]
  27. S. Varro and F. Ehlotsky, Phys. Rev. A 49, 3106 (1994).
    [CrossRef]

1998 (1)

J. Phys. Chem. A 102(23), 4021 (1998).

1997 (4)

S. Ogawa, H. Nagano, and H. Petek, Phys. Rev. B 55, 10869 (1997).
[CrossRef]

H. Petek, A. P. Heberle, W. Nessler, H. Nagano, S. Kubota, S. Matsunami, N. Moriya, and S. Ogawa, Phys. Rev. Lett. 79, 4649 (1997).
[CrossRef]

T. A. Luce, W. Hubner, and K. H. Bennemann, Z. Phys. B 102, 223 (1997).
[CrossRef]

N. A. Papadogiannis and S. D. Moustaizis, Opt. Commun. 137, 174 (1997).
[CrossRef]

1996 (2)

J. Hohlfeld, U. Conrad, and E. Matthias, Appl. Phys. B 63, 541 (1996).

A. T. Georges, Phys. Rev. A 54, 2412 (1996).
[CrossRef] [PubMed]

1995 (2)

A. T. Georges, Phys. Rev. B 51, 13735 (1995).
[CrossRef]

J. P. Girardeau-Montaut and C. Girardeau-Montaut, Phys. Rev. B 51, 13560 (1995).
[CrossRef]

1994 (3)

C. K. Sun, F. Vallee, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, Phys. Rev. B 50, 15337 (1994).
[CrossRef]

X. Y. Wang, D. M. Riffe, Y. S. Lee, and M. C. Downer, Phys. Rev. B 50, 8016 (1994).
[CrossRef]

S. Varro and F. Ehlotsky, Phys. Rev. A 49, 3106 (1994).
[CrossRef]

1993 (1)

D. Steinmuller-Nethl, R. A. Hopfel, A. Leitner, F. R. Aussenegg, and A. Wokaun, Appl. Phys. A 57, 261 (1993).
[CrossRef]

1992 (2)

W. S. Fann, R. Storz, H. W. K. Tom, and J. Bokor, Phys. Rev. B 46, 13592 (1992).
[CrossRef]

W. S. Fann, R. Storz, H. W. K. Tom, and J. Bokor, Phys. Rev. Lett. 68, 2834 (1992).
[CrossRef] [PubMed]

1988 (1)

H. W. K. Tom, G. D. Aumiller, and C. H. Brito-Cruz, Phys. Rev. Lett. 60, 1483 (1988).
[CrossRef]

1987 (1)

S. D. Brorson, J. G. Fujimoto, and E. P. Ippen, Phys. Rev. Lett. 59, 1962 (1987).
[CrossRef] [PubMed]

1983 (1)

C. V. Shank, R. Yen, and C. Hirlimann, Phys. Rev. Lett. 51, 900 (1983).
[CrossRef]

1981 (1)

R. Lasser, N. V. Smith, and R. L. Benbow, Phys Rev. B 24, 1895 (1981).
[CrossRef]

1977 (1)

J. H. Bechtel, W. L. Smith, and N. Bloembergen, Phys. Rev. B 15, 4557 (1977).
[CrossRef]

1974 (1)

S. I. Anisimov, B. L. Kapeliovich, and T. L. Perel’man, Sov. Phys. JETP 39, 375 (1974).

1970 (1)

M. Theye, Phys. Rev. B 2, 3060 (1970).
[CrossRef]

1966 (1)

S. M. Sze, C. R. Crowell, G. P. Carey, and E. E. Labate, J. Appl. Phys. 37, 2690 (1966).
[CrossRef]

1964 (1)

S. M. Sze, J. L. Moll, and T. Sugano, Solid State Electron. 7, 509 (1964).
[CrossRef]

Acioli, L. H.

C. K. Sun, F. Vallee, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, Phys. Rev. B 50, 15337 (1994).
[CrossRef]

Anisimov, S. I.

S. I. Anisimov, B. L. Kapeliovich, and T. L. Perel’man, Sov. Phys. JETP 39, 375 (1974).

Aumiller, G. D.

H. W. K. Tom, G. D. Aumiller, and C. H. Brito-Cruz, Phys. Rev. Lett. 60, 1483 (1988).
[CrossRef]

Aussenegg, F. R.

D. Steinmuller-Nethl, R. A. Hopfel, A. Leitner, F. R. Aussenegg, and A. Wokaun, Appl. Phys. A 57, 261 (1993).
[CrossRef]

Balling, P.

A. H. Chin, R. W. Schoenlein, T. E. Glover, P. Balling, W. P. Leemans, and C. V. Shank, in Ultrafast Phenomena XI, T. Elsaesser, J. G. Fujimoto, D. A. Weirsma, and W. Zinth, eds. (Springer, New York, 1998), pp. 401–403.
[CrossRef]

Barty, C. J. P.

R. Jimenez, C. Rose-Petruck, T. Guo, K. R. Wilson, and C. J. P. Barty, in Ultrafast Phenomena XI, T. Elsaesser, J. G. Fujimoto, D. A. Weirsma, and W. Zinth, eds. (Springer, New York, 1998), pp. 404–406.
[CrossRef]

Bechtel, J. H.

J. H. Bechtel, W. L. Smith, and N. Bloembergen, Phys. Rev. B 15, 4557 (1977).
[CrossRef]

Benbow, R. L.

R. Lasser, N. V. Smith, and R. L. Benbow, Phys Rev. B 24, 1895 (1981).
[CrossRef]

Bennemann, K. H.

T. A. Luce, W. Hubner, and K. H. Bennemann, Z. Phys. B 102, 223 (1997).
[CrossRef]

Bloembergen, N.

J. H. Bechtel, W. L. Smith, and N. Bloembergen, Phys. Rev. B 15, 4557 (1977).
[CrossRef]

Bokor, J.

W. S. Fann, R. Storz, H. W. K. Tom, and J. Bokor, Phys. Rev. Lett. 68, 2834 (1992).
[CrossRef] [PubMed]

W. S. Fann, R. Storz, H. W. K. Tom, and J. Bokor, Phys. Rev. B 46, 13592 (1992).
[CrossRef]

Brito-Cruz, C. H.

H. W. K. Tom, G. D. Aumiller, and C. H. Brito-Cruz, Phys. Rev. Lett. 60, 1483 (1988).
[CrossRef]

Brorson, S. D.

S. D. Brorson, J. G. Fujimoto, and E. P. Ippen, Phys. Rev. Lett. 59, 1962 (1987).
[CrossRef] [PubMed]

Carey, G. P.

S. M. Sze, C. R. Crowell, G. P. Carey, and E. E. Labate, J. Appl. Phys. 37, 2690 (1966).
[CrossRef]

Chin, A. H.

A. H. Chin, R. W. Schoenlein, T. E. Glover, P. Balling, W. P. Leemans, and C. V. Shank, in Ultrafast Phenomena XI, T. Elsaesser, J. G. Fujimoto, D. A. Weirsma, and W. Zinth, eds. (Springer, New York, 1998), pp. 401–403.
[CrossRef]

Conrad, U.

J. Hohlfeld, U. Conrad, and E. Matthias, Appl. Phys. B 63, 541 (1996).

Crowell, C. R.

S. M. Sze, C. R. Crowell, G. P. Carey, and E. E. Labate, J. Appl. Phys. 37, 2690 (1966).
[CrossRef]

Downer, M. C.

X. Y. Wang, D. M. Riffe, Y. S. Lee, and M. C. Downer, Phys. Rev. B 50, 8016 (1994).
[CrossRef]

Ehlotsky, F.

S. Varro and F. Ehlotsky, Phys. Rev. A 49, 3106 (1994).
[CrossRef]

Fann, W. S.

W. S. Fann, R. Storz, H. W. K. Tom, and J. Bokor, Phys. Rev. Lett. 68, 2834 (1992).
[CrossRef] [PubMed]

W. S. Fann, R. Storz, H. W. K. Tom, and J. Bokor, Phys. Rev. B 46, 13592 (1992).
[CrossRef]

Fujimoto, J. G.

C. K. Sun, F. Vallee, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, Phys. Rev. B 50, 15337 (1994).
[CrossRef]

S. D. Brorson, J. G. Fujimoto, and E. P. Ippen, Phys. Rev. Lett. 59, 1962 (1987).
[CrossRef] [PubMed]

Georges, A. T.

A. T. Georges, Phys. Rev. A 54, 2412 (1996).
[CrossRef] [PubMed]

A. T. Georges, Phys. Rev. B 51, 13735 (1995).
[CrossRef]

Girardeau-Montaut, C.

J. P. Girardeau-Montaut and C. Girardeau-Montaut, Phys. Rev. B 51, 13560 (1995).
[CrossRef]

Girardeau-Montaut, J. P.

J. P. Girardeau-Montaut and C. Girardeau-Montaut, Phys. Rev. B 51, 13560 (1995).
[CrossRef]

Glover, T. E.

A. H. Chin, R. W. Schoenlein, T. E. Glover, P. Balling, W. P. Leemans, and C. V. Shank, in Ultrafast Phenomena XI, T. Elsaesser, J. G. Fujimoto, D. A. Weirsma, and W. Zinth, eds. (Springer, New York, 1998), pp. 401–403.
[CrossRef]

Guo, T.

R. Jimenez, C. Rose-Petruck, T. Guo, K. R. Wilson, and C. J. P. Barty, in Ultrafast Phenomena XI, T. Elsaesser, J. G. Fujimoto, D. A. Weirsma, and W. Zinth, eds. (Springer, New York, 1998), pp. 404–406.
[CrossRef]

Heberle, A. P.

H. Petek, A. P. Heberle, W. Nessler, H. Nagano, S. Kubota, S. Matsunami, N. Moriya, and S. Ogawa, Phys. Rev. Lett. 79, 4649 (1997).
[CrossRef]

Hirlimann, C.

C. V. Shank, R. Yen, and C. Hirlimann, Phys. Rev. Lett. 51, 900 (1983).
[CrossRef]

Hohlfeld, J.

J. Hohlfeld, U. Conrad, and E. Matthias, Appl. Phys. B 63, 541 (1996).

Hopfel, R. A.

D. Steinmuller-Nethl, R. A. Hopfel, A. Leitner, F. R. Aussenegg, and A. Wokaun, Appl. Phys. A 57, 261 (1993).
[CrossRef]

Hubner, W.

T. A. Luce, W. Hubner, and K. H. Bennemann, Z. Phys. B 102, 223 (1997).
[CrossRef]

Ippen, E. P.

C. K. Sun, F. Vallee, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, Phys. Rev. B 50, 15337 (1994).
[CrossRef]

S. D. Brorson, J. G. Fujimoto, and E. P. Ippen, Phys. Rev. Lett. 59, 1962 (1987).
[CrossRef] [PubMed]

Jimenez, R.

R. Jimenez, C. Rose-Petruck, T. Guo, K. R. Wilson, and C. J. P. Barty, in Ultrafast Phenomena XI, T. Elsaesser, J. G. Fujimoto, D. A. Weirsma, and W. Zinth, eds. (Springer, New York, 1998), pp. 404–406.
[CrossRef]

Kapeliovich, B. L.

S. I. Anisimov, B. L. Kapeliovich, and T. L. Perel’man, Sov. Phys. JETP 39, 375 (1974).

Kubota, S.

H. Petek, A. P. Heberle, W. Nessler, H. Nagano, S. Kubota, S. Matsunami, N. Moriya, and S. Ogawa, Phys. Rev. Lett. 79, 4649 (1997).
[CrossRef]

Labate, E. E.

S. M. Sze, C. R. Crowell, G. P. Carey, and E. E. Labate, J. Appl. Phys. 37, 2690 (1966).
[CrossRef]

Lasser, R.

R. Lasser, N. V. Smith, and R. L. Benbow, Phys Rev. B 24, 1895 (1981).
[CrossRef]

Lee, Y. S.

X. Y. Wang, D. M. Riffe, Y. S. Lee, and M. C. Downer, Phys. Rev. B 50, 8016 (1994).
[CrossRef]

Leemans, W. P.

A. H. Chin, R. W. Schoenlein, T. E. Glover, P. Balling, W. P. Leemans, and C. V. Shank, in Ultrafast Phenomena XI, T. Elsaesser, J. G. Fujimoto, D. A. Weirsma, and W. Zinth, eds. (Springer, New York, 1998), pp. 401–403.
[CrossRef]

Leitner, A.

D. Steinmuller-Nethl, R. A. Hopfel, A. Leitner, F. R. Aussenegg, and A. Wokaun, Appl. Phys. A 57, 261 (1993).
[CrossRef]

Luce, T. A.

T. A. Luce, W. Hubner, and K. H. Bennemann, Z. Phys. B 102, 223 (1997).
[CrossRef]

Matsunami, S.

H. Petek, A. P. Heberle, W. Nessler, H. Nagano, S. Kubota, S. Matsunami, N. Moriya, and S. Ogawa, Phys. Rev. Lett. 79, 4649 (1997).
[CrossRef]

Matthias, E.

J. Hohlfeld, U. Conrad, and E. Matthias, Appl. Phys. B 63, 541 (1996).

Moll, J. L.

S. M. Sze, J. L. Moll, and T. Sugano, Solid State Electron. 7, 509 (1964).
[CrossRef]

Moriya, N.

H. Petek, A. P. Heberle, W. Nessler, H. Nagano, S. Kubota, S. Matsunami, N. Moriya, and S. Ogawa, Phys. Rev. Lett. 79, 4649 (1997).
[CrossRef]

Moustaizis, S. D.

N. A. Papadogiannis and S. D. Moustaizis, Opt. Commun. 137, 174 (1997).
[CrossRef]

Nagano, H.

S. Ogawa, H. Nagano, and H. Petek, Phys. Rev. B 55, 10869 (1997).
[CrossRef]

H. Petek, A. P. Heberle, W. Nessler, H. Nagano, S. Kubota, S. Matsunami, N. Moriya, and S. Ogawa, Phys. Rev. Lett. 79, 4649 (1997).
[CrossRef]

Nessler, W.

H. Petek, A. P. Heberle, W. Nessler, H. Nagano, S. Kubota, S. Matsunami, N. Moriya, and S. Ogawa, Phys. Rev. Lett. 79, 4649 (1997).
[CrossRef]

Nozieres, P.

D. Pine and P. Nozieres, The Theory of Quantum Liquids (Benjamin, New York, 1966).

Ogawa, S.

H. Petek, A. P. Heberle, W. Nessler, H. Nagano, S. Kubota, S. Matsunami, N. Moriya, and S. Ogawa, Phys. Rev. Lett. 79, 4649 (1997).
[CrossRef]

S. Ogawa, H. Nagano, and H. Petek, Phys. Rev. B 55, 10869 (1997).
[CrossRef]

Papadogiannis, N. A.

N. A. Papadogiannis and S. D. Moustaizis, Opt. Commun. 137, 174 (1997).
[CrossRef]

Perel’man, T. L.

S. I. Anisimov, B. L. Kapeliovich, and T. L. Perel’man, Sov. Phys. JETP 39, 375 (1974).

Petek, H.

S. Ogawa, H. Nagano, and H. Petek, Phys. Rev. B 55, 10869 (1997).
[CrossRef]

H. Petek, A. P. Heberle, W. Nessler, H. Nagano, S. Kubota, S. Matsunami, N. Moriya, and S. Ogawa, Phys. Rev. Lett. 79, 4649 (1997).
[CrossRef]

Pine, D.

D. Pine and P. Nozieres, The Theory of Quantum Liquids (Benjamin, New York, 1966).

Riffe, D. M.

X. Y. Wang, D. M. Riffe, Y. S. Lee, and M. C. Downer, Phys. Rev. B 50, 8016 (1994).
[CrossRef]

Rose-Petruck, C.

R. Jimenez, C. Rose-Petruck, T. Guo, K. R. Wilson, and C. J. P. Barty, in Ultrafast Phenomena XI, T. Elsaesser, J. G. Fujimoto, D. A. Weirsma, and W. Zinth, eds. (Springer, New York, 1998), pp. 404–406.
[CrossRef]

Schoenlein, R. W.

A. H. Chin, R. W. Schoenlein, T. E. Glover, P. Balling, W. P. Leemans, and C. V. Shank, in Ultrafast Phenomena XI, T. Elsaesser, J. G. Fujimoto, D. A. Weirsma, and W. Zinth, eds. (Springer, New York, 1998), pp. 401–403.
[CrossRef]

Shank, C. V.

C. V. Shank, R. Yen, and C. Hirlimann, Phys. Rev. Lett. 51, 900 (1983).
[CrossRef]

A. H. Chin, R. W. Schoenlein, T. E. Glover, P. Balling, W. P. Leemans, and C. V. Shank, in Ultrafast Phenomena XI, T. Elsaesser, J. G. Fujimoto, D. A. Weirsma, and W. Zinth, eds. (Springer, New York, 1998), pp. 401–403.
[CrossRef]

Smith, N. V.

R. Lasser, N. V. Smith, and R. L. Benbow, Phys Rev. B 24, 1895 (1981).
[CrossRef]

Smith, W. L.

J. H. Bechtel, W. L. Smith, and N. Bloembergen, Phys. Rev. B 15, 4557 (1977).
[CrossRef]

Steinmuller-Nethl, D.

D. Steinmuller-Nethl, R. A. Hopfel, A. Leitner, F. R. Aussenegg, and A. Wokaun, Appl. Phys. A 57, 261 (1993).
[CrossRef]

Storz, R.

W. S. Fann, R. Storz, H. W. K. Tom, and J. Bokor, Phys. Rev. B 46, 13592 (1992).
[CrossRef]

W. S. Fann, R. Storz, H. W. K. Tom, and J. Bokor, Phys. Rev. Lett. 68, 2834 (1992).
[CrossRef] [PubMed]

Sugano, T.

S. M. Sze, J. L. Moll, and T. Sugano, Solid State Electron. 7, 509 (1964).
[CrossRef]

Sun, C. K.

C. K. Sun, F. Vallee, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, Phys. Rev. B 50, 15337 (1994).
[CrossRef]

Sze, S. M.

S. M. Sze, C. R. Crowell, G. P. Carey, and E. E. Labate, J. Appl. Phys. 37, 2690 (1966).
[CrossRef]

S. M. Sze, J. L. Moll, and T. Sugano, Solid State Electron. 7, 509 (1964).
[CrossRef]

Theye, M.

M. Theye, Phys. Rev. B 2, 3060 (1970).
[CrossRef]

Tom, H. W. K.

W. S. Fann, R. Storz, H. W. K. Tom, and J. Bokor, Phys. Rev. B 46, 13592 (1992).
[CrossRef]

W. S. Fann, R. Storz, H. W. K. Tom, and J. Bokor, Phys. Rev. Lett. 68, 2834 (1992).
[CrossRef] [PubMed]

H. W. K. Tom, G. D. Aumiller, and C. H. Brito-Cruz, Phys. Rev. Lett. 60, 1483 (1988).
[CrossRef]

Vallee, F.

C. K. Sun, F. Vallee, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, Phys. Rev. B 50, 15337 (1994).
[CrossRef]

Varro, S.

S. Varro and F. Ehlotsky, Phys. Rev. A 49, 3106 (1994).
[CrossRef]

Wang, X. Y.

X. Y. Wang, D. M. Riffe, Y. S. Lee, and M. C. Downer, Phys. Rev. B 50, 8016 (1994).
[CrossRef]

Wilson, K. R.

R. Jimenez, C. Rose-Petruck, T. Guo, K. R. Wilson, and C. J. P. Barty, in Ultrafast Phenomena XI, T. Elsaesser, J. G. Fujimoto, D. A. Weirsma, and W. Zinth, eds. (Springer, New York, 1998), pp. 404–406.
[CrossRef]

Wokaun, A.

D. Steinmuller-Nethl, R. A. Hopfel, A. Leitner, F. R. Aussenegg, and A. Wokaun, Appl. Phys. A 57, 261 (1993).
[CrossRef]

Yen, R.

C. V. Shank, R. Yen, and C. Hirlimann, Phys. Rev. Lett. 51, 900 (1983).
[CrossRef]

Appl. Phys. A (1)

D. Steinmuller-Nethl, R. A. Hopfel, A. Leitner, F. R. Aussenegg, and A. Wokaun, Appl. Phys. A 57, 261 (1993).
[CrossRef]

Appl. Phys. B (1)

J. Hohlfeld, U. Conrad, and E. Matthias, Appl. Phys. B 63, 541 (1996).

J. Appl. Phys. (1)

S. M. Sze, C. R. Crowell, G. P. Carey, and E. E. Labate, J. Appl. Phys. 37, 2690 (1966).
[CrossRef]

J. Phys. Chem. A (1)

J. Phys. Chem. A 102(23), 4021 (1998).

Opt. Commun. (1)

N. A. Papadogiannis and S. D. Moustaizis, Opt. Commun. 137, 174 (1997).
[CrossRef]

Phys Rev. B (1)

R. Lasser, N. V. Smith, and R. L. Benbow, Phys Rev. B 24, 1895 (1981).
[CrossRef]

Phys. Rev. A (2)

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Figures (2)

Fig. 1
Fig. 1

Second-harmonic yield as a function of peak pump-laser intensity: (a) Supraquadratic dependence of the harmonic signal on pump-laser intensity is measured at each pulse duration. The data indicate that the electron distribution has not relaxed on a 30-fs time scale. (b) Second-harmonic signal plotted against model predictions for a 29-fs pulse. Note the expanded scales in (b) compared with (a).

Fig. 2
Fig. 2

Difference in population between the nonequilibrium, photoexcited distribution and the initial, thermalized FD distribution. The nonequilibrium distribution relaxes to a thermalized distribution with a temperature of 1570 K; the difference between this distribution and the initial distribution is also shown (dotted curve). The Fermi energy (5.5 eV in gold) corresponds to zero energy, and all calculations are for a 29-fs pulse with an intensity of 1×1011 W/cm2. Inset, detail of the photoexcited distribution for energy greater than zero.

Equations (2)

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Nn+1i=Nni+nγIωρni-ω1-ρni-ρni1-ρni+ω,
W2ωtn0f,tn1-f+ω,tn×1-f+2ω,tn1-f,tnd,

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