Abstract

Intracavity measurements of degenerate four-wave mixing have been performed with femtosecond laser pulses to determine the phase relaxation time of the absorbing dye, diethyloxadicarbocyanine iodide (DODCI), in ethylene glycol. The influence of various broadening mechanisms (homogeneous, inhomogeneous, cross relaxation) and pulse parameters (frequency, pulse shape, phase modulation, and energy) is investigated. The dependence of the signal energy on probe delay is found to be strongly affected by the phase modulation of the pulse; hence determination of the phase relaxation time requires accurate diagnostics of the laser source. The rise of the signal provides an upper limit of 10 fsec for the phase relaxation time of the main absorption band of the dye DODCI. The decay of the signal is found to be related to the phase relaxation time of a two-photon absorption in the same dye. Accurate fitting of the data with the theory yields 50 ± 10 fsec for the dephasing time of the two-photon excitation in DODCI.

© 1986 Optical Society of America

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  1. W. Dietel, J. J. Fontaine, J.-C. Diels, “Intracavity pulse compression with glass: a new method of generating pulses shorter than 60 femtoseconds,” Opt. Lett. 8, 4 (1983).
    [CrossRef] [PubMed]
  2. J. J. Fontaine, W. Dietel, J.-C. Diels, “Chirp in a mode-locked ring dye laser,” IEEE J. Quantum Electron. QE-19, 1467 (1983).
    [CrossRef]
  3. J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. (Moscow) 10, 2398–2410 (1983) [Sov. J. Quantum Electron. 13, 1562 (1983)].
  4. J. Herrmann, F. Weidner, “Theory of passively mode-locked cw dye lasers,” Appl. Phys. B 27, 105–113 (1982); J. Herrman, B. Wilhelmi, in Laser für Ultrakurze Lichtimpulse (Akademie-Verlag, Berlin, 1984), pp. 181–185.
    [CrossRef]
  5. J.-C. Diels, I. C. McMichael, J. Fontaine, C. Y. Wang, “Subpicosecond pulse shape measurement and modeling of a passively mode-locked dye laser including mutual interaction in a dye jet,” in Picosecond Phenomena III (Springer-Verlag, Berlin, 1982), pp. 116–119.
    [CrossRef]
  6. M. S. Stix, E. P. Ippen, “Pulse shaping in passively mode-locked ring dye lasers,” IEEE J. Quantum Electron. QE-19, 520 (1983).
    [CrossRef]
  7. J.-C. Diels, I. C. McMichael, H. Vanherzeele, “Degenerate four wave mixing of picosecond pulses in the saturable amplification of a dye laser,” IEEE J. Quantum Electron. QE-20, 630–636 (1984).
    [CrossRef]
  8. J. H. Menders, “Development of a coherent subpicosecond pulse laser and the determination of dephasing times of dyes,” Ph.D. dissertation (Department of Physics, University of Southern California, Los Angeles, Calif., 1983) (unpublished).
  9. A. M. Weiner, E. P. Ippen, “Novel transient scattering technique for femtosecond dephasing measurements,” Opt. Lett. 9, 53–55 (1984).
    [CrossRef] [PubMed]
  10. R. L. Fork, B. I. Greene, 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]
  11. J.-C. Diels, J. J. Fontaine, I. C. McMichael, F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt.24, 1270–1282 (1985); J.-C. Diels, W. Dietel, E. Dopel, J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, R. Torti, H. Vanherzeele, B. Wilhelmi, “Colliding pulse femtosecond lasers and applications to the measurement of optical parameters,” in Proceedings of the Fourth International Picosecond Conference, D. H. Auston, K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 30–34.
    [CrossRef]
  12. A. M. Weiner, J. G. Fujimoto, E. P. Ippen, “Femtosecond time-resolved reflectometry measurements of multiple-layer dielectric mirrors,” Opt. Lett. 10, 71–73 (1985).
    [CrossRef] [PubMed]
  13. T. Yajima, Y. Taira, “Spatial optical parametric coupling of picosecond light pulses and transverse relaxation effect in resonant media,” J. Phys. Soc. Jpn. 47, 1620–1626 (1979).
    [CrossRef]
  14. T. Yajima, Y. Ishida, Y. Taira, “Investigation of subpicosecond dephasing processes by transient spatial parametric effect in resonant media,” in Picosecond Phenomena II, R. M. Hochstrasser, W. Kaiser, C. V. Shank, eds. (Springer-Verlag, New York, 1980), pp. 190–194.
    [CrossRef]
  15. I. C. McMichael, J.-C. Diels, “Degenerate four wave mixing of femtosecond pulses in the saturable absorber of a ring dye laser,” presented at the XIIIth International Quantum Electronics Conference, Anaheim, Calif., June 1984.
  16. A. von Jena, H. E. Lessing, “Coherent coupling effects in picosecond absorption experiments,” Appl. Phys. 19, 131–144 (1979); T. Yajima, H. Souma, Y. Ishida, “Study of ultra-fast relaxation processes by resonant Rayleigh-type optical mixing,” Phys. Rev. A 17, 324 (1978).
    [CrossRef]
  17. B. S. Wherrett, A. L. Smirl, T. F. Bogges, “Theory of degenerate four-wave mixing in picosecond excitation probe experiments,” IEEE J. Quantum Electron. QE-19, 680–690 (1983).
    [CrossRef]
  18. J.-C. Diels, W. C. Wang, H. Winful, “Dynamics of the nonlinear four-wave mixing interaction,” Appl. Phys. B 26, 105–110 (1981).
    [CrossRef]
  19. Y. Silberberg, I. Bar-Joseph, “Transient effects in degenerate four-wave mixing in saturable absorbers,” IEEE J. Quantum Electron. QE-17, 1967–1970 (1981).
    [CrossRef]
  20. J.-C. Diels, W. Dietel, J. J. Fontaine, W. Rudolph, B. Wilhelmi, “Analysis of a mode-locked ring laser: chirped-solitary-pulse solutions,” J. Opt. Soc. Am. B 2, 680–686 (1985).
    [CrossRef]
  21. S. Besnainou, J.-C. Diels, J. Stone, “Molecular multiphoton excitation of phase coherent pulse pairs,” J. Chem. Phys. 81, 143–149 (1984).
    [CrossRef]
  22. S. Rentsch, “Bestimmung von Lebensdauern und Transienten-absorptionsspektren von Polymethinfarbstoffen aus Pikosekundenspektroskopischen Messungen,” J. Signalaufzeichnungsmaterialien 12, 319–328 (1984); D. Khetshinashvili, S. Rentsch, B. Schroder, H. Wabnitz, “Picosecond absorption and fluorescence studies of DODCI,” presented at the IVth International Symposium on Ultrafast Phenomena in Spectroscopy, Reinhardsbrunn, German Democratic Republic, October 1985.

1985

1984

S. Besnainou, J.-C. Diels, J. Stone, “Molecular multiphoton excitation of phase coherent pulse pairs,” J. Chem. Phys. 81, 143–149 (1984).
[CrossRef]

S. Rentsch, “Bestimmung von Lebensdauern und Transienten-absorptionsspektren von Polymethinfarbstoffen aus Pikosekundenspektroskopischen Messungen,” J. Signalaufzeichnungsmaterialien 12, 319–328 (1984); D. Khetshinashvili, S. Rentsch, B. Schroder, H. Wabnitz, “Picosecond absorption and fluorescence studies of DODCI,” presented at the IVth International Symposium on Ultrafast Phenomena in Spectroscopy, Reinhardsbrunn, German Democratic Republic, October 1985.

J.-C. Diels, I. C. McMichael, H. Vanherzeele, “Degenerate four wave mixing of picosecond pulses in the saturable amplification of a dye laser,” IEEE J. Quantum Electron. QE-20, 630–636 (1984).
[CrossRef]

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

1983

W. Dietel, J. J. Fontaine, J.-C. Diels, “Intracavity pulse compression with glass: a new method of generating pulses shorter than 60 femtoseconds,” Opt. Lett. 8, 4 (1983).
[CrossRef] [PubMed]

J. J. Fontaine, W. Dietel, J.-C. Diels, “Chirp in a mode-locked ring dye laser,” IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. (Moscow) 10, 2398–2410 (1983) [Sov. J. Quantum Electron. 13, 1562 (1983)].

B. S. Wherrett, A. L. Smirl, T. F. Bogges, “Theory of degenerate four-wave mixing in picosecond excitation probe experiments,” IEEE J. Quantum Electron. QE-19, 680–690 (1983).
[CrossRef]

M. S. Stix, E. P. Ippen, “Pulse shaping in passively mode-locked ring dye lasers,” IEEE J. Quantum Electron. QE-19, 520 (1983).
[CrossRef]

1982

J. Herrmann, F. Weidner, “Theory of passively mode-locked cw dye lasers,” Appl. Phys. B 27, 105–113 (1982); J. Herrman, B. Wilhelmi, in Laser für Ultrakurze Lichtimpulse (Akademie-Verlag, Berlin, 1984), pp. 181–185.
[CrossRef]

1981

R. L. Fork, B. I. Greene, 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]

J.-C. Diels, W. C. Wang, H. Winful, “Dynamics of the nonlinear four-wave mixing interaction,” Appl. Phys. B 26, 105–110 (1981).
[CrossRef]

Y. Silberberg, I. Bar-Joseph, “Transient effects in degenerate four-wave mixing in saturable absorbers,” IEEE J. Quantum Electron. QE-17, 1967–1970 (1981).
[CrossRef]

1979

T. Yajima, Y. Taira, “Spatial optical parametric coupling of picosecond light pulses and transverse relaxation effect in resonant media,” J. Phys. Soc. Jpn. 47, 1620–1626 (1979).
[CrossRef]

A. von Jena, H. E. Lessing, “Coherent coupling effects in picosecond absorption experiments,” Appl. Phys. 19, 131–144 (1979); T. Yajima, H. Souma, Y. Ishida, “Study of ultra-fast relaxation processes by resonant Rayleigh-type optical mixing,” Phys. Rev. A 17, 324 (1978).
[CrossRef]

Bar-Joseph, I.

Y. Silberberg, I. Bar-Joseph, “Transient effects in degenerate four-wave mixing in saturable absorbers,” IEEE J. Quantum Electron. QE-17, 1967–1970 (1981).
[CrossRef]

Besnainou, S.

S. Besnainou, J.-C. Diels, J. Stone, “Molecular multiphoton excitation of phase coherent pulse pairs,” J. Chem. Phys. 81, 143–149 (1984).
[CrossRef]

Bogges, T. F.

B. S. Wherrett, A. L. Smirl, T. F. Bogges, “Theory of degenerate four-wave mixing in picosecond excitation probe experiments,” IEEE J. Quantum Electron. QE-19, 680–690 (1983).
[CrossRef]

Diels, J.-C.

J.-C. Diels, W. Dietel, J. J. Fontaine, W. Rudolph, B. Wilhelmi, “Analysis of a mode-locked ring laser: chirped-solitary-pulse solutions,” J. Opt. Soc. Am. B 2, 680–686 (1985).
[CrossRef]

S. Besnainou, J.-C. Diels, J. Stone, “Molecular multiphoton excitation of phase coherent pulse pairs,” J. Chem. Phys. 81, 143–149 (1984).
[CrossRef]

J.-C. Diels, I. C. McMichael, H. Vanherzeele, “Degenerate four wave mixing of picosecond pulses in the saturable amplification of a dye laser,” IEEE J. Quantum Electron. QE-20, 630–636 (1984).
[CrossRef]

J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. (Moscow) 10, 2398–2410 (1983) [Sov. J. Quantum Electron. 13, 1562 (1983)].

W. Dietel, J. J. Fontaine, J.-C. Diels, “Intracavity pulse compression with glass: a new method of generating pulses shorter than 60 femtoseconds,” Opt. Lett. 8, 4 (1983).
[CrossRef] [PubMed]

J. J. Fontaine, W. Dietel, J.-C. Diels, “Chirp in a mode-locked ring dye laser,” IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

J.-C. Diels, W. C. Wang, H. Winful, “Dynamics of the nonlinear four-wave mixing interaction,” Appl. Phys. B 26, 105–110 (1981).
[CrossRef]

J.-C. Diels, J. J. Fontaine, I. C. McMichael, F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt.24, 1270–1282 (1985); J.-C. Diels, W. Dietel, E. Dopel, J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, R. Torti, H. Vanherzeele, B. Wilhelmi, “Colliding pulse femtosecond lasers and applications to the measurement of optical parameters,” in Proceedings of the Fourth International Picosecond Conference, D. H. Auston, K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 30–34.
[CrossRef]

I. C. McMichael, J.-C. Diels, “Degenerate four wave mixing of femtosecond pulses in the saturable absorber of a ring dye laser,” presented at the XIIIth International Quantum Electronics Conference, Anaheim, Calif., June 1984.

J.-C. Diels, I. C. McMichael, J. Fontaine, C. Y. Wang, “Subpicosecond pulse shape measurement and modeling of a passively mode-locked dye laser including mutual interaction in a dye jet,” in Picosecond Phenomena III (Springer-Verlag, Berlin, 1982), pp. 116–119.
[CrossRef]

Dietel, W.

J.-C. Diels, W. Dietel, J. J. Fontaine, W. Rudolph, B. Wilhelmi, “Analysis of a mode-locked ring laser: chirped-solitary-pulse solutions,” J. Opt. Soc. Am. B 2, 680–686 (1985).
[CrossRef]

J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. (Moscow) 10, 2398–2410 (1983) [Sov. J. Quantum Electron. 13, 1562 (1983)].

W. Dietel, J. J. Fontaine, J.-C. Diels, “Intracavity pulse compression with glass: a new method of generating pulses shorter than 60 femtoseconds,” Opt. Lett. 8, 4 (1983).
[CrossRef] [PubMed]

J. J. Fontaine, W. Dietel, J.-C. Diels, “Chirp in a mode-locked ring dye laser,” IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

Fontaine, J.

J.-C. Diels, I. C. McMichael, J. Fontaine, C. Y. Wang, “Subpicosecond pulse shape measurement and modeling of a passively mode-locked dye laser including mutual interaction in a dye jet,” in Picosecond Phenomena III (Springer-Verlag, Berlin, 1982), pp. 116–119.
[CrossRef]

Fontaine, J. J.

J.-C. Diels, W. Dietel, J. J. Fontaine, W. Rudolph, B. Wilhelmi, “Analysis of a mode-locked ring laser: chirped-solitary-pulse solutions,” J. Opt. Soc. Am. B 2, 680–686 (1985).
[CrossRef]

J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. (Moscow) 10, 2398–2410 (1983) [Sov. J. Quantum Electron. 13, 1562 (1983)].

W. Dietel, J. J. Fontaine, J.-C. Diels, “Intracavity pulse compression with glass: a new method of generating pulses shorter than 60 femtoseconds,” Opt. Lett. 8, 4 (1983).
[CrossRef] [PubMed]

J. J. Fontaine, W. Dietel, J.-C. Diels, “Chirp in a mode-locked ring dye laser,” IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

J.-C. Diels, J. J. Fontaine, I. C. McMichael, F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt.24, 1270–1282 (1985); J.-C. Diels, W. Dietel, E. Dopel, J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, R. Torti, H. Vanherzeele, B. Wilhelmi, “Colliding pulse femtosecond lasers and applications to the measurement of optical parameters,” in Proceedings of the Fourth International Picosecond Conference, D. H. Auston, K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 30–34.
[CrossRef]

Fork, R. L.

R. L. Fork, B. I. Greene, 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]

Fujimoto, J. G.

Greene, B. I.

R. L. Fork, B. I. Greene, 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]

Herrmann, J.

J. Herrmann, F. Weidner, “Theory of passively mode-locked cw dye lasers,” Appl. Phys. B 27, 105–113 (1982); J. Herrman, B. Wilhelmi, in Laser für Ultrakurze Lichtimpulse (Akademie-Verlag, Berlin, 1984), pp. 181–185.
[CrossRef]

Ippen, E. P.

Ishida, Y.

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

Kuhlke, D.

J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. (Moscow) 10, 2398–2410 (1983) [Sov. J. Quantum Electron. 13, 1562 (1983)].

Lessing, H. E.

A. von Jena, H. E. Lessing, “Coherent coupling effects in picosecond absorption experiments,” Appl. Phys. 19, 131–144 (1979); T. Yajima, H. Souma, Y. Ishida, “Study of ultra-fast relaxation processes by resonant Rayleigh-type optical mixing,” Phys. Rev. A 17, 324 (1978).
[CrossRef]

McMichael, I. C.

J.-C. Diels, I. C. McMichael, H. Vanherzeele, “Degenerate four wave mixing of picosecond pulses in the saturable amplification of a dye laser,” IEEE J. Quantum Electron. QE-20, 630–636 (1984).
[CrossRef]

J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. (Moscow) 10, 2398–2410 (1983) [Sov. J. Quantum Electron. 13, 1562 (1983)].

J.-C. Diels, J. J. Fontaine, I. C. McMichael, F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt.24, 1270–1282 (1985); J.-C. Diels, W. Dietel, E. Dopel, J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, R. Torti, H. Vanherzeele, B. Wilhelmi, “Colliding pulse femtosecond lasers and applications to the measurement of optical parameters,” in Proceedings of the Fourth International Picosecond Conference, D. H. Auston, K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 30–34.
[CrossRef]

I. C. McMichael, J.-C. Diels, “Degenerate four wave mixing of femtosecond pulses in the saturable absorber of a ring dye laser,” presented at the XIIIth International Quantum Electronics Conference, Anaheim, Calif., June 1984.

J.-C. Diels, I. C. McMichael, J. Fontaine, C. Y. Wang, “Subpicosecond pulse shape measurement and modeling of a passively mode-locked dye laser including mutual interaction in a dye jet,” in Picosecond Phenomena III (Springer-Verlag, Berlin, 1982), pp. 116–119.
[CrossRef]

Menders, J. H.

J. H. Menders, “Development of a coherent subpicosecond pulse laser and the determination of dephasing times of dyes,” Ph.D. dissertation (Department of Physics, University of Southern California, Los Angeles, Calif., 1983) (unpublished).

Rentsch, S.

S. Rentsch, “Bestimmung von Lebensdauern und Transienten-absorptionsspektren von Polymethinfarbstoffen aus Pikosekundenspektroskopischen Messungen,” J. Signalaufzeichnungsmaterialien 12, 319–328 (1984); D. Khetshinashvili, S. Rentsch, B. Schroder, H. Wabnitz, “Picosecond absorption and fluorescence studies of DODCI,” presented at the IVth International Symposium on Ultrafast Phenomena in Spectroscopy, Reinhardsbrunn, German Democratic Republic, October 1985.

Rudolph, W.

J.-C. Diels, W. Dietel, J. J. Fontaine, W. Rudolph, B. Wilhelmi, “Analysis of a mode-locked ring laser: chirped-solitary-pulse solutions,” J. Opt. Soc. Am. B 2, 680–686 (1985).
[CrossRef]

J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. (Moscow) 10, 2398–2410 (1983) [Sov. J. Quantum Electron. 13, 1562 (1983)].

Shank, C. V.

R. L. Fork, B. I. Greene, 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]

Silberberg, Y.

Y. Silberberg, I. Bar-Joseph, “Transient effects in degenerate four-wave mixing in saturable absorbers,” IEEE J. Quantum Electron. QE-17, 1967–1970 (1981).
[CrossRef]

Simoni, F.

J.-C. Diels, J. J. Fontaine, I. C. McMichael, F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt.24, 1270–1282 (1985); J.-C. Diels, W. Dietel, E. Dopel, J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, R. Torti, H. Vanherzeele, B. Wilhelmi, “Colliding pulse femtosecond lasers and applications to the measurement of optical parameters,” in Proceedings of the Fourth International Picosecond Conference, D. H. Auston, K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 30–34.
[CrossRef]

Smirl, A. L.

B. S. Wherrett, A. L. Smirl, T. F. Bogges, “Theory of degenerate four-wave mixing in picosecond excitation probe experiments,” IEEE J. Quantum Electron. QE-19, 680–690 (1983).
[CrossRef]

Stix, M. S.

M. S. Stix, E. P. Ippen, “Pulse shaping in passively mode-locked ring dye lasers,” IEEE J. Quantum Electron. QE-19, 520 (1983).
[CrossRef]

Stone, J.

S. Besnainou, J.-C. Diels, J. Stone, “Molecular multiphoton excitation of phase coherent pulse pairs,” J. Chem. Phys. 81, 143–149 (1984).
[CrossRef]

Taira, Y.

T. Yajima, Y. Taira, “Spatial optical parametric coupling of picosecond light pulses and transverse relaxation effect in resonant media,” J. Phys. Soc. Jpn. 47, 1620–1626 (1979).
[CrossRef]

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

Vanherzeele, H.

J.-C. Diels, I. C. McMichael, H. Vanherzeele, “Degenerate four wave mixing of picosecond pulses in the saturable amplification of a dye laser,” IEEE J. Quantum Electron. QE-20, 630–636 (1984).
[CrossRef]

von Jena, A.

A. von Jena, H. E. Lessing, “Coherent coupling effects in picosecond absorption experiments,” Appl. Phys. 19, 131–144 (1979); T. Yajima, H. Souma, Y. Ishida, “Study of ultra-fast relaxation processes by resonant Rayleigh-type optical mixing,” Phys. Rev. A 17, 324 (1978).
[CrossRef]

Wang, C. Y.

J.-C. Diels, I. C. McMichael, J. Fontaine, C. Y. Wang, “Subpicosecond pulse shape measurement and modeling of a passively mode-locked dye laser including mutual interaction in a dye jet,” in Picosecond Phenomena III (Springer-Verlag, Berlin, 1982), pp. 116–119.
[CrossRef]

Wang, W. C.

J.-C. Diels, W. C. Wang, H. Winful, “Dynamics of the nonlinear four-wave mixing interaction,” Appl. Phys. B 26, 105–110 (1981).
[CrossRef]

Weidner, F.

J. Herrmann, F. Weidner, “Theory of passively mode-locked cw dye lasers,” Appl. Phys. B 27, 105–113 (1982); J. Herrman, B. Wilhelmi, in Laser für Ultrakurze Lichtimpulse (Akademie-Verlag, Berlin, 1984), pp. 181–185.
[CrossRef]

Weiner, A. M.

Wherrett, B. S.

B. S. Wherrett, A. L. Smirl, T. F. Bogges, “Theory of degenerate four-wave mixing in picosecond excitation probe experiments,” IEEE J. Quantum Electron. QE-19, 680–690 (1983).
[CrossRef]

Wilhelmi, B.

J.-C. Diels, W. Dietel, J. J. Fontaine, W. Rudolph, B. Wilhelmi, “Analysis of a mode-locked ring laser: chirped-solitary-pulse solutions,” J. Opt. Soc. Am. B 2, 680–686 (1985).
[CrossRef]

J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. (Moscow) 10, 2398–2410 (1983) [Sov. J. Quantum Electron. 13, 1562 (1983)].

Winful, H.

J.-C. Diels, W. C. Wang, H. Winful, “Dynamics of the nonlinear four-wave mixing interaction,” Appl. Phys. B 26, 105–110 (1981).
[CrossRef]

Yajima, T.

T. Yajima, Y. Taira, “Spatial optical parametric coupling of picosecond light pulses and transverse relaxation effect in resonant media,” J. Phys. Soc. Jpn. 47, 1620–1626 (1979).
[CrossRef]

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

Appl. Phys.

A. von Jena, H. E. Lessing, “Coherent coupling effects in picosecond absorption experiments,” Appl. Phys. 19, 131–144 (1979); T. Yajima, H. Souma, Y. Ishida, “Study of ultra-fast relaxation processes by resonant Rayleigh-type optical mixing,” Phys. Rev. A 17, 324 (1978).
[CrossRef]

Appl. Phys. B

J.-C. Diels, W. C. Wang, H. Winful, “Dynamics of the nonlinear four-wave mixing interaction,” Appl. Phys. B 26, 105–110 (1981).
[CrossRef]

J. Herrmann, F. Weidner, “Theory of passively mode-locked cw dye lasers,” Appl. Phys. B 27, 105–113 (1982); J. Herrman, B. Wilhelmi, in Laser für Ultrakurze Lichtimpulse (Akademie-Verlag, Berlin, 1984), pp. 181–185.
[CrossRef]

Appl. Phys. Lett.

R. L. Fork, B. I. Greene, 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]

IEEE J. Quantum Electron.

Y. Silberberg, I. Bar-Joseph, “Transient effects in degenerate four-wave mixing in saturable absorbers,” IEEE J. Quantum Electron. QE-17, 1967–1970 (1981).
[CrossRef]

B. S. Wherrett, A. L. Smirl, T. F. Bogges, “Theory of degenerate four-wave mixing in picosecond excitation probe experiments,” IEEE J. Quantum Electron. QE-19, 680–690 (1983).
[CrossRef]

J. J. Fontaine, W. Dietel, J.-C. Diels, “Chirp in a mode-locked ring dye laser,” IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

M. S. Stix, E. P. Ippen, “Pulse shaping in passively mode-locked ring dye lasers,” IEEE J. Quantum Electron. QE-19, 520 (1983).
[CrossRef]

J.-C. Diels, I. C. McMichael, H. Vanherzeele, “Degenerate four wave mixing of picosecond pulses in the saturable amplification of a dye laser,” IEEE J. Quantum Electron. QE-20, 630–636 (1984).
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S. Besnainou, J.-C. Diels, J. Stone, “Molecular multiphoton excitation of phase coherent pulse pairs,” J. Chem. Phys. 81, 143–149 (1984).
[CrossRef]

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J. Phys. Soc. Jpn.

T. Yajima, Y. Taira, “Spatial optical parametric coupling of picosecond light pulses and transverse relaxation effect in resonant media,” J. Phys. Soc. Jpn. 47, 1620–1626 (1979).
[CrossRef]

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S. Rentsch, “Bestimmung von Lebensdauern und Transienten-absorptionsspektren von Polymethinfarbstoffen aus Pikosekundenspektroskopischen Messungen,” J. Signalaufzeichnungsmaterialien 12, 319–328 (1984); D. Khetshinashvili, S. Rentsch, B. Schroder, H. Wabnitz, “Picosecond absorption and fluorescence studies of DODCI,” presented at the IVth International Symposium on Ultrafast Phenomena in Spectroscopy, Reinhardsbrunn, German Democratic Republic, October 1985.

Kvantovaya Elektron. (Moscow)

J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. (Moscow) 10, 2398–2410 (1983) [Sov. J. Quantum Electron. 13, 1562 (1983)].

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Other

J.-C. Diels, I. C. McMichael, J. Fontaine, C. Y. Wang, “Subpicosecond pulse shape measurement and modeling of a passively mode-locked dye laser including mutual interaction in a dye jet,” in Picosecond Phenomena III (Springer-Verlag, Berlin, 1982), pp. 116–119.
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I. C. McMichael, J.-C. Diels, “Degenerate four wave mixing of femtosecond pulses in the saturable absorber of a ring dye laser,” presented at the XIIIth International Quantum Electronics Conference, Anaheim, Calif., June 1984.

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[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Sketch of the DFWM geometry. The probe pulse is shown first traversing the dye jet, inducing a polarization in the medium, which subsides for a time T2. Two intracavity pump pulses collide subsequently in the medium, each of them forming a grating with the induced polarization on which the other scatters to form the DFWM signal. The rise time of the signal versus delay is directly related to the phase relaxation time T2.

Fig. 2
Fig. 2

Experimental setup for the measurement of DFWM signal versus delay.

Fig. 3
Fig. 3

Determination of the pulse shape and chirp. The fitting of the experimental recordings (crosses) of (a) the pulse intensity autocorrelation, (b) the pulse spectrum, and (c) the interferometric autocorrelation with the corresponding calculated functions (solid lines) is shown. The pulse shape corresponding to the solid lines is indicated in the upper right-hand side of the figure. The delays are normalized to the FWHM of the intensity autocorrelation.

Fig. 4
Fig. 4

DFWM signal versus delay for the probe polarized perpendicular to the polarization of the pump beams.

Fig. 5
Fig. 5

Calculated DFWM signal versus delay for two values of the phase relaxation time T2 = τp, and T2 = 0.1τp. The dashed line pertains to pure homogeneous broadening. The solid lines correspond to the case of infinite inhomogeneous broadening. In the case of τp = T2, the dashed and solid lines are superimposed. The calculations were performed for unchirped sech pulses E(t) = sech(t/τ) of duration (FWHM) τp = 1.76τ.

Fig. 6
Fig. 6

Width (FWHM) of the DFWM signal versus delay as a function of the phase relaxation time T2 for linearly chirped sech pulses. The electric field of the probe and pump pulses is proportional to exp[−ic(t/τ)2] sech(t/τ) of duration (FWHM) τp = 1.76τ.

Fig. 7
Fig. 7

Calculated DFWM signal versus delay (solid line) for the pulse shape determined experimentally [Eq. (1)] assuming a homogeneously broadened absorber with T2 = 0.1τp = 7.6 fsec. The unit delay is the FWHM of the intensity autocorrelation. The crosses are the experimental values of the DFWM versus delay.

Fig. 8
Fig. 8

Sketch illustrating the mechanism of two-photon-resonant DFWM. Two intracavity pump pulses collide when they first enter the medium, inducing a two-photon excitation in the medium (off-diagonal element of the density matrix oscillating at the frequency 2ω). If the delayed probe enters the medium within the decay time T2 of the off-diagonal element of the density matrix, a DFWM signal is generated by two-photon stimulated emission. The decay of the DFWM signal versus delay is directly related to the phase relaxation time T2 of the two-photon excitation.

Fig. 9
Fig. 9

Calculated DFWM signal versus delay (solid line) for the pulse shape determined experimentally [Eq. (1)], assuming a homogeneously broadened two-photon absorber with T2 = 2τp/3. The unit delay is the FWHM of the intensity autocorrelation. The crosses are the experimental values of the DFWM versus delay.

Equations (43)

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E ( t ) = exp [ - 0.15 i ( t / τ ) 2 ] exp ( - t / τ R ) + exp ( t / τ F ) ,
( t + i Δ ω + 1 / T 2 ) Q = - E W ,
[ t W + ( W - S ) / T 3 ] = Re [ Q * E ] .
S = g ( ω 0 ) W ( ω 0 ) d ω 0 .
E z = - Q ( ω 0 ) g ( ω 0 ) d ω 0 .
E = 2 E 1 cos ( k z ) + E 3 exp ( - i q r ) + E 4 exp ( i q r ) ,
W = W 0 + 2 W 1 cos ( 2 k z ) + [ W 3 exp ( - i q r ) + W 3 * exp ( i q r ) ] cos ( k z ) .
[ t + i Δ ω + 1 / T 2 ] Q 1 = - E 1 [ W 0 + W 1 ] ,
[ t + i Δ ω + 1 / T 2 ] Q 3 = - E 3 W 0 - E 1 W 3 ,
[ t + i Δ ω + 1 / T 2 ] Q 4 = - E 1 W 3 * ,
W ˙ 0 + ( W 0 - S 0 ) / T 3 = 2 Re [ E 1 Q 1 * ] ,
W ˙ 1 + ( W 1 - S 1 ) / T 3 = Re [ E 1 Q 1 * ] ,
W ˙ 3 + ( W 3 - S 3 ) / T 3 = Q 1 * E 3 + E 1 * Q 3 .
E 1 = exp [ - i c ( t / τ ) 2 ] sech ( t / τ ) .
G 1 ( τ ) = - J ( δ ) G ( τ + δ ) d S ,
F 1 ( τ D ) = - J ( δ ) F ( τ D , δ ) d δ .
Q = E 1 2 - Q / T 2 .
E 4 = α 4 E 1 * ( t - τ d ) Q .
R T 2 2 2 Δ ω 1 2 { Δ ω 1 2 + ( 1 T 1 2 ) 2 } 2 [ Δ ω 1 T 2 2 ] 2 .
[ t + i Δ ω + 1 / T 2 ] Q 1 = - E 1 W 0 ,
[ t + i Δ ω + 1 / T 2 ] Q 3 = - E 3 W 0 ,
[ t + i Δ ω + 1 / T 2 ] Q 4 = - E 1 W 3 * ,
W ˙ 3 = Q 1 E 3 * + E 1 Q 3 .
Q 4 = E 1 - t E 1 E 3 * W 0 Δ ω 2 + 1 / T 2 2 d t .
Q 4 E 1 - t E 1 E 3 * d t ,
Q 4 W 0 exp { [ ( 1 / T 2 ) - i Δ ω ] τ d } exp { - [ 1 / T 2 ) + i Δ ω ] t } ,             τ d < 0 < t .
W 0 exp [ - ( Δ ω T 2 * ) 2 ] .
Q 4 exp [ ( - t + τ d ) / T 2 ] exp { [ ( t + τ d ) / 2 T 2 * ] 2 } .
Q 4 exp ( 2 τ d / T 2 ) δ ( t + τ d ) ,             τ d < 0 < t .
Q 4 2 d t exp ( 4 τ d / T 2 ) ,             τ d < 0.
d c k d t = i ω k c k + j μ k j E sin ( ω t ) c j ,
c ˙ 0 = - E 01 * c 1 ,
c ˙ 1 = E 01 c 0 + i Δ ω 1 c 1 - E 12 * c 2 ,
c ˙ 2 = E 12 c 1 + i Δ ω 2 c 2 ,
Q ˙ = i Δ ω 1 Q - W E - Q / T 1 2 ,
W ˙ = Re ( Q E * ) .
Q 4 E 1 E 2 E 3 * τ Δ ω 1 2 + ( 1 T 1 2 ) 2 ,
E 4 2 E 1 E 2 E 3 2 1 [ Δ ω 1 2 + ( 1 T 1 2 ) 2 ] 2 .
c 1 i Δ ω 1 [ E 1 c 0 - E 2 * c 2 ] .
Q ˙ = ( i Δ 2 - 1 T 2 2 ) Q - E 01 E 12 Δ ω 1 W ,
W ˙ = 4 Re [ E 01 E 12 Δ ω 1 Q * ] ,
Q - T 2 2 Δ ω 1 ( E 1 E 2 ) .
E 4 2 = Q E 3 * 2 = E 1 E 2 E 3 2 [ T 2 2 Δ ω 1 ] 2 .

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