Abstract

We have studied the influence of coherent coupling on the transient spectra observed in optical pump–probe spectroscopy. If the pump and probe pulses have temporal overlap, a strong increase of the pump–probe signal occurs at probe frequencies close to the pump frequency. This leads to sharp peaks in the transient spectra, which might erroneously be interpreted as spectral holes. We derive an explicit expression for both the delay dependence and the probe-frequency dependence of the pump–probe signal for the case of a homogeneously broadened absorption band. As an illustration, we use this expression to estimate the effect of coherent coupling on vibrational pump–probe spectroscopy on the OH stretch band of hydrogen-bonded systems.

© 2000 Optical Society of America

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References

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  1. H. J. Eichler, P. Günter, and D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1986).
  2. A. von Jena and H. E. Lessing, “Coherent coupling effects in picosecond absorption experiments,” Appl. Phys. 19, 131–144 (1979).
    [CrossRef]
  3. Z. Vardeny and J. Tauc, “Picosecond coherence coupling in the pump and probe technique,” Opt. Commun. 39, 396–400 (1981).
    [CrossRef]
  4. B. S. Wherrett, A. L. Smirl, and T. F. Boggess, “Theory of degenerate four-wave mixing in picosecond excitation–probe experiments,” IEEE J. Quantum Electron. 19, 680–690 (1983).
    [CrossRef]
  5. R. W. Boyd and S. Mukamel, “Origin of spectral holes in pump–probe studies of homogeneously broadened lines,” Phys. Rev. A 29, 1973–1983 (1983).
    [CrossRef]
  6. C. H. Brito Cruz, J. P. Gordon, P. C. Becker, R. L. Fork, and C. V. Shank, “Dynamics of spectral hole burning,” IEEE J. Quantum Electron. 24, 261–266 (1988).
    [CrossRef]
  7. H. A. Ferwerda, J. Terpstra, and D. A. Wiersma, “Discussion of a ‘coherent artifact’ in four-wave mixing experiments,” J. Chem. Phys. 91, 3296–3305 (1989).
    [CrossRef]
  8. E. Gaižauskas and L. Valkūnas, “Coherent transients of pump–probe spectroscopy in two-level approximation,” Opt. Commun. 109, 75–80 (1994).
    [CrossRef]
  9. S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford Univ. Press, Oxford, UK, 1995).
  10. M. Bonn, S. Woutersen, and H. J. Bakker, “Coherent picosecond vibron polaritons as probes of vibrational lifetimes,” Opt. Commun. 147, 138–142 (1998).
    [CrossRef]
  11. R. Laenen and C. Rauscher, “Numerical study of induced polarization dynamics in ultrafast spectral hole-burning experiments,” Chem. Phys. 230, 223–236 (1998).
    [CrossRef]
  12. R. Laenen, C. Rauscher, and A. Laubereau, “Transient hole burning in the infrared in an ethanol solution,” J. Phys. Chem. A 101, 3201–3206 (1997).
    [CrossRef]
  13. S. Woutersen, U. Emmerichs, and H. J. Bakker, “A femtosecond mid-infrared pump–probe study of hydrogen-bonding in ethanol,” J. Chem. Phys. 107, 1483–1490 (1997).
    [CrossRef]
  14. R. Laenen, C. Rauscher, and A. Laubereau, “Vibrational energy redistribution of ethanol oligomers and dissociation of hydrogen bonds after ultrafast infrared excitation,” Chem. Phys. Lett. 283, 7–14 (1998).
    [CrossRef]
  15. R. Laenen, C. Rauscher, and A. Laubereau, “Dynamics of local substructures in water observed by ultrafast infrared hole burning,” Phys. Rev. Lett. 80, 2622–2625 (1998).
    [CrossRef]
  16. S. Woutersen, U. Emmerichs, H.-K. Nienhuys, and H. J. Bakker, “Anomalous temperature dependence of vibrational lifetimes in water and ice,” Phys. Rev. Lett. 81, 1106–1109 (1998).
    [CrossRef]
  17. G. M. Gale, G. Gallot, F. Hache, N. Lascoux, S. Bratos, and J.-C. Leicknam, “Femtosecond dynamics of hydrogen bonds in liquid water: a real time study,” Phys. Rev. Lett. 82, 1068–1071 (1999).
    [CrossRef]
  18. H. R. Wyss and M. Falk, “Infrared spectra of HDO in water and in NaCl solution,” Can. J. Chem. 48, 607–614 (1970).
    [CrossRef]
  19. H. Graener, G. Seifert, and A. Laubereau, “New spectroscopy of water using tunable picosecond pulses in the infrared,” Phys. Rev. Lett. 66, 2092–2095 (1991).
    [CrossRef] [PubMed]

1999 (1)

G. M. Gale, G. Gallot, F. Hache, N. Lascoux, S. Bratos, and J.-C. Leicknam, “Femtosecond dynamics of hydrogen bonds in liquid water: a real time study,” Phys. Rev. Lett. 82, 1068–1071 (1999).
[CrossRef]

1998 (5)

R. Laenen, C. Rauscher, and A. Laubereau, “Vibrational energy redistribution of ethanol oligomers and dissociation of hydrogen bonds after ultrafast infrared excitation,” Chem. Phys. Lett. 283, 7–14 (1998).
[CrossRef]

R. Laenen, C. Rauscher, and A. Laubereau, “Dynamics of local substructures in water observed by ultrafast infrared hole burning,” Phys. Rev. Lett. 80, 2622–2625 (1998).
[CrossRef]

S. Woutersen, U. Emmerichs, H.-K. Nienhuys, and H. J. Bakker, “Anomalous temperature dependence of vibrational lifetimes in water and ice,” Phys. Rev. Lett. 81, 1106–1109 (1998).
[CrossRef]

M. Bonn, S. Woutersen, and H. J. Bakker, “Coherent picosecond vibron polaritons as probes of vibrational lifetimes,” Opt. Commun. 147, 138–142 (1998).
[CrossRef]

R. Laenen and C. Rauscher, “Numerical study of induced polarization dynamics in ultrafast spectral hole-burning experiments,” Chem. Phys. 230, 223–236 (1998).
[CrossRef]

1997 (2)

R. Laenen, C. Rauscher, and A. Laubereau, “Transient hole burning in the infrared in an ethanol solution,” J. Phys. Chem. A 101, 3201–3206 (1997).
[CrossRef]

S. Woutersen, U. Emmerichs, and H. J. Bakker, “A femtosecond mid-infrared pump–probe study of hydrogen-bonding in ethanol,” J. Chem. Phys. 107, 1483–1490 (1997).
[CrossRef]

1994 (1)

E. Gaižauskas and L. Valkūnas, “Coherent transients of pump–probe spectroscopy in two-level approximation,” Opt. Commun. 109, 75–80 (1994).
[CrossRef]

1991 (1)

H. Graener, G. Seifert, and A. Laubereau, “New spectroscopy of water using tunable picosecond pulses in the infrared,” Phys. Rev. Lett. 66, 2092–2095 (1991).
[CrossRef] [PubMed]

1989 (1)

H. A. Ferwerda, J. Terpstra, and D. A. Wiersma, “Discussion of a ‘coherent artifact’ in four-wave mixing experiments,” J. Chem. Phys. 91, 3296–3305 (1989).
[CrossRef]

1988 (1)

C. H. Brito Cruz, J. P. Gordon, P. C. Becker, R. L. Fork, and C. V. Shank, “Dynamics of spectral hole burning,” IEEE J. Quantum Electron. 24, 261–266 (1988).
[CrossRef]

1983 (2)

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

R. W. Boyd and S. Mukamel, “Origin of spectral holes in pump–probe studies of homogeneously broadened lines,” Phys. Rev. A 29, 1973–1983 (1983).
[CrossRef]

1981 (1)

Z. Vardeny and J. Tauc, “Picosecond coherence coupling in the pump and probe technique,” Opt. Commun. 39, 396–400 (1981).
[CrossRef]

1979 (1)

A. von Jena and H. E. Lessing, “Coherent coupling effects in picosecond absorption experiments,” Appl. Phys. 19, 131–144 (1979).
[CrossRef]

1970 (1)

H. R. Wyss and M. Falk, “Infrared spectra of HDO in water and in NaCl solution,” Can. J. Chem. 48, 607–614 (1970).
[CrossRef]

Bakker, H. J.

M. Bonn, S. Woutersen, and H. J. Bakker, “Coherent picosecond vibron polaritons as probes of vibrational lifetimes,” Opt. Commun. 147, 138–142 (1998).
[CrossRef]

S. Woutersen, U. Emmerichs, H.-K. Nienhuys, and H. J. Bakker, “Anomalous temperature dependence of vibrational lifetimes in water and ice,” Phys. Rev. Lett. 81, 1106–1109 (1998).
[CrossRef]

S. Woutersen, U. Emmerichs, and H. J. Bakker, “A femtosecond mid-infrared pump–probe study of hydrogen-bonding in ethanol,” J. Chem. Phys. 107, 1483–1490 (1997).
[CrossRef]

Becker, P. C.

C. H. Brito Cruz, J. P. Gordon, P. C. Becker, R. L. Fork, and C. V. Shank, “Dynamics of spectral hole burning,” IEEE J. Quantum Electron. 24, 261–266 (1988).
[CrossRef]

Boggess, T. F.

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

Bonn, M.

M. Bonn, S. Woutersen, and H. J. Bakker, “Coherent picosecond vibron polaritons as probes of vibrational lifetimes,” Opt. Commun. 147, 138–142 (1998).
[CrossRef]

Boyd, R. W.

R. W. Boyd and S. Mukamel, “Origin of spectral holes in pump–probe studies of homogeneously broadened lines,” Phys. Rev. A 29, 1973–1983 (1983).
[CrossRef]

Bratos, S.

G. M. Gale, G. Gallot, F. Hache, N. Lascoux, S. Bratos, and J.-C. Leicknam, “Femtosecond dynamics of hydrogen bonds in liquid water: a real time study,” Phys. Rev. Lett. 82, 1068–1071 (1999).
[CrossRef]

Brito Cruz, C. H.

C. H. Brito Cruz, J. P. Gordon, P. C. Becker, R. L. Fork, and C. V. Shank, “Dynamics of spectral hole burning,” IEEE J. Quantum Electron. 24, 261–266 (1988).
[CrossRef]

Emmerichs, U.

S. Woutersen, U. Emmerichs, H.-K. Nienhuys, and H. J. Bakker, “Anomalous temperature dependence of vibrational lifetimes in water and ice,” Phys. Rev. Lett. 81, 1106–1109 (1998).
[CrossRef]

S. Woutersen, U. Emmerichs, and H. J. Bakker, “A femtosecond mid-infrared pump–probe study of hydrogen-bonding in ethanol,” J. Chem. Phys. 107, 1483–1490 (1997).
[CrossRef]

Falk, M.

H. R. Wyss and M. Falk, “Infrared spectra of HDO in water and in NaCl solution,” Can. J. Chem. 48, 607–614 (1970).
[CrossRef]

Ferwerda, H. A.

H. A. Ferwerda, J. Terpstra, and D. A. Wiersma, “Discussion of a ‘coherent artifact’ in four-wave mixing experiments,” J. Chem. Phys. 91, 3296–3305 (1989).
[CrossRef]

Fork, R. L.

C. H. Brito Cruz, J. P. Gordon, P. C. Becker, R. L. Fork, and C. V. Shank, “Dynamics of spectral hole burning,” IEEE J. Quantum Electron. 24, 261–266 (1988).
[CrossRef]

Gaižauskas, E.

E. Gaižauskas and L. Valkūnas, “Coherent transients of pump–probe spectroscopy in two-level approximation,” Opt. Commun. 109, 75–80 (1994).
[CrossRef]

Gale, G. M.

G. M. Gale, G. Gallot, F. Hache, N. Lascoux, S. Bratos, and J.-C. Leicknam, “Femtosecond dynamics of hydrogen bonds in liquid water: a real time study,” Phys. Rev. Lett. 82, 1068–1071 (1999).
[CrossRef]

Gallot, G.

G. M. Gale, G. Gallot, F. Hache, N. Lascoux, S. Bratos, and J.-C. Leicknam, “Femtosecond dynamics of hydrogen bonds in liquid water: a real time study,” Phys. Rev. Lett. 82, 1068–1071 (1999).
[CrossRef]

Gordon, J. P.

C. H. Brito Cruz, J. P. Gordon, P. C. Becker, R. L. Fork, and C. V. Shank, “Dynamics of spectral hole burning,” IEEE J. Quantum Electron. 24, 261–266 (1988).
[CrossRef]

Graener, H.

H. Graener, G. Seifert, and A. Laubereau, “New spectroscopy of water using tunable picosecond pulses in the infrared,” Phys. Rev. Lett. 66, 2092–2095 (1991).
[CrossRef] [PubMed]

Hache, F.

G. M. Gale, G. Gallot, F. Hache, N. Lascoux, S. Bratos, and J.-C. Leicknam, “Femtosecond dynamics of hydrogen bonds in liquid water: a real time study,” Phys. Rev. Lett. 82, 1068–1071 (1999).
[CrossRef]

Laenen, R.

R. Laenen, C. Rauscher, and A. Laubereau, “Vibrational energy redistribution of ethanol oligomers and dissociation of hydrogen bonds after ultrafast infrared excitation,” Chem. Phys. Lett. 283, 7–14 (1998).
[CrossRef]

R. Laenen, C. Rauscher, and A. Laubereau, “Dynamics of local substructures in water observed by ultrafast infrared hole burning,” Phys. Rev. Lett. 80, 2622–2625 (1998).
[CrossRef]

R. Laenen and C. Rauscher, “Numerical study of induced polarization dynamics in ultrafast spectral hole-burning experiments,” Chem. Phys. 230, 223–236 (1998).
[CrossRef]

R. Laenen, C. Rauscher, and A. Laubereau, “Transient hole burning in the infrared in an ethanol solution,” J. Phys. Chem. A 101, 3201–3206 (1997).
[CrossRef]

Lascoux, N.

G. M. Gale, G. Gallot, F. Hache, N. Lascoux, S. Bratos, and J.-C. Leicknam, “Femtosecond dynamics of hydrogen bonds in liquid water: a real time study,” Phys. Rev. Lett. 82, 1068–1071 (1999).
[CrossRef]

Laubereau, A.

R. Laenen, C. Rauscher, and A. Laubereau, “Dynamics of local substructures in water observed by ultrafast infrared hole burning,” Phys. Rev. Lett. 80, 2622–2625 (1998).
[CrossRef]

R. Laenen, C. Rauscher, and A. Laubereau, “Vibrational energy redistribution of ethanol oligomers and dissociation of hydrogen bonds after ultrafast infrared excitation,” Chem. Phys. Lett. 283, 7–14 (1998).
[CrossRef]

R. Laenen, C. Rauscher, and A. Laubereau, “Transient hole burning in the infrared in an ethanol solution,” J. Phys. Chem. A 101, 3201–3206 (1997).
[CrossRef]

H. Graener, G. Seifert, and A. Laubereau, “New spectroscopy of water using tunable picosecond pulses in the infrared,” Phys. Rev. Lett. 66, 2092–2095 (1991).
[CrossRef] [PubMed]

Leicknam, J.-C.

G. M. Gale, G. Gallot, F. Hache, N. Lascoux, S. Bratos, and J.-C. Leicknam, “Femtosecond dynamics of hydrogen bonds in liquid water: a real time study,” Phys. Rev. Lett. 82, 1068–1071 (1999).
[CrossRef]

Lessing, H. E.

A. von Jena and H. E. Lessing, “Coherent coupling effects in picosecond absorption experiments,” Appl. Phys. 19, 131–144 (1979).
[CrossRef]

Mukamel, S.

R. W. Boyd and S. Mukamel, “Origin of spectral holes in pump–probe studies of homogeneously broadened lines,” Phys. Rev. A 29, 1973–1983 (1983).
[CrossRef]

Nienhuys, H.-K.

S. Woutersen, U. Emmerichs, H.-K. Nienhuys, and H. J. Bakker, “Anomalous temperature dependence of vibrational lifetimes in water and ice,” Phys. Rev. Lett. 81, 1106–1109 (1998).
[CrossRef]

Rauscher, C.

R. Laenen and C. Rauscher, “Numerical study of induced polarization dynamics in ultrafast spectral hole-burning experiments,” Chem. Phys. 230, 223–236 (1998).
[CrossRef]

R. Laenen, C. Rauscher, and A. Laubereau, “Vibrational energy redistribution of ethanol oligomers and dissociation of hydrogen bonds after ultrafast infrared excitation,” Chem. Phys. Lett. 283, 7–14 (1998).
[CrossRef]

R. Laenen, C. Rauscher, and A. Laubereau, “Dynamics of local substructures in water observed by ultrafast infrared hole burning,” Phys. Rev. Lett. 80, 2622–2625 (1998).
[CrossRef]

R. Laenen, C. Rauscher, and A. Laubereau, “Transient hole burning in the infrared in an ethanol solution,” J. Phys. Chem. A 101, 3201–3206 (1997).
[CrossRef]

Seifert, G.

H. Graener, G. Seifert, and A. Laubereau, “New spectroscopy of water using tunable picosecond pulses in the infrared,” Phys. Rev. Lett. 66, 2092–2095 (1991).
[CrossRef] [PubMed]

Shank, C. V.

C. H. Brito Cruz, J. P. Gordon, P. C. Becker, R. L. Fork, and C. V. Shank, “Dynamics of spectral hole burning,” IEEE J. Quantum Electron. 24, 261–266 (1988).
[CrossRef]

Smirl, A. L.

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

Tauc, J.

Z. Vardeny and J. Tauc, “Picosecond coherence coupling in the pump and probe technique,” Opt. Commun. 39, 396–400 (1981).
[CrossRef]

Terpstra, J.

H. A. Ferwerda, J. Terpstra, and D. A. Wiersma, “Discussion of a ‘coherent artifact’ in four-wave mixing experiments,” J. Chem. Phys. 91, 3296–3305 (1989).
[CrossRef]

Valkunas, L.

E. Gaižauskas and L. Valkūnas, “Coherent transients of pump–probe spectroscopy in two-level approximation,” Opt. Commun. 109, 75–80 (1994).
[CrossRef]

Vardeny, Z.

Z. Vardeny and J. Tauc, “Picosecond coherence coupling in the pump and probe technique,” Opt. Commun. 39, 396–400 (1981).
[CrossRef]

von Jena, A.

A. von Jena and H. E. Lessing, “Coherent coupling effects in picosecond absorption experiments,” Appl. Phys. 19, 131–144 (1979).
[CrossRef]

Wherrett, B. S.

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

Wiersma, D. A.

H. A. Ferwerda, J. Terpstra, and D. A. Wiersma, “Discussion of a ‘coherent artifact’ in four-wave mixing experiments,” J. Chem. Phys. 91, 3296–3305 (1989).
[CrossRef]

Woutersen, S.

M. Bonn, S. Woutersen, and H. J. Bakker, “Coherent picosecond vibron polaritons as probes of vibrational lifetimes,” Opt. Commun. 147, 138–142 (1998).
[CrossRef]

S. Woutersen, U. Emmerichs, H.-K. Nienhuys, and H. J. Bakker, “Anomalous temperature dependence of vibrational lifetimes in water and ice,” Phys. Rev. Lett. 81, 1106–1109 (1998).
[CrossRef]

S. Woutersen, U. Emmerichs, and H. J. Bakker, “A femtosecond mid-infrared pump–probe study of hydrogen-bonding in ethanol,” J. Chem. Phys. 107, 1483–1490 (1997).
[CrossRef]

Wyss, H. R.

H. R. Wyss and M. Falk, “Infrared spectra of HDO in water and in NaCl solution,” Can. J. Chem. 48, 607–614 (1970).
[CrossRef]

Appl. Phys. (1)

A. von Jena and H. E. Lessing, “Coherent coupling effects in picosecond absorption experiments,” Appl. Phys. 19, 131–144 (1979).
[CrossRef]

Can. J. Chem. (1)

H. R. Wyss and M. Falk, “Infrared spectra of HDO in water and in NaCl solution,” Can. J. Chem. 48, 607–614 (1970).
[CrossRef]

Chem. Phys. (1)

R. Laenen and C. Rauscher, “Numerical study of induced polarization dynamics in ultrafast spectral hole-burning experiments,” Chem. Phys. 230, 223–236 (1998).
[CrossRef]

Chem. Phys. Lett. (1)

R. Laenen, C. Rauscher, and A. Laubereau, “Vibrational energy redistribution of ethanol oligomers and dissociation of hydrogen bonds after ultrafast infrared excitation,” Chem. Phys. Lett. 283, 7–14 (1998).
[CrossRef]

IEEE J. Quantum Electron. (2)

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

C. H. Brito Cruz, J. P. Gordon, P. C. Becker, R. L. Fork, and C. V. Shank, “Dynamics of spectral hole burning,” IEEE J. Quantum Electron. 24, 261–266 (1988).
[CrossRef]

J. Chem. Phys. (2)

H. A. Ferwerda, J. Terpstra, and D. A. Wiersma, “Discussion of a ‘coherent artifact’ in four-wave mixing experiments,” J. Chem. Phys. 91, 3296–3305 (1989).
[CrossRef]

S. Woutersen, U. Emmerichs, and H. J. Bakker, “A femtosecond mid-infrared pump–probe study of hydrogen-bonding in ethanol,” J. Chem. Phys. 107, 1483–1490 (1997).
[CrossRef]

J. Phys. Chem. A (1)

R. Laenen, C. Rauscher, and A. Laubereau, “Transient hole burning in the infrared in an ethanol solution,” J. Phys. Chem. A 101, 3201–3206 (1997).
[CrossRef]

Opt. Commun. (3)

M. Bonn, S. Woutersen, and H. J. Bakker, “Coherent picosecond vibron polaritons as probes of vibrational lifetimes,” Opt. Commun. 147, 138–142 (1998).
[CrossRef]

E. Gaižauskas and L. Valkūnas, “Coherent transients of pump–probe spectroscopy in two-level approximation,” Opt. Commun. 109, 75–80 (1994).
[CrossRef]

Z. Vardeny and J. Tauc, “Picosecond coherence coupling in the pump and probe technique,” Opt. Commun. 39, 396–400 (1981).
[CrossRef]

Phys. Rev. A (1)

R. W. Boyd and S. Mukamel, “Origin of spectral holes in pump–probe studies of homogeneously broadened lines,” Phys. Rev. A 29, 1973–1983 (1983).
[CrossRef]

Phys. Rev. Lett. (4)

R. Laenen, C. Rauscher, and A. Laubereau, “Dynamics of local substructures in water observed by ultrafast infrared hole burning,” Phys. Rev. Lett. 80, 2622–2625 (1998).
[CrossRef]

S. Woutersen, U. Emmerichs, H.-K. Nienhuys, and H. J. Bakker, “Anomalous temperature dependence of vibrational lifetimes in water and ice,” Phys. Rev. Lett. 81, 1106–1109 (1998).
[CrossRef]

G. M. Gale, G. Gallot, F. Hache, N. Lascoux, S. Bratos, and J.-C. Leicknam, “Femtosecond dynamics of hydrogen bonds in liquid water: a real time study,” Phys. Rev. Lett. 82, 1068–1071 (1999).
[CrossRef]

H. Graener, G. Seifert, and A. Laubereau, “New spectroscopy of water using tunable picosecond pulses in the infrared,” Phys. Rev. Lett. 66, 2092–2095 (1991).
[CrossRef] [PubMed]

Other (2)

H. J. Eichler, P. Günter, and D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1986).

S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford Univ. Press, Oxford, UK, 1995).

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Figures (2)

Fig. 1
Fig. 1

Calculated transient spectra for delay values of (a) τ=-2 ps, (b) τ=0 ps, (c) τ=1 ps, and (d) τ=3 ps. The pump frequency is 3490 cm-1 (indicated by an arrow on the frequency axis). The FWHM’s of the power spectra of pump and probe are 7 and 15 cm-1, respectively, and the relaxation parameters are γ1=1.35 THz and γ2=23.6 THz. Note that the vertical axes have different scales.

Fig. 2
Fig. 2

Delay scans calculated from Eq. (15), with a pump frequency of 3410 cm-1 and probe frequencies of (a) 3410 cm-1 and (b) 3340 cm-1. The FWHM’s of the power spectra of pump and probe are 7 and 15 cm-1, respectively, and the relaxation parameters are γ1=1.35 THz and γ2=23.6 THz.

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

E(r, t)=12[E˜1(t)exp (ik1·r-iΩ1t)+E˜2(t-τ)exp (ik2·r-iΩ2t+iω2τ)]×exp(-iω0t)+c.c.,
Pkj(1)(r, t)=12P˜kj(1)(t)exp(ikj·r-iω0t)+c.c.,
Pkj(3)(r, t)=12P˜kj(3)(t)exp(ikj·r-iω0t)+c.c.,
dP˜k1(1)dt=iN|μ12|2E˜1(t)exp(-iΩ1t)-γ2P˜k1(1),
dP˜k2(1)dt=iN|μ12|2E˜2(t-τ)exp(-iΩ2t+iω2τ)-γ2P˜k2(1),
dn0(2)dt=i4N[E˜1(t)exp(-iΩ1t)P˜k1(1)*-E˜1*(t)exp(iΩ1t)P˜k1(1)]-γ1n0(2),
dnk2-k1(2)dt=i4N[E˜2(t-τ)exp(-iΩ2t+iω2τ)P˜k1(1)*-E˜1*(t)exp(iΩ1t)P˜k2(1)]-γ1nk2-k1(2),
dP˜k2(3)dt=-2iN|μ12|2[E˜1(t)exp(-iΩ1t)nk2-k1(2)+E˜2(t-τ)exp(-iΩ2t+iω2τ)n0(2)]-γ2P˜k2(3),
P˜k1(1)(t)=iN|μ12|2-tdtE˜1(t)×exp[-iΩ1t+γ2(t-t)].
P˜k1(1)(t)=iN|μ12|2E˜1(t)exp(-iΩ1t)γ2-iΩ1
P˜k2(1)(t)=iN|μ12|2E˜2(t-τ)exp(-iΩ2t+iω2τ)γ2-iΩ2.
P˜k2(3)(t)=-iN|μ12|431γ2-iΩ2
×exp(-iΩ2t+iω2τ)-0dt
×2γ2γ22+Ω12exp(γ1t)E˜2(t-τ)|E˜1(t+t)|2
+1γ2+iΩ1+1γ2-iΩ2
×exp[i(Ω1-Ω2)t+γ1t]
×E˜1(t)E˜1*(t+t)E˜2(t+t-τ),
S(Ω1, Ω2, τ)
=-Im-dtE˜2*(t-τ) exp(iΩ2t-iω2τ)P˜k2(3)(t)=N|μ12|432γ22(γ22+Ω12)(γ22+Ω22)×-0 dt exp(γ1t)-dt|E˜2(t-τ)|2|E˜1(t+t)|2+Re1γ2-iΩ21γ2+iΩ1+1γ2-iΩ2×-0dt exp[i(Ω1-Ω2)t+γ1t]×-dtE˜2*(t-τ)E˜1(t)E˜1*(t+t)×E˜2(t+t-τ).
E˜j(t)=exp(-djt2),
S(Ω1, Ω2, τ)
=πN|μ12|423γ22d1d2(γ22+Ω12)(γ22+Ω22)×expγ1γ1(d1+d2)-8d1d2τ8d1d2×1+erf4d2d1τ-γ1(d1+d2)22(d1+d2)d1d2+Re1(d1+d2)(γ2-iΩ2)1γ2+iΩ1+1γ2-iΩ2×exp[γ1+i(Ω1-Ω2)]2-4d1d2τ22(d1+d2)×1-erfγ1+i(Ω1-Ω2)2(d1+d2).

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