Abstract

We show that in order to describe completely the coherent coupling between the pump and probe pulses in a pump– probe measurement of transient absorption, the influence of induced phase gratings must be included. The importance of phase gratings is demonstrated experimentally for the case of a bleachable dye and analyzed in terms of transient four-wave mixing. These results are relevant to the interpretation of pump–probe measurements on all time scales performed with pulses from a single laser, particularly when the pulse duration is comparable with the material response time.

© 1985 Optical Society of America

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References

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  1. E. P. Ippen, C. V. Shank, in Ultrashort Light Pulses, S. L. Shapiro, ed., Vol. 18 of Topics in Applied Physics (Springer-Verlag, Berlin, 1977), p. 83.
    [CrossRef]
  2. Z. Vardeny, J. Tauc, “Picosecond coherence coupling in the pump and probe technique,” Opt. Commun. 39, 396 (1981).
    [CrossRef]
  3. B. S. Wherrett, A. L. Smirl, T. F. Boggess, “Theory of degenerate four-wave mixing in picosecond excitation-probe experiments,” IEEE J. Quantum Electron. QE-19, 680 (1983), and references therein.
    [CrossRef]
  4. T. F. Heinz, S. L. Palfrey, K. B. Eisenthal, “Coherent coupling effects in pump–probe measurements with collinear, copropagating beams,” Opt. Lett. 9, 359 (1984).
    [CrossRef] [PubMed]
  5. Rigorously speaking, as is clear below, phase and amplitude gratings are associated with variations in the real and imaginary parts of the susceptibility.
  6. It should be mentioned that contributions to the coherent signal from a phase grating have been noted previously [C. V. Shank and D. H. Auston, “Parametric coupling in an optically excited plasma in Ge,” Phys. Rev. Lett. 34, 479 (1975)]. The effect that they discuss, however, depends quadratically on the induced nonlinear polarization. This is a higher-order contribution than the interference between the nonlinear polarization and the probe considered here.
  7. We neglect in this discussion the off-resonant contribution to the nonlinear susceptibility. Since this term is real and corresponds to an instantaneous response, it will not affect the signal considered here.
  8. This analysis can be extended in a straightforward fashion to the case of optically thick samples by integrating the wave equation. See, for example, the treatment in Ref. 3.
  9. H. Nakatsuka, D. Grischkowsky, A. C. Balant, “Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion,” Phys. Rev. Lett. 47, 910 (1981).
    [CrossRef]
  10. A. J. Taylor, D. J. Erskine, C. L. Tang, “Equal-pulse correlation technique for measuring femtosecond excited state relaxation times,” Appl. Phys. Lett. 43, 989 (1983).
    [CrossRef]
  11. J-L. Oudar, “Coherent phenomena involved in the time-resolved optical Kerr effect,” IEEE J. Quantum Electron. QE-19, 713 (1983).
    [CrossRef]

1984 (1)

1983 (3)

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

A. J. Taylor, D. J. Erskine, C. L. Tang, “Equal-pulse correlation technique for measuring femtosecond excited state relaxation times,” Appl. Phys. Lett. 43, 989 (1983).
[CrossRef]

J-L. Oudar, “Coherent phenomena involved in the time-resolved optical Kerr effect,” IEEE J. Quantum Electron. QE-19, 713 (1983).
[CrossRef]

1981 (2)

Z. Vardeny, J. Tauc, “Picosecond coherence coupling in the pump and probe technique,” Opt. Commun. 39, 396 (1981).
[CrossRef]

H. Nakatsuka, D. Grischkowsky, A. C. Balant, “Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion,” Phys. Rev. Lett. 47, 910 (1981).
[CrossRef]

Balant, A. C.

H. Nakatsuka, D. Grischkowsky, A. C. Balant, “Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion,” Phys. Rev. Lett. 47, 910 (1981).
[CrossRef]

Boggess, T. F.

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

Eisenthal, K. B.

Erskine, D. J.

A. J. Taylor, D. J. Erskine, C. L. Tang, “Equal-pulse correlation technique for measuring femtosecond excited state relaxation times,” Appl. Phys. Lett. 43, 989 (1983).
[CrossRef]

Grischkowsky, D.

H. Nakatsuka, D. Grischkowsky, A. C. Balant, “Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion,” Phys. Rev. Lett. 47, 910 (1981).
[CrossRef]

Heinz, T. F.

Ippen, E. P.

E. P. Ippen, C. V. Shank, in Ultrashort Light Pulses, S. L. Shapiro, ed., Vol. 18 of Topics in Applied Physics (Springer-Verlag, Berlin, 1977), p. 83.
[CrossRef]

Nakatsuka, H.

H. Nakatsuka, D. Grischkowsky, A. C. Balant, “Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion,” Phys. Rev. Lett. 47, 910 (1981).
[CrossRef]

Oudar, J-L.

J-L. Oudar, “Coherent phenomena involved in the time-resolved optical Kerr effect,” IEEE J. Quantum Electron. QE-19, 713 (1983).
[CrossRef]

Palfrey, S. L.

Shank, C. V.

E. P. Ippen, C. V. Shank, in Ultrashort Light Pulses, S. L. Shapiro, ed., Vol. 18 of Topics in Applied Physics (Springer-Verlag, Berlin, 1977), p. 83.
[CrossRef]

Smirl, A. L.

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

Tang, C. L.

A. J. Taylor, D. J. Erskine, C. L. Tang, “Equal-pulse correlation technique for measuring femtosecond excited state relaxation times,” Appl. Phys. Lett. 43, 989 (1983).
[CrossRef]

Tauc, J.

Z. Vardeny, J. Tauc, “Picosecond coherence coupling in the pump and probe technique,” Opt. Commun. 39, 396 (1981).
[CrossRef]

Taylor, A. J.

A. J. Taylor, D. J. Erskine, C. L. Tang, “Equal-pulse correlation technique for measuring femtosecond excited state relaxation times,” Appl. Phys. Lett. 43, 989 (1983).
[CrossRef]

Vardeny, Z.

Z. Vardeny, J. Tauc, “Picosecond coherence coupling in the pump and probe technique,” Opt. Commun. 39, 396 (1981).
[CrossRef]

Wherrett, B. S.

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

Appl. Phys. Lett. (1)

A. J. Taylor, D. J. Erskine, C. L. Tang, “Equal-pulse correlation technique for measuring femtosecond excited state relaxation times,” Appl. Phys. Lett. 43, 989 (1983).
[CrossRef]

IEEE J. Quantum Electron. (2)

J-L. Oudar, “Coherent phenomena involved in the time-resolved optical Kerr effect,” IEEE J. Quantum Electron. QE-19, 713 (1983).
[CrossRef]

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

Opt. Commun. (1)

Z. Vardeny, J. Tauc, “Picosecond coherence coupling in the pump and probe technique,” Opt. Commun. 39, 396 (1981).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

H. Nakatsuka, D. Grischkowsky, A. C. Balant, “Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion,” Phys. Rev. Lett. 47, 910 (1981).
[CrossRef]

Other (5)

Rigorously speaking, as is clear below, phase and amplitude gratings are associated with variations in the real and imaginary parts of the susceptibility.

It should be mentioned that contributions to the coherent signal from a phase grating have been noted previously [C. V. Shank and D. H. Auston, “Parametric coupling in an optically excited plasma in Ge,” Phys. Rev. Lett. 34, 479 (1975)]. The effect that they discuss, however, depends quadratically on the induced nonlinear polarization. This is a higher-order contribution than the interference between the nonlinear polarization and the probe considered here.

We neglect in this discussion the off-resonant contribution to the nonlinear susceptibility. Since this term is real and corresponds to an instantaneous response, it will not affect the signal considered here.

This analysis can be extended in a straightforward fashion to the case of optically thick samples by integrating the wave equation. See, for example, the treatment in Ref. 3.

E. P. Ippen, C. V. Shank, in Ultrashort Light Pulses, S. L. Shapiro, ed., Vol. 18 of Topics in Applied Physics (Springer-Verlag, Berlin, 1977), p. 83.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Probe transmission in Nile blue for nearly transform-limited pulses taken at (a) 625 nm and (b) 585 nm; (c) and (d) show the data corresponding to (a) and (b) after subtracting the incoherent signal as well as the results of the theoretical fits (solid lines).

Fig. 2
Fig. 2

Same as Fig. 1, but with pulses spectrally broadened in an optical fiber.

Fig. 3
Fig. 3

Four-level model of the Nile blue energy-level structure.

Equations (9)

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P i ( 3 ) ( t ) = E j ( t ) d t E k * ( t ) E l ( t ) [ A i j k l ( t t ) + i A i j k l ( t t ) ] .
S = Im { E 2 * ( t ) E 1 ( t ) E 1 * ( t ) E 2 ( t ) × [ A x x x x ( t t ) + i A x x x x ( t t ) ] d t d t + E 2 * ( t ) E 2 ( t ) E 1 * ( t ) E 1 ( t ) × [ A x x x x ( t t ) + i A x x x x ( t t ) ] d t d t }
E 1 ( t ) = E ( t )
E 2 ( t ) = E ( t τ ) e i ω τ .
S ( τ ) = γ ( τ ) + β 1 ( τ ) β 2 ( τ ) ,
γ ( τ ) = | E ( t τ ) | 2 | E ( t ) | 2 A x x x x ( t t ) d t d t ,
β 1 ( τ ) = Re { E * ( t τ ) E ( t ) E * ( t ) × E ( t τ ) A x x x x ( t t ) d t d t } ,
β 2 ( τ ) = Im { E * ( t τ ) E ( t ) E * ( t ) × E ( t τ ) A x x x x ( t t ) d t d t } .
χ ( 3 ) ( A ω ω a + i Γ a + B ω ω b + i Γ b ) Δ N ,

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