Abstract

A novel transient three-pulse scattering technique for measuring ultrafast dephasing times in condensed matter is analyzed using a perturbative solution of the density matrix equation. The advantages of this technique include subpulsewidth resolution, a clear distinction between homogeneous and inhomogeneous broadening, and sensitivity to spectral cross-relaxation. Its application to the case of a multilevel resonance is also considered. We report results of femtosecond dephasing experiments with dye molecules in liquids and in a polymer host. The dephasing time is determined to be less than 20 fsec for dyes in solution at room temperature. At low temperatures in polymers, a transition from homogeneous to inhomogeneous broadening has been observed and studied as a function of temperature.

© 1985 Optical Society of America

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  1. D. E. Cooper, R. W. Olson, and M. D. Fayer, “Intermolecular interaction dynamics and optical dephasing: picosecond photon echo measurements in mixed molecular crystals,” J. Chem. Phys. 72, 2332–2339 (1980).
    [Crossref]
  2. B. Golding and J. E. Graebner, “Relaxation times of tunneling systems in glasses,” in Amorphous Solids, W. A. Philips, ed. (Springer-Verlag, Berlin, 1981), pp. 107–134.
    [Crossref]
  3. H. Souma, T. Yajima, and Y. Taira, “Ultrafast relaxation study by resonant Rayleigh-type mixing spectroscopy using picosecond pulses,” J. Phys. Soc. Jpn. 48, 2040–2047 (1980).
    [Crossref]
  4. A. M. Weiner and E. P. Ippen, “Novel transient scattering technique for femtosecond dephasing measurements,” Opt. Lett. 9, 53–55 (1984).
    [Crossref] [PubMed]
  5. J. Hegarty, L. Goldner, and M. D. Sturge, Bell Laboratories Murray Hill, New Jersey 07974 (personal communication).
  6. J. Friedrich, H. Wolfrum, and D. Haarer, “Photochemical holes: a spectral probe of the amorphous state in the optical domain,” J. Chem. Phys. 77, 2309–2316 (1982).
    [Crossref]
  7. H. P. H. Thijssen, R. Von Den Berg, and S. Volker, “Thermal broadening of optical homogeneous linewidths in organic glasses and polymers studied via photochemical hole-burning,” Chem. Phys. Lett. 97, 295–302 (1983).
    [Crossref]
  8. B. L. Fearey, T. P. Carter, and G. J. Small, “Efficient nonphotochemical hole burning of dye molecules in polymers,” J. Phys. Chem. 87, 3590–3592 (1983).
    [Crossref]
  9. T. P. Carter, B. L. Fearey, J. M. Hayes, and G. J. Small, “Optical dephasing of cresyl violet in a polyvinyl alcohol polymer by non-photochemical hole burning,” Chem. Phys. Lett. 102, 272–276 (1983).
    [Crossref]
  10. A. Szabo, “Observation of the optical analog of the Mössbaue effect in ruby,” Phys. Rev. Lett. 27, 323–326 (1971).
    [Crossref]
  11. M. D. Levenson, R. M. MacFarland, and R. M. Shelby, “Polarization-spectroscopy measurement of the homogeneous linewidth of an inhomogeneously broadened color-center band,” Phys. Rev. B 22, 4915–4929 (1980).
    [Crossref]
  12. I. D. Abella, N. A. Kurnit, and S. R. Hartmann, “Photon echoes,” Phys. Rev. A 141, 391–406 (1966).
  13. T. Mossberg, A. Flusberg, R. Kachru, and S. R. Hartmann, “Total scattering cross section for Na on He measured by stimulated photon echoes,” Phys. Rev. lett. 42, 1665–1669 (1979).
    [Crossref]
  14. W. H. Hesselink and D. A. Wiersma, “Picosecond photon echoes stimulated from an accumulated grating,” Phys. Rev. Lett. 43, 1991–1994 (1979).
    [Crossref]
  15. T. Yajima, Y. Ishida, and Y. Taira, “Investigation of subpicosecond dephasing processes by transient spatial parametric effect in resonant media,” in Picosecond Phenomena II, R. M. Hochstrasser, W. Kaiser, and C. V. Shank, eds. (Springer-Verlag, Berlin, 1980), pp. 190–194.
    [Crossref]
  16. A. M. Weiner, S. De Silvestri, and E. P. Ippen, “Femtosecond dephasing measurements using transient induced gratings,” in Ultrafast Phenomena IV, D. H. Auston and K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 230–232.
    [Crossref]
  17. A. M. Weiner, “Femtosecond optical pulse generation and dephasing measurements in condensed matter,” ScD. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1984).
  18. S. De Silvestri, A. M. Weiner, J. G. Fujimoto, and E. P. Ippen, “Femtosecond dephasing studies of dye molecules in a polymer host,” Chem. Phys. Lett. (to be published).
  19. N. Bloembergen, Nonlinear Optics (Benjamin, Reading, Mass., 1965).
  20. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York1983).
  21. R. Kubo, “A stochastic theory of line-shape and relaxation,” in Fluctuations, Relaxation and Resonance in Magnetic Systems, D. ter Haar, ed. (Plenum, New York, 1962), pp. 23–68.
  22. H. J. Eicher, U. Klein, and D. Langhans, “Coherence time measurement of picosecond pulses by a light-induced grating method,” Appl. Phys. 21, 215–219 (1980).
    [Crossref]
  23. G. Mourou, “Spectral hole burning in dye solution,” IEEE J. Quantum Electron. QE-11, 1–8 (1975).
    [Crossref]
  24. S. Asaka, H. Nakatsuka, M. Fujiwara, and H. Matsuoka, “Accumulated photon echoes with incoherent light in Nd3+-doped silicate glass,” Phys. Rev. A 29, 2286–2289 (1984).
    [Crossref]
  25. N. Morita, T. Yajima, and Y. Ishia, “Coherent transient spectroscopy with ultra-high time-resolution using incoherent light,” in Ultrafast Phenomena IV, D. H. Auston and K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 239–241.
    [Crossref]
  26. R. L. Fork, B. I. Green, and C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode-locking,” Appl. Phys. Lett. 38, 671–672 (1981).
    [Crossref]
  27. R. L. Fork, C. V. Shank, and R. T. Yen, “Amplification of 70-fs optical pulses to gigawatt powers,” Appl. Phys. Lett. 41, 223–225 (1982).
    [Crossref]
  28. D. W. Phillon, D. J. Kuizenga, and A. E. Siegman, “Subnanosecond relaxation time measurements using a transient induced grating method,” Appl. Phys. Lett. 27, 85–89 (1975).
    [Crossref]
  29. A. M. Weiner and E. P. Ippen (unpublished results).

1984 (2)

S. Asaka, H. Nakatsuka, M. Fujiwara, and H. Matsuoka, “Accumulated photon echoes with incoherent light in Nd3+-doped silicate glass,” Phys. Rev. A 29, 2286–2289 (1984).
[Crossref]

A. M. Weiner and E. P. Ippen, “Novel transient scattering technique for femtosecond dephasing measurements,” Opt. Lett. 9, 53–55 (1984).
[Crossref] [PubMed]

1983 (3)

H. P. H. Thijssen, R. Von Den Berg, and S. Volker, “Thermal broadening of optical homogeneous linewidths in organic glasses and polymers studied via photochemical hole-burning,” Chem. Phys. Lett. 97, 295–302 (1983).
[Crossref]

B. L. Fearey, T. P. Carter, and G. J. Small, “Efficient nonphotochemical hole burning of dye molecules in polymers,” J. Phys. Chem. 87, 3590–3592 (1983).
[Crossref]

T. P. Carter, B. L. Fearey, J. M. Hayes, and G. J. Small, “Optical dephasing of cresyl violet in a polyvinyl alcohol polymer by non-photochemical hole burning,” Chem. Phys. Lett. 102, 272–276 (1983).
[Crossref]

1982 (2)

R. L. Fork, C. V. Shank, and R. T. Yen, “Amplification of 70-fs optical pulses to gigawatt powers,” Appl. Phys. Lett. 41, 223–225 (1982).
[Crossref]

J. Friedrich, H. Wolfrum, and D. Haarer, “Photochemical holes: a spectral probe of the amorphous state in the optical domain,” J. Chem. Phys. 77, 2309–2316 (1982).
[Crossref]

1981 (1)

R. L. Fork, B. I. Green, and C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode-locking,” Appl. Phys. Lett. 38, 671–672 (1981).
[Crossref]

1980 (4)

H. J. Eicher, U. Klein, and D. Langhans, “Coherence time measurement of picosecond pulses by a light-induced grating method,” Appl. Phys. 21, 215–219 (1980).
[Crossref]

D. E. Cooper, R. W. Olson, and M. D. Fayer, “Intermolecular interaction dynamics and optical dephasing: picosecond photon echo measurements in mixed molecular crystals,” J. Chem. Phys. 72, 2332–2339 (1980).
[Crossref]

H. Souma, T. Yajima, and Y. Taira, “Ultrafast relaxation study by resonant Rayleigh-type mixing spectroscopy using picosecond pulses,” J. Phys. Soc. Jpn. 48, 2040–2047 (1980).
[Crossref]

M. D. Levenson, R. M. MacFarland, and R. M. Shelby, “Polarization-spectroscopy measurement of the homogeneous linewidth of an inhomogeneously broadened color-center band,” Phys. Rev. B 22, 4915–4929 (1980).
[Crossref]

1979 (2)

T. Mossberg, A. Flusberg, R. Kachru, and S. R. Hartmann, “Total scattering cross section for Na on He measured by stimulated photon echoes,” Phys. Rev. lett. 42, 1665–1669 (1979).
[Crossref]

W. H. Hesselink and D. A. Wiersma, “Picosecond photon echoes stimulated from an accumulated grating,” Phys. Rev. Lett. 43, 1991–1994 (1979).
[Crossref]

1975 (2)

D. W. Phillon, D. J. Kuizenga, and A. E. Siegman, “Subnanosecond relaxation time measurements using a transient induced grating method,” Appl. Phys. Lett. 27, 85–89 (1975).
[Crossref]

G. Mourou, “Spectral hole burning in dye solution,” IEEE J. Quantum Electron. QE-11, 1–8 (1975).
[Crossref]

1971 (1)

A. Szabo, “Observation of the optical analog of the Mössbaue effect in ruby,” Phys. Rev. Lett. 27, 323–326 (1971).
[Crossref]

1966 (1)

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, “Photon echoes,” Phys. Rev. A 141, 391–406 (1966).

Abella, I. D.

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, “Photon echoes,” Phys. Rev. A 141, 391–406 (1966).

Asaka, S.

S. Asaka, H. Nakatsuka, M. Fujiwara, and H. Matsuoka, “Accumulated photon echoes with incoherent light in Nd3+-doped silicate glass,” Phys. Rev. A 29, 2286–2289 (1984).
[Crossref]

Bloembergen, N.

N. Bloembergen, Nonlinear Optics (Benjamin, Reading, Mass., 1965).

Carter, T. P.

B. L. Fearey, T. P. Carter, and G. J. Small, “Efficient nonphotochemical hole burning of dye molecules in polymers,” J. Phys. Chem. 87, 3590–3592 (1983).
[Crossref]

T. P. Carter, B. L. Fearey, J. M. Hayes, and G. J. Small, “Optical dephasing of cresyl violet in a polyvinyl alcohol polymer by non-photochemical hole burning,” Chem. Phys. Lett. 102, 272–276 (1983).
[Crossref]

Cooper, D. E.

D. E. Cooper, R. W. Olson, and M. D. Fayer, “Intermolecular interaction dynamics and optical dephasing: picosecond photon echo measurements in mixed molecular crystals,” J. Chem. Phys. 72, 2332–2339 (1980).
[Crossref]

De Silvestri, S.

A. M. Weiner, S. De Silvestri, and E. P. Ippen, “Femtosecond dephasing measurements using transient induced gratings,” in Ultrafast Phenomena IV, D. H. Auston and K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 230–232.
[Crossref]

S. De Silvestri, A. M. Weiner, J. G. Fujimoto, and E. P. Ippen, “Femtosecond dephasing studies of dye molecules in a polymer host,” Chem. Phys. Lett. (to be published).

Eicher, H. J.

H. J. Eicher, U. Klein, and D. Langhans, “Coherence time measurement of picosecond pulses by a light-induced grating method,” Appl. Phys. 21, 215–219 (1980).
[Crossref]

Fayer, M. D.

D. E. Cooper, R. W. Olson, and M. D. Fayer, “Intermolecular interaction dynamics and optical dephasing: picosecond photon echo measurements in mixed molecular crystals,” J. Chem. Phys. 72, 2332–2339 (1980).
[Crossref]

Fearey, B. L.

T. P. Carter, B. L. Fearey, J. M. Hayes, and G. J. Small, “Optical dephasing of cresyl violet in a polyvinyl alcohol polymer by non-photochemical hole burning,” Chem. Phys. Lett. 102, 272–276 (1983).
[Crossref]

B. L. Fearey, T. P. Carter, and G. J. Small, “Efficient nonphotochemical hole burning of dye molecules in polymers,” J. Phys. Chem. 87, 3590–3592 (1983).
[Crossref]

Flusberg, A.

T. Mossberg, A. Flusberg, R. Kachru, and S. R. Hartmann, “Total scattering cross section for Na on He measured by stimulated photon echoes,” Phys. Rev. lett. 42, 1665–1669 (1979).
[Crossref]

Fork, R. L.

R. L. Fork, C. V. Shank, and R. T. Yen, “Amplification of 70-fs optical pulses to gigawatt powers,” Appl. Phys. Lett. 41, 223–225 (1982).
[Crossref]

R. L. Fork, B. I. Green, and C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode-locking,” Appl. Phys. Lett. 38, 671–672 (1981).
[Crossref]

Friedrich, J.

J. Friedrich, H. Wolfrum, and D. Haarer, “Photochemical holes: a spectral probe of the amorphous state in the optical domain,” J. Chem. Phys. 77, 2309–2316 (1982).
[Crossref]

Fujimoto, J. G.

S. De Silvestri, A. M. Weiner, J. G. Fujimoto, and E. P. Ippen, “Femtosecond dephasing studies of dye molecules in a polymer host,” Chem. Phys. Lett. (to be published).

Fujiwara, M.

S. Asaka, H. Nakatsuka, M. Fujiwara, and H. Matsuoka, “Accumulated photon echoes with incoherent light in Nd3+-doped silicate glass,” Phys. Rev. A 29, 2286–2289 (1984).
[Crossref]

Golding, B.

B. Golding and J. E. Graebner, “Relaxation times of tunneling systems in glasses,” in Amorphous Solids, W. A. Philips, ed. (Springer-Verlag, Berlin, 1981), pp. 107–134.
[Crossref]

Goldner, L.

J. Hegarty, L. Goldner, and M. D. Sturge, Bell Laboratories Murray Hill, New Jersey 07974 (personal communication).

Graebner, J. E.

B. Golding and J. E. Graebner, “Relaxation times of tunneling systems in glasses,” in Amorphous Solids, W. A. Philips, ed. (Springer-Verlag, Berlin, 1981), pp. 107–134.
[Crossref]

Green, B. I.

R. L. Fork, B. I. Green, and C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode-locking,” Appl. Phys. Lett. 38, 671–672 (1981).
[Crossref]

Haarer, D.

J. Friedrich, H. Wolfrum, and D. Haarer, “Photochemical holes: a spectral probe of the amorphous state in the optical domain,” J. Chem. Phys. 77, 2309–2316 (1982).
[Crossref]

Hartmann, S. R.

T. Mossberg, A. Flusberg, R. Kachru, and S. R. Hartmann, “Total scattering cross section for Na on He measured by stimulated photon echoes,” Phys. Rev. lett. 42, 1665–1669 (1979).
[Crossref]

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, “Photon echoes,” Phys. Rev. A 141, 391–406 (1966).

Hayes, J. M.

T. P. Carter, B. L. Fearey, J. M. Hayes, and G. J. Small, “Optical dephasing of cresyl violet in a polyvinyl alcohol polymer by non-photochemical hole burning,” Chem. Phys. Lett. 102, 272–276 (1983).
[Crossref]

Hegarty, J.

J. Hegarty, L. Goldner, and M. D. Sturge, Bell Laboratories Murray Hill, New Jersey 07974 (personal communication).

Hesselink, W. H.

W. H. Hesselink and D. A. Wiersma, “Picosecond photon echoes stimulated from an accumulated grating,” Phys. Rev. Lett. 43, 1991–1994 (1979).
[Crossref]

Ippen, E. P.

A. M. Weiner and E. P. Ippen, “Novel transient scattering technique for femtosecond dephasing measurements,” Opt. Lett. 9, 53–55 (1984).
[Crossref] [PubMed]

A. M. Weiner, S. De Silvestri, and E. P. Ippen, “Femtosecond dephasing measurements using transient induced gratings,” in Ultrafast Phenomena IV, D. H. Auston and K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 230–232.
[Crossref]

S. De Silvestri, A. M. Weiner, J. G. Fujimoto, and E. P. Ippen, “Femtosecond dephasing studies of dye molecules in a polymer host,” Chem. Phys. Lett. (to be published).

A. M. Weiner and E. P. Ippen (unpublished results).

Ishia, Y.

N. Morita, T. Yajima, and Y. Ishia, “Coherent transient spectroscopy with ultra-high time-resolution using incoherent light,” in Ultrafast Phenomena IV, D. H. Auston and K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 239–241.
[Crossref]

Ishida, Y.

T. Yajima, Y. Ishida, and Y. Taira, “Investigation of subpicosecond dephasing processes by transient spatial parametric effect in resonant media,” in Picosecond Phenomena II, R. M. Hochstrasser, W. Kaiser, and C. V. Shank, eds. (Springer-Verlag, Berlin, 1980), pp. 190–194.
[Crossref]

Kachru, R.

T. Mossberg, A. Flusberg, R. Kachru, and S. R. Hartmann, “Total scattering cross section for Na on He measured by stimulated photon echoes,” Phys. Rev. lett. 42, 1665–1669 (1979).
[Crossref]

Klein, U.

H. J. Eicher, U. Klein, and D. Langhans, “Coherence time measurement of picosecond pulses by a light-induced grating method,” Appl. Phys. 21, 215–219 (1980).
[Crossref]

Kubo, R.

R. Kubo, “A stochastic theory of line-shape and relaxation,” in Fluctuations, Relaxation and Resonance in Magnetic Systems, D. ter Haar, ed. (Plenum, New York, 1962), pp. 23–68.

Kuizenga, D. J.

D. W. Phillon, D. J. Kuizenga, and A. E. Siegman, “Subnanosecond relaxation time measurements using a transient induced grating method,” Appl. Phys. Lett. 27, 85–89 (1975).
[Crossref]

Kurnit, N. A.

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, “Photon echoes,” Phys. Rev. A 141, 391–406 (1966).

Langhans, D.

H. J. Eicher, U. Klein, and D. Langhans, “Coherence time measurement of picosecond pulses by a light-induced grating method,” Appl. Phys. 21, 215–219 (1980).
[Crossref]

Levenson, M. D.

M. D. Levenson, R. M. MacFarland, and R. M. Shelby, “Polarization-spectroscopy measurement of the homogeneous linewidth of an inhomogeneously broadened color-center band,” Phys. Rev. B 22, 4915–4929 (1980).
[Crossref]

MacFarland, R. M.

M. D. Levenson, R. M. MacFarland, and R. M. Shelby, “Polarization-spectroscopy measurement of the homogeneous linewidth of an inhomogeneously broadened color-center band,” Phys. Rev. B 22, 4915–4929 (1980).
[Crossref]

Matsuoka, H.

S. Asaka, H. Nakatsuka, M. Fujiwara, and H. Matsuoka, “Accumulated photon echoes with incoherent light in Nd3+-doped silicate glass,” Phys. Rev. A 29, 2286–2289 (1984).
[Crossref]

Morita, N.

N. Morita, T. Yajima, and Y. Ishia, “Coherent transient spectroscopy with ultra-high time-resolution using incoherent light,” in Ultrafast Phenomena IV, D. H. Auston and K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 239–241.
[Crossref]

Mossberg, T.

T. Mossberg, A. Flusberg, R. Kachru, and S. R. Hartmann, “Total scattering cross section for Na on He measured by stimulated photon echoes,” Phys. Rev. lett. 42, 1665–1669 (1979).
[Crossref]

Mourou, G.

G. Mourou, “Spectral hole burning in dye solution,” IEEE J. Quantum Electron. QE-11, 1–8 (1975).
[Crossref]

Nakatsuka, H.

S. Asaka, H. Nakatsuka, M. Fujiwara, and H. Matsuoka, “Accumulated photon echoes with incoherent light in Nd3+-doped silicate glass,” Phys. Rev. A 29, 2286–2289 (1984).
[Crossref]

Olson, R. W.

D. E. Cooper, R. W. Olson, and M. D. Fayer, “Intermolecular interaction dynamics and optical dephasing: picosecond photon echo measurements in mixed molecular crystals,” J. Chem. Phys. 72, 2332–2339 (1980).
[Crossref]

Phillon, D. W.

D. W. Phillon, D. J. Kuizenga, and A. E. Siegman, “Subnanosecond relaxation time measurements using a transient induced grating method,” Appl. Phys. Lett. 27, 85–89 (1975).
[Crossref]

Shank, C. V.

R. L. Fork, C. V. Shank, and R. T. Yen, “Amplification of 70-fs optical pulses to gigawatt powers,” Appl. Phys. Lett. 41, 223–225 (1982).
[Crossref]

R. L. Fork, B. I. Green, and C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode-locking,” Appl. Phys. Lett. 38, 671–672 (1981).
[Crossref]

Shelby, R. M.

M. D. Levenson, R. M. MacFarland, and R. M. Shelby, “Polarization-spectroscopy measurement of the homogeneous linewidth of an inhomogeneously broadened color-center band,” Phys. Rev. B 22, 4915–4929 (1980).
[Crossref]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York1983).

Siegman, A. E.

D. W. Phillon, D. J. Kuizenga, and A. E. Siegman, “Subnanosecond relaxation time measurements using a transient induced grating method,” Appl. Phys. Lett. 27, 85–89 (1975).
[Crossref]

Small, G. J.

T. P. Carter, B. L. Fearey, J. M. Hayes, and G. J. Small, “Optical dephasing of cresyl violet in a polyvinyl alcohol polymer by non-photochemical hole burning,” Chem. Phys. Lett. 102, 272–276 (1983).
[Crossref]

B. L. Fearey, T. P. Carter, and G. J. Small, “Efficient nonphotochemical hole burning of dye molecules in polymers,” J. Phys. Chem. 87, 3590–3592 (1983).
[Crossref]

Souma, H.

H. Souma, T. Yajima, and Y. Taira, “Ultrafast relaxation study by resonant Rayleigh-type mixing spectroscopy using picosecond pulses,” J. Phys. Soc. Jpn. 48, 2040–2047 (1980).
[Crossref]

Sturge, M. D.

J. Hegarty, L. Goldner, and M. D. Sturge, Bell Laboratories Murray Hill, New Jersey 07974 (personal communication).

Szabo, A.

A. Szabo, “Observation of the optical analog of the Mössbaue effect in ruby,” Phys. Rev. Lett. 27, 323–326 (1971).
[Crossref]

Taira, Y.

H. Souma, T. Yajima, and Y. Taira, “Ultrafast relaxation study by resonant Rayleigh-type mixing spectroscopy using picosecond pulses,” J. Phys. Soc. Jpn. 48, 2040–2047 (1980).
[Crossref]

T. Yajima, Y. Ishida, and Y. Taira, “Investigation of subpicosecond dephasing processes by transient spatial parametric effect in resonant media,” in Picosecond Phenomena II, R. M. Hochstrasser, W. Kaiser, and C. V. Shank, eds. (Springer-Verlag, Berlin, 1980), pp. 190–194.
[Crossref]

Thijssen, H. P. H.

H. P. H. Thijssen, R. Von Den Berg, and S. Volker, “Thermal broadening of optical homogeneous linewidths in organic glasses and polymers studied via photochemical hole-burning,” Chem. Phys. Lett. 97, 295–302 (1983).
[Crossref]

Volker, S.

H. P. H. Thijssen, R. Von Den Berg, and S. Volker, “Thermal broadening of optical homogeneous linewidths in organic glasses and polymers studied via photochemical hole-burning,” Chem. Phys. Lett. 97, 295–302 (1983).
[Crossref]

Von Den Berg, R.

H. P. H. Thijssen, R. Von Den Berg, and S. Volker, “Thermal broadening of optical homogeneous linewidths in organic glasses and polymers studied via photochemical hole-burning,” Chem. Phys. Lett. 97, 295–302 (1983).
[Crossref]

Weiner, A. M.

A. M. Weiner and E. P. Ippen, “Novel transient scattering technique for femtosecond dephasing measurements,” Opt. Lett. 9, 53–55 (1984).
[Crossref] [PubMed]

A. M. Weiner, S. De Silvestri, and E. P. Ippen, “Femtosecond dephasing measurements using transient induced gratings,” in Ultrafast Phenomena IV, D. H. Auston and K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 230–232.
[Crossref]

A. M. Weiner, “Femtosecond optical pulse generation and dephasing measurements in condensed matter,” ScD. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1984).

S. De Silvestri, A. M. Weiner, J. G. Fujimoto, and E. P. Ippen, “Femtosecond dephasing studies of dye molecules in a polymer host,” Chem. Phys. Lett. (to be published).

A. M. Weiner and E. P. Ippen (unpublished results).

Wiersma, D. A.

W. H. Hesselink and D. A. Wiersma, “Picosecond photon echoes stimulated from an accumulated grating,” Phys. Rev. Lett. 43, 1991–1994 (1979).
[Crossref]

Wolfrum, H.

J. Friedrich, H. Wolfrum, and D. Haarer, “Photochemical holes: a spectral probe of the amorphous state in the optical domain,” J. Chem. Phys. 77, 2309–2316 (1982).
[Crossref]

Yajima, T.

H. Souma, T. Yajima, and Y. Taira, “Ultrafast relaxation study by resonant Rayleigh-type mixing spectroscopy using picosecond pulses,” J. Phys. Soc. Jpn. 48, 2040–2047 (1980).
[Crossref]

T. Yajima, Y. Ishida, and Y. Taira, “Investigation of subpicosecond dephasing processes by transient spatial parametric effect in resonant media,” in Picosecond Phenomena II, R. M. Hochstrasser, W. Kaiser, and C. V. Shank, eds. (Springer-Verlag, Berlin, 1980), pp. 190–194.
[Crossref]

N. Morita, T. Yajima, and Y. Ishia, “Coherent transient spectroscopy with ultra-high time-resolution using incoherent light,” in Ultrafast Phenomena IV, D. H. Auston and K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 239–241.
[Crossref]

Yen, R. T.

R. L. Fork, C. V. Shank, and R. T. Yen, “Amplification of 70-fs optical pulses to gigawatt powers,” Appl. Phys. Lett. 41, 223–225 (1982).
[Crossref]

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[Crossref]

R. L. Fork, C. V. Shank, and R. T. Yen, “Amplification of 70-fs optical pulses to gigawatt powers,” Appl. Phys. Lett. 41, 223–225 (1982).
[Crossref]

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[Crossref]

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H. P. H. Thijssen, R. Von Den Berg, and S. Volker, “Thermal broadening of optical homogeneous linewidths in organic glasses and polymers studied via photochemical hole-burning,” Chem. Phys. Lett. 97, 295–302 (1983).
[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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A. M. Weiner and E. P. Ippen (unpublished results).

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Figures (10)

Fig. 1
Fig. 1

Interaction scheme for dephasing measurements by the three-pulse scattering technique.

Fig. 2
Fig. 2

Calculated scattered energy for Gaussian pulses as a function of the normalized delay τ/tp between pulses #1 and #2, in a homogeneously broadened medium for several values of T2/tp. The laser frequency is on resonance.

Fig. 3
Fig. 3

Off-resonance scattering curves for Gaussian pulses as a function of τ/tp for various frequency offsets Δωtp/2π. The dephasing time T2 was set to 2.5tp.

Fig. 4
Fig. 4

Calculated scattered energy, for Gaussian pulses as a function of τ/tp for different values of T2/tp in the case of wide inhomogeneous broadening.

Fig. 5
Fig. 5

Normalized peak shift τs/tp as a function of the normalized dephasing time T2/tp.

Fig. 6
Fig. 6

Calculated scattered energy for delta-function pulses as a function of τ/T2 for different values of T/T3, in a inhomogeneously broadened medium with Δω/T2 = 10. TgT is assumed.

Fig. 7
Fig. 7

Scattered data for Rhodamine 640 and Nile blue in methanol, using parallel polarization.

Fig. 8
Fig. 8

Scattered energy for (a) cresyl violet and (b) oxazine 720 in PMMA at 15 K as a function of the delay T of pulse #3. Pulses #1 and #2 are set at zero relative delay.

Fig. 9
Fig. 9

Scattered energy for cresyl violet in PMMA as a function of delay τ between pulses #1 and #2. The temperatures are (a) 15 K, (b) 290 K. The delay of pulse #3 was set to 1.3 psec.

Fig. 10
Fig. 10

Scattered energy for Nile blue in PMMA at 15 K as a function of the delay τ between pulses #1 and #2. The delay of pulse #3 was set to 1.3 psec.

Equations (20)

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ρ ̂ g e ( 3 ) ( r ¯ , t ) t d t Ê ( r ¯ , t ) exp [ ( 1 T 2 + i Δ ω ) ( t t ) ] × t d t t d t { exp [ ( t t ) / T g ] × exp [ ( t t ) / T e ] } { Ê * ( r ¯ , t ) Ê ( r ¯ , t ) × exp [ ( 1 T 2 + i Δ ω ) ( t t ) ] + c.c }
Ê ( r ¯ , t ) = a 1 e ( t + τ ) exp ( i k ¯ 1 · r ¯ ) + a 2 e ( t ) exp ( i k ¯ 2 · r ¯ ) + a 3 e ( t T ) exp ( i k ¯ 3 · r ¯ ) ,
P ̂ k 4 ( 3 ) ( r ¯ , t ) exp ( i k ¯ 4 · r ¯ ) d ω 0 g ( ω 0 ) t d t e ( t T ) × exp [ ( 1 T 2 + i Δ ω ) ( t t ) ] × exp ( T / T g ) γ ̂ ( τ , Δ ω ) ,
γ ̂ ( τ , Δ ω ) d t t d t { e * ( t ) e ( t + τ ) × exp [ ( 1 T 2 + i Δ ω ) ( t t ) ] + e ( t + τ ) e * ( t ) × exp [ ( 1 T 2 i Δ ω ) ( t t ) ] } .
γ ( r ¯ , τ , Δ ω ) = exp ( T / T g ) × { γ ̂ ( τ , Δ ω ) × exp [ i ( k ¯ 1 k ¯ 2 ) · r ¯ ] + c.c. } ,
U k 4 ( τ ) d t | P ̂ k 4 ( 3 ) ( r ¯ , t ) | 2
U k 4 = U k 5 | γ ̂ ( τ , Δ ω ) | 2 .
U k 4 = U k 5 exp ( 2 | τ | / T 2 ) .
U k 4 = U k 5 | d t e ( t ) e * ( t + τ ) | 2 .
γ ̂ ( τ , Δ ω ) d τ h T ( τ + τ ) exp [ i Δ ω ( τ + τ ) ] G ( τ ) + d τ h T * ( τ τ ) exp [ i Δ ω ( τ τ ) ] G * ( τ )
γ ̂ ( τ , Δ ω ) d Ω exp ( i Ω τ ) α ( ω L + Ω ) ϕ ( ω L + Ω ) ,
γ ( r ¯ , τ , Δ ω ) exp ( | τ | / T 2 ) cos [ ( k ¯ 1 k ¯ 2 ) · r ¯ Δ ω τ ] .
( P ̂ k 4 ( 3 ) + P ̂ k 5 ( 3 ) ) exp ( ( t T + | τ | ) / T 2 ] d ω 0 g ( ω 0 ) × ( exp { i [ k ¯ 4 · r ¯ Δ ω ( t T + τ ) ] } × exp { i [ k ¯ 5 · r ¯ Δ ω ( t T τ ) ] } ) .
τ 0 ; U k 4 = 0 ; U k 5 exp ( 4 τ / T 2 ) ,
τ 0 ; U k 4 exp ( 4 τ / T 2 ) ; U k 5 = 0 .
P ̂ k 4 ( 3 ) ( r ¯ , t ) exp ( i k ¯ 4 · r ¯ ) × d t | h T ( t t ) | 2 q ( t t ) G * ( t t + τ ) .
U k 4 ( τ ) d τ d τ | h T ( τ ) | 2 | h T ( τ ) | 2 Q ( τ τ ) G * ( τ + τ ) G ( τ + τ ) ,
γ ̂ TOTAL ( τ ) d ω 0 g ( ω 0 ) γ ̂ ( τ , Δ ω ) .
γ ̂ TOTAL ( τ ) d Ω exp(i Ω τ ) α TOTAL ( ω L + Ω ) ϕ ( ω L + Ω ) .
p ( ω 0 ω 0 ) = g ( ω 0 ) / T 3 .

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