Abstract

Femtosecond time-resolved impulsive stimulated Raman scattering (ISRS) experiments on optic phonon–polariton modes are discussd. The effects of polariton dispersion and propagation are treated. The results provide guidance of accurate analysis of ISRS data from polar phonons.

© 1992 Optical Society of America

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References

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  1. Y.-X. Yan, K. A. Nelson, J. Chem. Phys. 87, 6240 (1987).
    [CrossRef]
  2. Y.-X. Yan, K. A. Nelson, J. Chem. Phys. 87, 6257 (1987).
    [CrossRef]
  3. T. P. Dougherty, G. P. Wiederrecht, K. A. Nelson, Ferroelectrics 120, 79 (1991).
    [CrossRef]
  4. T. P. Dougherty, G. P. Wiederrecht, K. A. Nelson, “Femtosecond time-resolved spectroscopy of soft modes in structural phase transitions. I. KNbO3orthorhombic phases; II. BaTiO3 tetrahedral phase,” submitted to Phys. Rev. B.
  5. J. Etchepare, G. Grillon, A. Antonetti, J. C. Loulergue, M. D. Fontana, G. E. Kugel, Ultrafast Phenomena VII (Springer-Verlag, Berlin1990), p. 340.
    [CrossRef]
  6. J. Etchepare, G. Grillon, A. Antonetti, J. C. Loulergue, M. D. Fontana, G. E. Kugel, Phys. Rev. B 41, 12362 (1990).
    [CrossRef]
  7. Femtosecond time-resolved observation of optic phonons was also carried out with a different mechanism by M. C. Nuss, D. H. Auston, in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin1986), pp. 284–286;D. H. Auston, K. P. Cheung, J. A. Valdmanis, D. A. Kleinman, Phys. Rev. Lett. 53, 1555 (1984).
    [CrossRef]
  8. P. C. M. Planken, Ph.D. dissertation (University of Amsterdam, Amsterdam, 1991).
  9. R. Claus, L. Merten, J. Brandmuller, Light Scattering by Phonon–Polaritons (Springer-Verlag, Berlin, 1975).
  10. G. Lamprecht, L. Merten, Phys. Status Solidi b 55, 33 (1973).
    [CrossRef]
  11. A. S. Barker, R. Louden, Rev. Mod. Phys. 44, 18 (1972).
    [CrossRef]
  12. E. Burstein, Comm. Solid State Phys. 1, 202 (1968).
  13. E. Burstein, D. L. Mills, Comm. Solid State Phys. 2, 92, 111 (1968).
  14. R. Louden, Light Scattering Spectra of Solids (Springer-Verlag, New York, 1969), p. 25.
    [CrossRef]
  15. E. Hanamura, Phys. Rev. B 39, 1152 (1989).
    [CrossRef]
  16. M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Clarendon, Oxford, 1962).
  17. M. D. Fontana, G. Metrat, J. L. Servoin, F. Gervais, J. Phys. 16, 483 (1984).
  18. J.-C. Baumert, J. Hoffnagle, P. Günter, in 1984 European Conference on Optics, Optical Systems, and Applications, B. Bolger, H. A. Ferwerda, eds., Proc. Soc. Photo-Opt. Instrum. Eng.492, 374–385 (1983).
    [CrossRef]
  19. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, London, 1988).
  20. Ref. 11, Eq. (2.58).
  21. S. C. Abrahams, J. L. Bernstein, J. Phys. Chem. Solids 28, 1685 (1967);A. S. Barker, R. Louden, Phys. Rev. 158, 433 (1967);H. D. Megaw, Acta Crystallogr. A 24, 583 (1968).
    [CrossRef]
  22. S. C. Abrahams, W. C. Hamilton, A. Siqueira, J. Phys. Chem. Solids 28, 1693 (1967).
    [CrossRef]
  23. I. P. Kaminow, W. D. Johnson, Phys. Rev. 160, 519 (1967).
    [CrossRef]
  24. X. Yang, G. Lan, H. Wang, Phys. Status Solidi b 141, 287 (1987).
    [CrossRef]
  25. C. Raptis, Phys. Rev. B 38, 10007 (1988).
    [CrossRef]
  26. A. F. Penna, A. Chaves, P. da R. Andrade, S. P. S. Porto, Phys. Rev. B 13, 4907 (1976).
    [CrossRef]
  27. W. L. Bond, J. Appl. Phys. 36, 1674 (1965).From this reference the value of ∊∞= 4.5 can be deduced.
    [CrossRef]
  28. G. M. Gale, F. Vallee, C. Flytzanis, Phys. Rev. Lett. 57, 1867 (1986).
    [CrossRef] [PubMed]
  29. F. Vallee, G. M. Gale, C. Flytzanis, Phys. Rev. Lett. 61, 2102 (1988).
    [CrossRef]
  30. V. M. Agranovich, I. I. Lalov, Sov. Phys. Usp. 28, 484 (1985).
    [CrossRef]
  31. A. M. Glass, M. E. Lines, Phys. Rev. B 13, 180 (1976).
    [CrossRef]

1991 (1)

T. P. Dougherty, G. P. Wiederrecht, K. A. Nelson, Ferroelectrics 120, 79 (1991).
[CrossRef]

1990 (1)

J. Etchepare, G. Grillon, A. Antonetti, J. C. Loulergue, M. D. Fontana, G. E. Kugel, Phys. Rev. B 41, 12362 (1990).
[CrossRef]

1989 (1)

E. Hanamura, Phys. Rev. B 39, 1152 (1989).
[CrossRef]

1988 (2)

C. Raptis, Phys. Rev. B 38, 10007 (1988).
[CrossRef]

F. Vallee, G. M. Gale, C. Flytzanis, Phys. Rev. Lett. 61, 2102 (1988).
[CrossRef]

1987 (3)

X. Yang, G. Lan, H. Wang, Phys. Status Solidi b 141, 287 (1987).
[CrossRef]

Y.-X. Yan, K. A. Nelson, J. Chem. Phys. 87, 6240 (1987).
[CrossRef]

Y.-X. Yan, K. A. Nelson, J. Chem. Phys. 87, 6257 (1987).
[CrossRef]

1986 (1)

G. M. Gale, F. Vallee, C. Flytzanis, Phys. Rev. Lett. 57, 1867 (1986).
[CrossRef] [PubMed]

1985 (1)

V. M. Agranovich, I. I. Lalov, Sov. Phys. Usp. 28, 484 (1985).
[CrossRef]

1984 (1)

M. D. Fontana, G. Metrat, J. L. Servoin, F. Gervais, J. Phys. 16, 483 (1984).

1976 (2)

A. M. Glass, M. E. Lines, Phys. Rev. B 13, 180 (1976).
[CrossRef]

A. F. Penna, A. Chaves, P. da R. Andrade, S. P. S. Porto, Phys. Rev. B 13, 4907 (1976).
[CrossRef]

1973 (1)

G. Lamprecht, L. Merten, Phys. Status Solidi b 55, 33 (1973).
[CrossRef]

1972 (1)

A. S. Barker, R. Louden, Rev. Mod. Phys. 44, 18 (1972).
[CrossRef]

1968 (2)

E. Burstein, Comm. Solid State Phys. 1, 202 (1968).

E. Burstein, D. L. Mills, Comm. Solid State Phys. 2, 92, 111 (1968).

1967 (3)

S. C. Abrahams, J. L. Bernstein, J. Phys. Chem. Solids 28, 1685 (1967);A. S. Barker, R. Louden, Phys. Rev. 158, 433 (1967);H. D. Megaw, Acta Crystallogr. A 24, 583 (1968).
[CrossRef]

S. C. Abrahams, W. C. Hamilton, A. Siqueira, J. Phys. Chem. Solids 28, 1693 (1967).
[CrossRef]

I. P. Kaminow, W. D. Johnson, Phys. Rev. 160, 519 (1967).
[CrossRef]

1965 (1)

W. L. Bond, J. Appl. Phys. 36, 1674 (1965).From this reference the value of ∊∞= 4.5 can be deduced.
[CrossRef]

Abrahams, S. C.

S. C. Abrahams, J. L. Bernstein, J. Phys. Chem. Solids 28, 1685 (1967);A. S. Barker, R. Louden, Phys. Rev. 158, 433 (1967);H. D. Megaw, Acta Crystallogr. A 24, 583 (1968).
[CrossRef]

S. C. Abrahams, W. C. Hamilton, A. Siqueira, J. Phys. Chem. Solids 28, 1693 (1967).
[CrossRef]

Agranovich, V. M.

V. M. Agranovich, I. I. Lalov, Sov. Phys. Usp. 28, 484 (1985).
[CrossRef]

Andrade, P. da R.

A. F. Penna, A. Chaves, P. da R. Andrade, S. P. S. Porto, Phys. Rev. B 13, 4907 (1976).
[CrossRef]

Antonetti, A.

J. Etchepare, G. Grillon, A. Antonetti, J. C. Loulergue, M. D. Fontana, G. E. Kugel, Phys. Rev. B 41, 12362 (1990).
[CrossRef]

J. Etchepare, G. Grillon, A. Antonetti, J. C. Loulergue, M. D. Fontana, G. E. Kugel, Ultrafast Phenomena VII (Springer-Verlag, Berlin1990), p. 340.
[CrossRef]

Auston, D. H.

Femtosecond time-resolved observation of optic phonons was also carried out with a different mechanism by M. C. Nuss, D. H. Auston, in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin1986), pp. 284–286;D. H. Auston, K. P. Cheung, J. A. Valdmanis, D. A. Kleinman, Phys. Rev. Lett. 53, 1555 (1984).
[CrossRef]

Barker, A. S.

A. S. Barker, R. Louden, Rev. Mod. Phys. 44, 18 (1972).
[CrossRef]

Baumert, J.-C.

J.-C. Baumert, J. Hoffnagle, P. Günter, in 1984 European Conference on Optics, Optical Systems, and Applications, B. Bolger, H. A. Ferwerda, eds., Proc. Soc. Photo-Opt. Instrum. Eng.492, 374–385 (1983).
[CrossRef]

Bernstein, J. L.

S. C. Abrahams, J. L. Bernstein, J. Phys. Chem. Solids 28, 1685 (1967);A. S. Barker, R. Louden, Phys. Rev. 158, 433 (1967);H. D. Megaw, Acta Crystallogr. A 24, 583 (1968).
[CrossRef]

Bond, W. L.

W. L. Bond, J. Appl. Phys. 36, 1674 (1965).From this reference the value of ∊∞= 4.5 can be deduced.
[CrossRef]

Born, M.

M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Clarendon, Oxford, 1962).

Brandmuller, J.

R. Claus, L. Merten, J. Brandmuller, Light Scattering by Phonon–Polaritons (Springer-Verlag, Berlin, 1975).

Burstein, E.

E. Burstein, Comm. Solid State Phys. 1, 202 (1968).

E. Burstein, D. L. Mills, Comm. Solid State Phys. 2, 92, 111 (1968).

Chaves, A.

A. F. Penna, A. Chaves, P. da R. Andrade, S. P. S. Porto, Phys. Rev. B 13, 4907 (1976).
[CrossRef]

Claus, R.

R. Claus, L. Merten, J. Brandmuller, Light Scattering by Phonon–Polaritons (Springer-Verlag, Berlin, 1975).

Dougherty, T. P.

T. P. Dougherty, G. P. Wiederrecht, K. A. Nelson, Ferroelectrics 120, 79 (1991).
[CrossRef]

T. P. Dougherty, G. P. Wiederrecht, K. A. Nelson, “Femtosecond time-resolved spectroscopy of soft modes in structural phase transitions. I. KNbO3orthorhombic phases; II. BaTiO3 tetrahedral phase,” submitted to Phys. Rev. B.

Etchepare, J.

J. Etchepare, G. Grillon, A. Antonetti, J. C. Loulergue, M. D. Fontana, G. E. Kugel, Phys. Rev. B 41, 12362 (1990).
[CrossRef]

J. Etchepare, G. Grillon, A. Antonetti, J. C. Loulergue, M. D. Fontana, G. E. Kugel, Ultrafast Phenomena VII (Springer-Verlag, Berlin1990), p. 340.
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, London, 1988).

Flytzanis, C.

F. Vallee, G. M. Gale, C. Flytzanis, Phys. Rev. Lett. 61, 2102 (1988).
[CrossRef]

G. M. Gale, F. Vallee, C. Flytzanis, Phys. Rev. Lett. 57, 1867 (1986).
[CrossRef] [PubMed]

Fontana, M. D.

J. Etchepare, G. Grillon, A. Antonetti, J. C. Loulergue, M. D. Fontana, G. E. Kugel, Phys. Rev. B 41, 12362 (1990).
[CrossRef]

M. D. Fontana, G. Metrat, J. L. Servoin, F. Gervais, J. Phys. 16, 483 (1984).

J. Etchepare, G. Grillon, A. Antonetti, J. C. Loulergue, M. D. Fontana, G. E. Kugel, Ultrafast Phenomena VII (Springer-Verlag, Berlin1990), p. 340.
[CrossRef]

Gale, G. M.

F. Vallee, G. M. Gale, C. Flytzanis, Phys. Rev. Lett. 61, 2102 (1988).
[CrossRef]

G. M. Gale, F. Vallee, C. Flytzanis, Phys. Rev. Lett. 57, 1867 (1986).
[CrossRef] [PubMed]

Gervais, F.

M. D. Fontana, G. Metrat, J. L. Servoin, F. Gervais, J. Phys. 16, 483 (1984).

Glass, A. M.

A. M. Glass, M. E. Lines, Phys. Rev. B 13, 180 (1976).
[CrossRef]

Grillon, G.

J. Etchepare, G. Grillon, A. Antonetti, J. C. Loulergue, M. D. Fontana, G. E. Kugel, Phys. Rev. B 41, 12362 (1990).
[CrossRef]

J. Etchepare, G. Grillon, A. Antonetti, J. C. Loulergue, M. D. Fontana, G. E. Kugel, Ultrafast Phenomena VII (Springer-Verlag, Berlin1990), p. 340.
[CrossRef]

Günter, P.

J.-C. Baumert, J. Hoffnagle, P. Günter, in 1984 European Conference on Optics, Optical Systems, and Applications, B. Bolger, H. A. Ferwerda, eds., Proc. Soc. Photo-Opt. Instrum. Eng.492, 374–385 (1983).
[CrossRef]

Hamilton, W. C.

S. C. Abrahams, W. C. Hamilton, A. Siqueira, J. Phys. Chem. Solids 28, 1693 (1967).
[CrossRef]

Hanamura, E.

E. Hanamura, Phys. Rev. B 39, 1152 (1989).
[CrossRef]

Hoffnagle, J.

J.-C. Baumert, J. Hoffnagle, P. Günter, in 1984 European Conference on Optics, Optical Systems, and Applications, B. Bolger, H. A. Ferwerda, eds., Proc. Soc. Photo-Opt. Instrum. Eng.492, 374–385 (1983).
[CrossRef]

Huang, K.

M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Clarendon, Oxford, 1962).

Johnson, W. D.

I. P. Kaminow, W. D. Johnson, Phys. Rev. 160, 519 (1967).
[CrossRef]

Kaminow, I. P.

I. P. Kaminow, W. D. Johnson, Phys. Rev. 160, 519 (1967).
[CrossRef]

Kugel, G. E.

J. Etchepare, G. Grillon, A. Antonetti, J. C. Loulergue, M. D. Fontana, G. E. Kugel, Phys. Rev. B 41, 12362 (1990).
[CrossRef]

J. Etchepare, G. Grillon, A. Antonetti, J. C. Loulergue, M. D. Fontana, G. E. Kugel, Ultrafast Phenomena VII (Springer-Verlag, Berlin1990), p. 340.
[CrossRef]

Lalov, I. I.

V. M. Agranovich, I. I. Lalov, Sov. Phys. Usp. 28, 484 (1985).
[CrossRef]

Lamprecht, G.

G. Lamprecht, L. Merten, Phys. Status Solidi b 55, 33 (1973).
[CrossRef]

Lan, G.

X. Yang, G. Lan, H. Wang, Phys. Status Solidi b 141, 287 (1987).
[CrossRef]

Lines, M. E.

A. M. Glass, M. E. Lines, Phys. Rev. B 13, 180 (1976).
[CrossRef]

Louden, R.

A. S. Barker, R. Louden, Rev. Mod. Phys. 44, 18 (1972).
[CrossRef]

R. Louden, Light Scattering Spectra of Solids (Springer-Verlag, New York, 1969), p. 25.
[CrossRef]

Loulergue, J. C.

J. Etchepare, G. Grillon, A. Antonetti, J. C. Loulergue, M. D. Fontana, G. E. Kugel, Phys. Rev. B 41, 12362 (1990).
[CrossRef]

J. Etchepare, G. Grillon, A. Antonetti, J. C. Loulergue, M. D. Fontana, G. E. Kugel, Ultrafast Phenomena VII (Springer-Verlag, Berlin1990), p. 340.
[CrossRef]

Merten, L.

G. Lamprecht, L. Merten, Phys. Status Solidi b 55, 33 (1973).
[CrossRef]

R. Claus, L. Merten, J. Brandmuller, Light Scattering by Phonon–Polaritons (Springer-Verlag, Berlin, 1975).

Metrat, G.

M. D. Fontana, G. Metrat, J. L. Servoin, F. Gervais, J. Phys. 16, 483 (1984).

Mills, D. L.

E. Burstein, D. L. Mills, Comm. Solid State Phys. 2, 92, 111 (1968).

Nelson, K. A.

T. P. Dougherty, G. P. Wiederrecht, K. A. Nelson, Ferroelectrics 120, 79 (1991).
[CrossRef]

Y.-X. Yan, K. A. Nelson, J. Chem. Phys. 87, 6240 (1987).
[CrossRef]

Y.-X. Yan, K. A. Nelson, J. Chem. Phys. 87, 6257 (1987).
[CrossRef]

T. P. Dougherty, G. P. Wiederrecht, K. A. Nelson, “Femtosecond time-resolved spectroscopy of soft modes in structural phase transitions. I. KNbO3orthorhombic phases; II. BaTiO3 tetrahedral phase,” submitted to Phys. Rev. B.

Nuss, M. C.

Femtosecond time-resolved observation of optic phonons was also carried out with a different mechanism by M. C. Nuss, D. H. Auston, in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin1986), pp. 284–286;D. H. Auston, K. P. Cheung, J. A. Valdmanis, D. A. Kleinman, Phys. Rev. Lett. 53, 1555 (1984).
[CrossRef]

Penna, A. F.

A. F. Penna, A. Chaves, P. da R. Andrade, S. P. S. Porto, Phys. Rev. B 13, 4907 (1976).
[CrossRef]

Planken, P. C. M.

P. C. M. Planken, Ph.D. dissertation (University of Amsterdam, Amsterdam, 1991).

Porto, S. P. S.

A. F. Penna, A. Chaves, P. da R. Andrade, S. P. S. Porto, Phys. Rev. B 13, 4907 (1976).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, London, 1988).

Raptis, C.

C. Raptis, Phys. Rev. B 38, 10007 (1988).
[CrossRef]

Servoin, J. L.

M. D. Fontana, G. Metrat, J. L. Servoin, F. Gervais, J. Phys. 16, 483 (1984).

Siqueira, A.

S. C. Abrahams, W. C. Hamilton, A. Siqueira, J. Phys. Chem. Solids 28, 1693 (1967).
[CrossRef]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, London, 1988).

Vallee, F.

F. Vallee, G. M. Gale, C. Flytzanis, Phys. Rev. Lett. 61, 2102 (1988).
[CrossRef]

G. M. Gale, F. Vallee, C. Flytzanis, Phys. Rev. Lett. 57, 1867 (1986).
[CrossRef] [PubMed]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, London, 1988).

Wang, H.

X. Yang, G. Lan, H. Wang, Phys. Status Solidi b 141, 287 (1987).
[CrossRef]

Wiederrecht, G. P.

T. P. Dougherty, G. P. Wiederrecht, K. A. Nelson, Ferroelectrics 120, 79 (1991).
[CrossRef]

T. P. Dougherty, G. P. Wiederrecht, K. A. Nelson, “Femtosecond time-resolved spectroscopy of soft modes in structural phase transitions. I. KNbO3orthorhombic phases; II. BaTiO3 tetrahedral phase,” submitted to Phys. Rev. B.

Yan, Y.-X.

Y.-X. Yan, K. A. Nelson, J. Chem. Phys. 87, 6257 (1987).
[CrossRef]

Y.-X. Yan, K. A. Nelson, J. Chem. Phys. 87, 6240 (1987).
[CrossRef]

Yang, X.

X. Yang, G. Lan, H. Wang, Phys. Status Solidi b 141, 287 (1987).
[CrossRef]

Comm. Solid State Phys. (2)

E. Burstein, Comm. Solid State Phys. 1, 202 (1968).

E. Burstein, D. L. Mills, Comm. Solid State Phys. 2, 92, 111 (1968).

Ferroelectrics (1)

T. P. Dougherty, G. P. Wiederrecht, K. A. Nelson, Ferroelectrics 120, 79 (1991).
[CrossRef]

J. Appl. Phys. (1)

W. L. Bond, J. Appl. Phys. 36, 1674 (1965).From this reference the value of ∊∞= 4.5 can be deduced.
[CrossRef]

J. Chem. Phys. (2)

Y.-X. Yan, K. A. Nelson, J. Chem. Phys. 87, 6240 (1987).
[CrossRef]

Y.-X. Yan, K. A. Nelson, J. Chem. Phys. 87, 6257 (1987).
[CrossRef]

J. Phys. (1)

M. D. Fontana, G. Metrat, J. L. Servoin, F. Gervais, J. Phys. 16, 483 (1984).

J. Phys. Chem. Solids (2)

S. C. Abrahams, J. L. Bernstein, J. Phys. Chem. Solids 28, 1685 (1967);A. S. Barker, R. Louden, Phys. Rev. 158, 433 (1967);H. D. Megaw, Acta Crystallogr. A 24, 583 (1968).
[CrossRef]

S. C. Abrahams, W. C. Hamilton, A. Siqueira, J. Phys. Chem. Solids 28, 1693 (1967).
[CrossRef]

Phys. Rev. (1)

I. P. Kaminow, W. D. Johnson, Phys. Rev. 160, 519 (1967).
[CrossRef]

Phys. Rev. B (5)

E. Hanamura, Phys. Rev. B 39, 1152 (1989).
[CrossRef]

C. Raptis, Phys. Rev. B 38, 10007 (1988).
[CrossRef]

A. F. Penna, A. Chaves, P. da R. Andrade, S. P. S. Porto, Phys. Rev. B 13, 4907 (1976).
[CrossRef]

A. M. Glass, M. E. Lines, Phys. Rev. B 13, 180 (1976).
[CrossRef]

J. Etchepare, G. Grillon, A. Antonetti, J. C. Loulergue, M. D. Fontana, G. E. Kugel, Phys. Rev. B 41, 12362 (1990).
[CrossRef]

Phys. Rev. Lett. (2)

G. M. Gale, F. Vallee, C. Flytzanis, Phys. Rev. Lett. 57, 1867 (1986).
[CrossRef] [PubMed]

F. Vallee, G. M. Gale, C. Flytzanis, Phys. Rev. Lett. 61, 2102 (1988).
[CrossRef]

Phys. Status Solidi b (2)

X. Yang, G. Lan, H. Wang, Phys. Status Solidi b 141, 287 (1987).
[CrossRef]

G. Lamprecht, L. Merten, Phys. Status Solidi b 55, 33 (1973).
[CrossRef]

Rev. Mod. Phys. (1)

A. S. Barker, R. Louden, Rev. Mod. Phys. 44, 18 (1972).
[CrossRef]

Sov. Phys. Usp. (1)

V. M. Agranovich, I. I. Lalov, Sov. Phys. Usp. 28, 484 (1985).
[CrossRef]

Other (10)

M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Clarendon, Oxford, 1962).

R. Louden, Light Scattering Spectra of Solids (Springer-Verlag, New York, 1969), p. 25.
[CrossRef]

J.-C. Baumert, J. Hoffnagle, P. Günter, in 1984 European Conference on Optics, Optical Systems, and Applications, B. Bolger, H. A. Ferwerda, eds., Proc. Soc. Photo-Opt. Instrum. Eng.492, 374–385 (1983).
[CrossRef]

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, London, 1988).

Ref. 11, Eq. (2.58).

Femtosecond time-resolved observation of optic phonons was also carried out with a different mechanism by M. C. Nuss, D. H. Auston, in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin1986), pp. 284–286;D. H. Auston, K. P. Cheung, J. A. Valdmanis, D. A. Kleinman, Phys. Rev. Lett. 53, 1555 (1984).
[CrossRef]

P. C. M. Planken, Ph.D. dissertation (University of Amsterdam, Amsterdam, 1991).

R. Claus, L. Merten, J. Brandmuller, Light Scattering by Phonon–Polaritons (Springer-Verlag, Berlin, 1975).

T. P. Dougherty, G. P. Wiederrecht, K. A. Nelson, “Femtosecond time-resolved spectroscopy of soft modes in structural phase transitions. I. KNbO3orthorhombic phases; II. BaTiO3 tetrahedral phase,” submitted to Phys. Rev. B.

J. Etchepare, G. Grillon, A. Antonetti, J. C. Loulergue, M. D. Fontana, G. E. Kugel, Ultrafast Phenomena VII (Springer-Verlag, Berlin1990), p. 340.
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Dispersion diagram for a single undamped polar mode. The solid curves represent the wave-vector dependent coupled-mode frequencies. The dashed curves, c′ and c″, represent the propagation of light in the high-k and low-k limits. The curves are generated from Eqs. (9) and (13) with ωT = 10 cm−1, Γ = 0, ωL = 16.25 cm−1, and = 5.

Fig. 2
Fig. 2

Dispersion diagram for two undamped polar modes. The solid curves represent the wave-vector-dependent coupled-mode frequencies. The dashed curves, c′ and c″, represent the propagation of light in the high-k and low-k limits. The curves are generated from Eqs. (19) and (25) with ωT1 = 10 cm−1, ωL1 = 16.25 cm−1, ωT2 = 20 cm−1, ωL2 = 25 cm−1, = 5, and all Γ’s equal to zero.

Fig. 3
Fig. 3

Frequency and damping rate of the lowest-frequency solutions to Eqs. (28) and (23). The following parameters from KNbO3 at 395.1 K (Ref. 3) were used with Eq. (26), ωT1 = 57.8 cm−1, ΓT1 = 61.5 cm−1, ωL1 = 421 cm−1, ΓL1 = 4.5 cm−1, and ′ = 12.47. Equation (23) used the same parameters for the uncoupled lowest-frequency mode and ωT2 = 516 cm−1, ΓT2 = 25 cm−1, ωL2 = 820 cm−1, ΓL2 = 16 cm−1 and = 4.94. Equation (28) is a good approximation to the full model for the lowest-frequency mode in the polariton region.

Fig. 4
Fig. 4

Predicted amplitude K1 and phase ϕ1 [see Eqs. (39) and (40)] of the lowest-frequency B2 symmetry mode of KNbO3 in the polariton region. The model’s values are calculated from ωT1 = 57.8 cm−1, ΓT1 = 61.5 cm−1, ωL1 = 421 cm−1, and ′ = 12.47.

Fig. 5
Fig. 5

Predicted amplitude K1 and phase ϕ1 [see Eqs. (39)(42)] of the lowest-frequency E symmetry mode of BaTiO3 in the polariton region. The mode is overdamped at large k and under-damped at small k. The crossover occurs where K1 diverges. The model’s values are calculated from ωT1 = 36.1 cm−1, ΓT1 = 98.1 cm−1, ωL1 = 710 cm−1, and = 5.22.

Fig. 6
Fig. 6

Predicted maximum amplitude Amax of the response for the two modes shown in Figs. 4 and 5 [see Eqs. (44)(47)]. Notice that the divergence in K1 for BaTiO3 at the crossover from overdamped to underdamped dynamics does not represent a divergence of the response.

Fig. 7
Fig. 7

Wave-vector dependence of the maximum amplitude Amax (a) and phase (b) predicted by the G22 response function [Eq. (32)] and parameters for the B2 soft optic mode in KNbO3. The dependence of Amax predicted by G11 for the same parameters is shown in Fig. 6(a). The dependence of the phase predicted by G11 is shown in Fig. 4(b). In this figure, however, ϕ1 is multiplied by ω1/π to demonstrate that G22 predicts a response more similar to a cosine (phase shift of π/2) than a sine.

Fig. 8
Fig. 8

A1 symmetry scattering in LiTaO3 at room temperature. The y-axis scale is logarithmic. The two experiments were performed at approximately the same wave vector, but (a) was performed with smaller spot sizes. The nonexponential decay is the result of excitation wave-packet propagation in the polariton region.

Fig. 9
Fig. 9

Experiments shown in Fig. 8 repeated with very large (3-mm) spot sizes in the wave-vector direction. At each scattering angle the response is well described by an exponential decay.

Fig. 10
Fig. 10

Wave-vector-dependent frequencies and damping rates are compared with the predictions of Eq. (28); the following parameters are used here: ωT = 206 cm−1, Γ = 26 cm−1, ωL = 402 cm−1, and ′ = 8.5. The agreement for the frequencies is good, but differences between experimental and predicted damping rates are significant.

Equations (69)

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I ( t ) | G ( t ) | 2 .
G ijkl = i j Q k l Q G ( t ) .
G ( t ) exp ( γ 1 t ) sin ( ω 1 t )
G ( t ) [ exp ( λ 1 t ) exp ( λ 2 t ) ]
ω 2 Q = B 11 Q + B 12 E ,
P = B 21 Q + B 22 E ,
E = 4 π ( n 2 1 ) P T 4 π P L ,
n 2 = 1 + 4 π B 22 + 4 π B 12 B 21 B 11 ω 2 .
n 2 = + ω T 2 ( 0 ) ω T 2 ω 2 ,
B 11 = ω T 2 ,
4 π B 12 B 21 = ω T 2 ( 0 ) ,
4 π B 22 = 1 ,
ω 2 = ω L 2 = 0 ω T 2 ,
n 2 = c 2 k 2 ω 2 .
ω 2 Q = ( B 11 + i ω Γ ) Q + B 12 E .
n 2 = + ω T 2 ( 0 ) ω T 2 ω 2 i ω Γ .
ω 4 + ω 3 ( i Γ ) ω 2 c 2 k 2 + ω T 2 0 ω i Γ c 2 k 2 + ω T 2 c 2 k 2 = 0 .
ω 2 = ( c 2 k 2 ) / ,
ω 2 + i ω Γ ω T 2 = 0 .
ω 2 + i ω Γ ω T 2 0 = 0 .
ω 2 = ( c 2 k 2 ) / 0 ,
ω 2 Q 1 = ( ω T 1 2 + i ω Γ T 1 ) Q 1 + B 13 E ,
ω 2 Q 2 = ( ω T 2 2 + i ω Γ T 2 ) Q 2 + B 23 E ,
P = B 31 Q 1 + B 32 Q 2 + 1 4 π E ,
E = 4 π ( n 2 1 ) P T 4 π P L .
n 2 = + A 1 ω T 1 2 i ω Γ T 1 ω 2 + A 2 ω T 2 2 i ω Γ T 2 ω 2 ,
ω 4 + i ω 3 ( Γ T 1 + Γ T 2 ) ω 2 ( ω T 1 2 + ω T 2 2 + Γ T 1 Γ T 2 + A 1 + A 2 ) i ω ( ω T 1 2 Γ T 2 + ω T 2 2 Γ T 1 + A 1 Γ T 2 + A 2 Γ T 1 ) + ω T 1 2 ω T 2 2 + A 1 ω T 2 2 + A 2 ω T 1 2 = 0 .
( ω L 1 2 i ω Γ L 1 ω 2 ) ( ω L 2 2 i ω Γ L 2 ω 2 ) = 0 ,
n 2 = ( ω L 1 2 i ω Γ L 1 ω 2 ) ( ω L 2 2 i ω Γ L 2 ω 2 ) ( ω T 1 2 i ω Γ T 1 ω 2 ) ( ω T 2 2 i ω Γ T 2 ω 2 ) .
n 2 = + j = 1 n A j ω T j 2 i ω Γ T j ω 2 ,
n 2 = j = 1 n ( ω L j 2 i ω Γ L j ω 2 ) ( ω T j 2 i ω Γ T j ω 2 ) .
A j = k = 1 n ( ω L k 2 i ω r j Γ L k ω r j 2 ) k = 1 , k j n ( ω T k 2 i ω r j Γ T k ω 2 ) .
ω r j = i Γ j 2 ± ( ω T j 2 Γ T j 2 / 4 ) 1 / 2 .
= j = 2 n ω L j 2 ω T j 2 .
ω 4 + ω 3 ( i Γ ) ω 2 c 2 k 2 + ω T 2 0 ω i Γ c 2 k 2 + ω T 2 c 2 k 2 = 0 .
[ ω T 1 2 i ω Γ T 1 ω 2 4 π B 12 n 2 1 B 21 n 2 n 2 1 ] ( Q P ) = ( F 1 F 2 ) .
L ( ω ) X ( ω ) = F ( ω ) ,
G ( ω ) = L 1 ( ω ) .
G ( ω ) = [ n 2 ( n 2 1 ) D 4 π B 12 ( n 2 1 ) D B 21 D ω T 1 2 i ω Γ T 1 ω 2 D ] ,
D = ( ω T 1 2 i ω Γ T 1 ω 2 ) ( n 2 n 2 1 ) 4 π B 12 B 21 n 2 1 ,
4 π B 12 B 12 = ω T 1 2 ( 0 ) .
X ( t ) = t d t G ( t t ) F ( t ) .
G 11 ( ω ) = c 2 k 2 ω 2 [ ω 4 + ω 3 ( i Γ ) ω 2 c 2 k 2 + ω T 2 0 ω i Γ c 2 k 2 + ω T 2 c 2 k 2 ] .
G ( ω ) = ω T 2 ( 0 ) [ c 2 k 2 ɛ ω 2 2 ω 2 ( 1 ) Z / z ] + ω 2 ( 1 ) 2 ( ω T 1 2 i ω Γ T 1 ω 2 ) ( Z / z ) 2 [ ω 4 + ω 3 ( i Γ ) ω 2 c 2 k 2 + ω T 2 0 ω i Γ c 2 k 2 + ω T 2 c 2 k 2 ] ,
G 11 ( t ) = i Res { exp ( i ω t ) ( c 2 k 2 ɛ ω 2 ) [ ω ( ω 1 i γ 1 ) ] [ ω ( ω 1 i γ 1 ) ] [ ω ( ω 2 i γ 2 ) ] [ ω ( ω 2 i γ 2 ) ] } .
G 11 ( t ) = 1 ( K 1 { exp ( γ 1 t ) sin [ ω 1 ( t ϕ 1 ) ] } + HF term ) ,
K 1 = 2 [ ( A C + B D ) 2 + ( A D B C ) 2 ] 1 / 2 C 2 + D 2 ,
ϕ 1 = tan 1 ( B C A D A C + B D ) / ω 1 ,
A = c 2 k 2 ( ω 1 2 γ 1 2 ) ,
B = 2 ω 1 γ 1 ,
C = 2 ω 1 [ ω 1 2 ω 2 2 ( γ 1 γ 2 ) 2 ] ,
D = 4 ω 1 2 ( γ 1 γ 2 ) .
G 11 ( t ) = i Res { exp ( i ω t ) ( c 2 k 2 ɛ ω 2 ) ( ω + i λ 1 ) ( ω + i λ 2 ) [ ω ( ω 2 i γ 2 ) ] [ ω ( ω 2 i γ 2 ) ] } .
G 11 ( t ) = 1 ( K 1 { exp [ λ 1 ( t + ϕ 1 ) ] exp [ λ 2 ( t + ϕ 1 ) ] } + HF term ) ,
K 1 = A exp [ λ 1 ln ( A / B ) λ 1 λ 2 ] = B exp [ λ 2 ln ( A / B ) λ 1 λ 2 ]
ϕ 1 = ln ( A / B ) λ 1 λ 2 ,
A = c 2 k 2 + λ 1 2 [ ω 2 2 + ( λ 1 γ 2 ) 2 ] ( λ 1 λ 2 ) ,
B = c 2 k 2 + λ 2 2 [ ω 2 2 + ( λ 2 γ 2 ) 2 ] ( λ 1 λ 2 ) .
A max = K 1 exp [ γ 1 ( z ω 1 + ϕ 1 ) ] sin ( z ) ,
z = arctan ( ω 1 γ 1 ) .
A max = exp ( λ 1 z ) exp ( λ 2 z ) ,
z = ln ( λ 1 / λ 2 ) λ 1 λ 2 .
0 = ( 1 i ω τ ) Q + B 12 E ,
n 2 = + 0 1 i ω τ .
ω 3 + i ω 2 ( 0 τ ) ω ( c 2 k 2 ) i c 2 k 2 τ = 0 .
η ( t ) exp ( 2 γ 1 t ) [ 1 cos ( 2 ω 1 t ) ] .
η ( t ) exp [ α 1 ( υ t ) 2 ] exp ( 2 γ 1 t ) × [ 1 exp ( α 2 ( υ t ) 2 ) cos ( 2 ω 1 t ) ] ,
α 1 = 2 cos 2 β ω p x 2 + ω e x 2 ,
α 2 = 2 cos 2 β ω e x 2 ,

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