Abstract

We numerically calculate the transient-four-wave-mixing (TFWM) response in systems that exhibit either a resonance frequency or a dephasing rate that depends on the level of excitation, which can occur in semiconductors or a dense atomic vapor. These effects change the intensity dependence of the TFWM signal, causing it to display noncubic behavior for significantly lower pulse areas and even a reduction in signal intensity for increasing pulse area. They also qualitatively change both the temporal behavior and spectrum of the TFWM signal in ways that cannot adequately be described in perturbation theory. For time-integrated TFWM, the saturation behavior is also found to depend on the delay between pulses. For comparison, the effects of local fields are also calculated as they produce similar effects. These results can help provide discrimination among the various phenomena.

© 2003 Optical Society of America

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    [CrossRef] [PubMed]
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  26. A. Knorr, T. O¨streich, K. Scho¨nhammer, R. Binder, and S. W. Koch, “Asymptotic analytic solution for Rabi oscillations in a system of weakly coupled excitons,” Phys. Rev. B 49, 14024-14027 (1994).
    [CrossRef]
  27. S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, and H. Nickel, “Rabi flopping in semiconductors,” Phys. Rev. Lett. 73, 1178-1181 (1994).
    [CrossRef] [PubMed]
  28. M. D. Webb, S. T. Cundiff, and D. G. Steel, “Observation of time-resolved picosecond stimulated photon echoes and free polarization decay in GaAs/AlGaAs multiple quantum wells,” Phys. Rev. Lett. 66, 934-937 (1991).
    [CrossRef] [PubMed]
  29. D.-S. Kim, J. Shah, T. C. Damen, W. Scha¨fer, F. Jahnke, S. Schmitt-Rink, and K. Ko¨hler, “Unusually slow temporal evolution of femtosecond four-wave-mixing signals in intrinsic GaAs quantum wells: direct evidence for the dominance of interaction effects,” Phys. Rev. Lett. 69, 2725-2728 (1992).
    [CrossRef] [PubMed]
  30. S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, “Collective effects in excitonic free induction decay: do semiconductors and atoms emit coherent light in different ways?,” Phys. Rev. Lett. 69, 2685-2688 (1992).
    [CrossRef] [PubMed]
  31. M. Koch, J. Feldmann, G. von Plessen, E. O. Go¨bel, P. Thomas, and K. Ko¨hler, “Quantum beats versus polarization interference: an experimental distinction,” Phys. Rev. Lett. 69, 3631-3634 (1992).
    [CrossRef] [PubMed]
  32. V. G. Lyssenko, J. Erland, I. Balslev, K.-H. Pantke, B. S. Razbirin, and J. M. Hvam, “Nature of nonlinear four-wave-mixing beats in semiconductors,” Phys. Rev. B 48, 5720–5723 (1993).
    [CrossRef]

2002

S. T. Cundiff, “Time domain observation of the Lorentz-local field,” Laser Phys. 12, 1073-1078 (2002).

J. M. Shacklette and S. T. Cundiff, “Role of excitation induced shift in the coherent optical response of semiconductors,” Phys. Rev. B 66, 045309 (2002).
[CrossRef]

2001

S. T. Cundiff, J. M. Shacklette, and V. O. Lorenz, “Interaction effects in optically dense materials,” in Ultrafast Phenomena in Semiconductors V, H. Jiang, K. T. Tsen, J.-J. Song, eds., Proc. SPIE 4280, 138-148 (2001).
[CrossRef]

1999

D. A. Blank, L. J. Kaufman, and G. R. Fleming, “Fifth-order two-dimensional Raman spectra of CS2 are dominated by third-order cascades,” J. Chem. Phys. 111, 3105-3114 (1999).
[CrossRef]

1997

P. Wang, A. Gallagher, and J. Cooper, “Selective reflection by Rb,” Phys. Rev. A 56, 1598-1606 (1997).
[CrossRef]

A. L. Smirl, W. J. Walecki, X. Y. Chen, and O. Buccafusca,“Dynamics of the amplitude, phase and polarization state of coherent emission from quantum wells,” Phys. Status Solidi B 204, 16-19 (1997).
[CrossRef]

1996

K. Victor, V. M. Axt, G. Bartels, A. Stahl, K. Bott, and P. Thomas, “Microscopic foundation of the phenomenological few-level approach to coherent semiconductor optics,” Z. Phys. B 99, 197-205 (1996).
[CrossRef]

J. Guo, A. Gallagher, and J. Cooper, “Lorentz-Lorenz shift in an inhomogeneously broadened medium,” Opt. Commun. 131, 219-222 (1996).
[CrossRef]

J. Guo, J. Cooper, and A. Gallagher, “Selective reflection from a dense atomic vapor,” Phys. Rev. A 53, 1130-1138 (1996).
[CrossRef] [PubMed]

V. A. Sautenkov, H. van Kampen, E. R. Eliel, and J. P. Woerdman, “Dipole-dipole broadened line shape in a partially excited dense atomic gas,” Phys. Rev. Lett. 77, 3327-3330 (1996).
[CrossRef] [PubMed]

A. E. Paul, I. A. Bolger, A. L. Smirl, and J. G. Pellegrino, “Time-resolved measurements of the polarization state of four-wave mixing signals from GaAs multiple quantum wells,” J. Opt. Soc. Am. B 13, 1016-1025 (1996).
[CrossRef]

1994

A. Leitenstorfer, A. Lohner, K. Rick, P. Leisching, T. Elsaesser, T. Kuhn, F. Rossi, W. Stolz, and K. Ploog, “Excitonic and free-carrier polarizations of bulk GaAs studied by femtosecond coherent spectroscopy,” Phys. Rev. B 49, 16372-16380 (1994).
[CrossRef]

A. Knorr, T. O¨streich, K. Scho¨nhammer, R. Binder, and S. W. Koch, “Asymptotic analytic solution for Rabi oscillations in a system of weakly coupled excitons,” Phys. Rev. B 49, 14024-14027 (1994).
[CrossRef]

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, and H. Nickel, “Rabi flopping in semiconductors,” Phys. Rev. Lett. 73, 1178-1181 (1994).
[CrossRef] [PubMed]

Y. Z. Hu, R. Binder, S. W. Koch, S. T. Cundiff, H. Wang, and D. G. Steel, “Excitation and polarization effects in semiconductor four-wave-mixing spectroscopy,” Phys. Rev. B 49, 14382-14386 (1994).
[CrossRef]

H. Wang, K. B. Ferrio, D. G. Steel, P. R. Berman, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient four-wave-mixing line shapes: effects of excitation-induced dephasing,” Phys. Rev. A 49, R1551-R1554 (1994).
[CrossRef] [PubMed]

1993

K. Bott, O. Heller, D. Bennhardt, S. T. Cundiff, P. Thomas, E. J. Mayer, G. O. Smith, R. Eccleston, J. Kuhl, and K. Ploog, “Influence of exciton-exciton interactions on the coherent optical response in GaAs quantum wells,” Phys. Rev. B 48, 17418-17426 (1993).
[CrossRef]

H. Wang, K. Ferrio, D. G. Steel, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient nonlinear optical response from excitation induced dephasing in GaAs,” Phys. Rev. Lett. 71, 1261-1264 (1993).
[CrossRef] [PubMed]

V. G. Lyssenko, J. Erland, I. Balslev, K.-H. Pantke, B. S. Razbirin, and J. M. Hvam, “Nature of nonlinear four-wave-mixing beats in semiconductors,” Phys. Rev. B 48, 5720–5723 (1993).
[CrossRef]

1992

D.-S. Kim, J. Shah, T. C. Damen, W. Scha¨fer, F. Jahnke, S. Schmitt-Rink, and K. Ko¨hler, “Unusually slow temporal evolution of femtosecond four-wave-mixing signals in intrinsic GaAs quantum wells: direct evidence for the dominance of interaction effects,” Phys. Rev. Lett. 69, 2725-2728 (1992).
[CrossRef] [PubMed]

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, “Collective effects in excitonic free induction decay: do semiconductors and atoms emit coherent light in different ways?,” Phys. Rev. Lett. 69, 2685-2688 (1992).
[CrossRef] [PubMed]

M. Koch, J. Feldmann, G. von Plessen, E. O. Go¨bel, P. Thomas, and K. Ko¨hler, “Quantum beats versus polarization interference: an experimental distinction,” Phys. Rev. Lett. 69, 3631-3634 (1992).
[CrossRef] [PubMed]

A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, “Theoretical study of resonant ultrashort-pulse propagation in semiconductors,” Phys. Rev. A 46, 7179-7186 (1992).
[CrossRef] [PubMed]

1991

M. D. Webb, S. T. Cundiff, and D. G. Steel, “Observation of time-resolved picosecond stimulated photon echoes and free polarization decay in GaAs/AlGaAs multiple quantum wells,” Phys. Rev. Lett. 66, 934-937 (1991).
[CrossRef] [PubMed]

J. J. Maki, M. S. Malcuit, J. E. Sipe, and R. W. Boyd, “Linear and nonlinear optical measurements of the Lorentz local field,” Phys. Rev. Lett. 67, 972-975 (1991).
[CrossRef] [PubMed]

1990

M. Wegener, D. S. Chemla, S. Schmitt-Rink, and W. Scha¨fer, “Line shape of time-resolved four-wave mixing,” Phys. Rev. A 42, 5675-5683 (1990).
[CrossRef] [PubMed]

K. Leo, M. Wegener, J. Shah, D. S. Chemla, E. O. Go¨bel, T. C. Damen, S. Schmitt-Rink, and W. Scha¨fer, “Effects of coherent polarization interactions on time-resolved degenerate four-wave mixing,” Phys. Rev. Lett. 65, 1340-1343 (1990).
[CrossRef] [PubMed]

1979

T. Yajima and 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]

Axt, V. M.

K. Victor, V. M. Axt, G. Bartels, A. Stahl, K. Bott, and P. Thomas, “Microscopic foundation of the phenomenological few-level approach to coherent semiconductor optics,” Z. Phys. B 99, 197-205 (1996).
[CrossRef]

Balslev, I.

V. G. Lyssenko, J. Erland, I. Balslev, K.-H. Pantke, B. S. Razbirin, and J. M. Hvam, “Nature of nonlinear four-wave-mixing beats in semiconductors,” Phys. Rev. B 48, 5720–5723 (1993).
[CrossRef]

Bartels, G.

K. Victor, V. M. Axt, G. Bartels, A. Stahl, K. Bott, and P. Thomas, “Microscopic foundation of the phenomenological few-level approach to coherent semiconductor optics,” Z. Phys. B 99, 197-205 (1996).
[CrossRef]

Bennhardt, D.

K. Bott, O. Heller, D. Bennhardt, S. T. Cundiff, P. Thomas, E. J. Mayer, G. O. Smith, R. Eccleston, J. Kuhl, and K. Ploog, “Influence of exciton-exciton interactions on the coherent optical response in GaAs quantum wells,” Phys. Rev. B 48, 17418-17426 (1993).
[CrossRef]

Berman, P. R.

H. Wang, K. B. Ferrio, D. G. Steel, P. R. Berman, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient four-wave-mixing line shapes: effects of excitation-induced dephasing,” Phys. Rev. A 49, R1551-R1554 (1994).
[CrossRef] [PubMed]

Bigot, J.-Y.

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, “Collective effects in excitonic free induction decay: do semiconductors and atoms emit coherent light in different ways?,” Phys. Rev. Lett. 69, 2685-2688 (1992).
[CrossRef] [PubMed]

Binder, R.

A. Knorr, T. O¨streich, K. Scho¨nhammer, R. Binder, and S. W. Koch, “Asymptotic analytic solution for Rabi oscillations in a system of weakly coupled excitons,” Phys. Rev. B 49, 14024-14027 (1994).
[CrossRef]

Y. Z. Hu, R. Binder, S. W. Koch, S. T. Cundiff, H. Wang, and D. G. Steel, “Excitation and polarization effects in semiconductor four-wave-mixing spectroscopy,” Phys. Rev. B 49, 14382-14386 (1994).
[CrossRef]

H. Wang, K. B. Ferrio, D. G. Steel, P. R. Berman, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient four-wave-mixing line shapes: effects of excitation-induced dephasing,” Phys. Rev. A 49, R1551-R1554 (1994).
[CrossRef] [PubMed]

H. Wang, K. Ferrio, D. G. Steel, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient nonlinear optical response from excitation induced dephasing in GaAs,” Phys. Rev. Lett. 71, 1261-1264 (1993).
[CrossRef] [PubMed]

A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, “Theoretical study of resonant ultrashort-pulse propagation in semiconductors,” Phys. Rev. A 46, 7179-7186 (1992).
[CrossRef] [PubMed]

Blank, D. A.

D. A. Blank, L. J. Kaufman, and G. R. Fleming, “Fifth-order two-dimensional Raman spectra of CS2 are dominated by third-order cascades,” J. Chem. Phys. 111, 3105-3114 (1999).
[CrossRef]

Bolger, I. A.

Bott, K.

K. Victor, V. M. Axt, G. Bartels, A. Stahl, K. Bott, and P. Thomas, “Microscopic foundation of the phenomenological few-level approach to coherent semiconductor optics,” Z. Phys. B 99, 197-205 (1996).
[CrossRef]

K. Bott, O. Heller, D. Bennhardt, S. T. Cundiff, P. Thomas, E. J. Mayer, G. O. Smith, R. Eccleston, J. Kuhl, and K. Ploog, “Influence of exciton-exciton interactions on the coherent optical response in GaAs quantum wells,” Phys. Rev. B 48, 17418-17426 (1993).
[CrossRef]

Boyd, R. W.

J. J. Maki, M. S. Malcuit, J. E. Sipe, and R. W. Boyd, “Linear and nonlinear optical measurements of the Lorentz local field,” Phys. Rev. Lett. 67, 972-975 (1991).
[CrossRef] [PubMed]

Buccafusca, O.

A. L. Smirl, W. J. Walecki, X. Y. Chen, and O. Buccafusca,“Dynamics of the amplitude, phase and polarization state of coherent emission from quantum wells,” Phys. Status Solidi B 204, 16-19 (1997).
[CrossRef]

Chemla, D. S.

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, “Collective effects in excitonic free induction decay: do semiconductors and atoms emit coherent light in different ways?,” Phys. Rev. Lett. 69, 2685-2688 (1992).
[CrossRef] [PubMed]

K. Leo, M. Wegener, J. Shah, D. S. Chemla, E. O. Go¨bel, T. C. Damen, S. Schmitt-Rink, and W. Scha¨fer, “Effects of coherent polarization interactions on time-resolved degenerate four-wave mixing,” Phys. Rev. Lett. 65, 1340-1343 (1990).
[CrossRef] [PubMed]

M. Wegener, D. S. Chemla, S. Schmitt-Rink, and W. Scha¨fer, “Line shape of time-resolved four-wave mixing,” Phys. Rev. A 42, 5675-5683 (1990).
[CrossRef] [PubMed]

Chen, X. Y.

A. L. Smirl, W. J. Walecki, X. Y. Chen, and O. Buccafusca,“Dynamics of the amplitude, phase and polarization state of coherent emission from quantum wells,” Phys. Status Solidi B 204, 16-19 (1997).
[CrossRef]

Cooper, J.

P. Wang, A. Gallagher, and J. Cooper, “Selective reflection by Rb,” Phys. Rev. A 56, 1598-1606 (1997).
[CrossRef]

J. Guo, A. Gallagher, and J. Cooper, “Lorentz-Lorenz shift in an inhomogeneously broadened medium,” Opt. Commun. 131, 219-222 (1996).
[CrossRef]

J. Guo, J. Cooper, and A. Gallagher, “Selective reflection from a dense atomic vapor,” Phys. Rev. A 53, 1130-1138 (1996).
[CrossRef] [PubMed]

Cundiff, S. T.

S. T. Cundiff, “Time domain observation of the Lorentz-local field,” Laser Phys. 12, 1073-1078 (2002).

J. M. Shacklette and S. T. Cundiff, “Role of excitation induced shift in the coherent optical response of semiconductors,” Phys. Rev. B 66, 045309 (2002).
[CrossRef]

S. T. Cundiff, J. M. Shacklette, and V. O. Lorenz, “Interaction effects in optically dense materials,” in Ultrafast Phenomena in Semiconductors V, H. Jiang, K. T. Tsen, J.-J. Song, eds., Proc. SPIE 4280, 138-148 (2001).
[CrossRef]

Y. Z. Hu, R. Binder, S. W. Koch, S. T. Cundiff, H. Wang, and D. G. Steel, “Excitation and polarization effects in semiconductor four-wave-mixing spectroscopy,” Phys. Rev. B 49, 14382-14386 (1994).
[CrossRef]

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, and H. Nickel, “Rabi flopping in semiconductors,” Phys. Rev. Lett. 73, 1178-1181 (1994).
[CrossRef] [PubMed]

K. Bott, O. Heller, D. Bennhardt, S. T. Cundiff, P. Thomas, E. J. Mayer, G. O. Smith, R. Eccleston, J. Kuhl, and K. Ploog, “Influence of exciton-exciton interactions on the coherent optical response in GaAs quantum wells,” Phys. Rev. B 48, 17418-17426 (1993).
[CrossRef]

M. D. Webb, S. T. Cundiff, and D. G. Steel, “Observation of time-resolved picosecond stimulated photon echoes and free polarization decay in GaAs/AlGaAs multiple quantum wells,” Phys. Rev. Lett. 66, 934-937 (1991).
[CrossRef] [PubMed]

Damen, T. C.

D.-S. Kim, J. Shah, T. C. Damen, W. Scha¨fer, F. Jahnke, S. Schmitt-Rink, and K. Ko¨hler, “Unusually slow temporal evolution of femtosecond four-wave-mixing signals in intrinsic GaAs quantum wells: direct evidence for the dominance of interaction effects,” Phys. Rev. Lett. 69, 2725-2728 (1992).
[CrossRef] [PubMed]

K. Leo, M. Wegener, J. Shah, D. S. Chemla, E. O. Go¨bel, T. C. Damen, S. Schmitt-Rink, and W. Scha¨fer, “Effects of coherent polarization interactions on time-resolved degenerate four-wave mixing,” Phys. Rev. Lett. 65, 1340-1343 (1990).
[CrossRef] [PubMed]

Eccleston, R.

K. Bott, O. Heller, D. Bennhardt, S. T. Cundiff, P. Thomas, E. J. Mayer, G. O. Smith, R. Eccleston, J. Kuhl, and K. Ploog, “Influence of exciton-exciton interactions on the coherent optical response in GaAs quantum wells,” Phys. Rev. B 48, 17418-17426 (1993).
[CrossRef]

Eliel, E. R.

V. A. Sautenkov, H. van Kampen, E. R. Eliel, and J. P. Woerdman, “Dipole-dipole broadened line shape in a partially excited dense atomic gas,” Phys. Rev. Lett. 77, 3327-3330 (1996).
[CrossRef] [PubMed]

Elsaesser, T.

A. Leitenstorfer, A. Lohner, K. Rick, P. Leisching, T. Elsaesser, T. Kuhn, F. Rossi, W. Stolz, and K. Ploog, “Excitonic and free-carrier polarizations of bulk GaAs studied by femtosecond coherent spectroscopy,” Phys. Rev. B 49, 16372-16380 (1994).
[CrossRef]

Erland, J.

V. G. Lyssenko, J. Erland, I. Balslev, K.-H. Pantke, B. S. Razbirin, and J. M. Hvam, “Nature of nonlinear four-wave-mixing beats in semiconductors,” Phys. Rev. B 48, 5720–5723 (1993).
[CrossRef]

Feldmann, J.

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, and H. Nickel, “Rabi flopping in semiconductors,” Phys. Rev. Lett. 73, 1178-1181 (1994).
[CrossRef] [PubMed]

M. Koch, J. Feldmann, G. von Plessen, E. O. Go¨bel, P. Thomas, and K. Ko¨hler, “Quantum beats versus polarization interference: an experimental distinction,” Phys. Rev. Lett. 69, 3631-3634 (1992).
[CrossRef] [PubMed]

Ferrio, K.

H. Wang, K. Ferrio, D. G. Steel, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient nonlinear optical response from excitation induced dephasing in GaAs,” Phys. Rev. Lett. 71, 1261-1264 (1993).
[CrossRef] [PubMed]

Ferrio, K. B.

H. Wang, K. B. Ferrio, D. G. Steel, P. R. Berman, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient four-wave-mixing line shapes: effects of excitation-induced dephasing,” Phys. Rev. A 49, R1551-R1554 (1994).
[CrossRef] [PubMed]

Fleming, G. R.

D. A. Blank, L. J. Kaufman, and G. R. Fleming, “Fifth-order two-dimensional Raman spectra of CS2 are dominated by third-order cascades,” J. Chem. Phys. 111, 3105-3114 (1999).
[CrossRef]

Gallagher, A.

P. Wang, A. Gallagher, and J. Cooper, “Selective reflection by Rb,” Phys. Rev. A 56, 1598-1606 (1997).
[CrossRef]

J. Guo, A. Gallagher, and J. Cooper, “Lorentz-Lorenz shift in an inhomogeneously broadened medium,” Opt. Commun. 131, 219-222 (1996).
[CrossRef]

J. Guo, J. Cooper, and A. Gallagher, “Selective reflection from a dense atomic vapor,” Phys. Rev. A 53, 1130-1138 (1996).
[CrossRef] [PubMed]

Go¨bel, E. O.

M. Koch, J. Feldmann, G. von Plessen, E. O. Go¨bel, P. Thomas, and K. Ko¨hler, “Quantum beats versus polarization interference: an experimental distinction,” Phys. Rev. Lett. 69, 3631-3634 (1992).
[CrossRef] [PubMed]

K. Leo, M. Wegener, J. Shah, D. S. Chemla, E. O. Go¨bel, T. C. Damen, S. Schmitt-Rink, and W. Scha¨fer, “Effects of coherent polarization interactions on time-resolved degenerate four-wave mixing,” Phys. Rev. Lett. 65, 1340-1343 (1990).
[CrossRef] [PubMed]

Guo, J.

J. Guo, J. Cooper, and A. Gallagher, “Selective reflection from a dense atomic vapor,” Phys. Rev. A 53, 1130-1138 (1996).
[CrossRef] [PubMed]

J. Guo, A. Gallagher, and J. Cooper, “Lorentz-Lorenz shift in an inhomogeneously broadened medium,” Opt. Commun. 131, 219-222 (1996).
[CrossRef]

Heller, O.

K. Bott, O. Heller, D. Bennhardt, S. T. Cundiff, P. Thomas, E. J. Mayer, G. O. Smith, R. Eccleston, J. Kuhl, and K. Ploog, “Influence of exciton-exciton interactions on the coherent optical response in GaAs quantum wells,” Phys. Rev. B 48, 17418-17426 (1993).
[CrossRef]

Hu, Y. Z.

H. Wang, K. B. Ferrio, D. G. Steel, P. R. Berman, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient four-wave-mixing line shapes: effects of excitation-induced dephasing,” Phys. Rev. A 49, R1551-R1554 (1994).
[CrossRef] [PubMed]

Y. Z. Hu, R. Binder, S. W. Koch, S. T. Cundiff, H. Wang, and D. G. Steel, “Excitation and polarization effects in semiconductor four-wave-mixing spectroscopy,” Phys. Rev. B 49, 14382-14386 (1994).
[CrossRef]

H. Wang, K. Ferrio, D. G. Steel, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient nonlinear optical response from excitation induced dephasing in GaAs,” Phys. Rev. Lett. 71, 1261-1264 (1993).
[CrossRef] [PubMed]

Hvam, J. M.

V. G. Lyssenko, J. Erland, I. Balslev, K.-H. Pantke, B. S. Razbirin, and J. M. Hvam, “Nature of nonlinear four-wave-mixing beats in semiconductors,” Phys. Rev. B 48, 5720–5723 (1993).
[CrossRef]

Jahnke, F.

D.-S. Kim, J. Shah, T. C. Damen, W. Scha¨fer, F. Jahnke, S. Schmitt-Rink, and K. Ko¨hler, “Unusually slow temporal evolution of femtosecond four-wave-mixing signals in intrinsic GaAs quantum wells: direct evidence for the dominance of interaction effects,” Phys. Rev. Lett. 69, 2725-2728 (1992).
[CrossRef] [PubMed]

Kaufman, L. J.

D. A. Blank, L. J. Kaufman, and G. R. Fleming, “Fifth-order two-dimensional Raman spectra of CS2 are dominated by third-order cascades,” J. Chem. Phys. 111, 3105-3114 (1999).
[CrossRef]

Kim, D.-S.

D.-S. Kim, J. Shah, T. C. Damen, W. Scha¨fer, F. Jahnke, S. Schmitt-Rink, and K. Ko¨hler, “Unusually slow temporal evolution of femtosecond four-wave-mixing signals in intrinsic GaAs quantum wells: direct evidence for the dominance of interaction effects,” Phys. Rev. Lett. 69, 2725-2728 (1992).
[CrossRef] [PubMed]

Knorr, A.

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, and H. Nickel, “Rabi flopping in semiconductors,” Phys. Rev. Lett. 73, 1178-1181 (1994).
[CrossRef] [PubMed]

A. Knorr, T. O¨streich, K. Scho¨nhammer, R. Binder, and S. W. Koch, “Asymptotic analytic solution for Rabi oscillations in a system of weakly coupled excitons,” Phys. Rev. B 49, 14024-14027 (1994).
[CrossRef]

A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, “Theoretical study of resonant ultrashort-pulse propagation in semiconductors,” Phys. Rev. A 46, 7179-7186 (1992).
[CrossRef] [PubMed]

Ko¨hler, K.

D.-S. Kim, J. Shah, T. C. Damen, W. Scha¨fer, F. Jahnke, S. Schmitt-Rink, and K. Ko¨hler, “Unusually slow temporal evolution of femtosecond four-wave-mixing signals in intrinsic GaAs quantum wells: direct evidence for the dominance of interaction effects,” Phys. Rev. Lett. 69, 2725-2728 (1992).
[CrossRef] [PubMed]

M. Koch, J. Feldmann, G. von Plessen, E. O. Go¨bel, P. Thomas, and K. Ko¨hler, “Quantum beats versus polarization interference: an experimental distinction,” Phys. Rev. Lett. 69, 3631-3634 (1992).
[CrossRef] [PubMed]

Koch, M.

M. Koch, J. Feldmann, G. von Plessen, E. O. Go¨bel, P. Thomas, and K. Ko¨hler, “Quantum beats versus polarization interference: an experimental distinction,” Phys. Rev. Lett. 69, 3631-3634 (1992).
[CrossRef] [PubMed]

Koch, S. W.

A. Knorr, T. O¨streich, K. Scho¨nhammer, R. Binder, and S. W. Koch, “Asymptotic analytic solution for Rabi oscillations in a system of weakly coupled excitons,” Phys. Rev. B 49, 14024-14027 (1994).
[CrossRef]

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, and H. Nickel, “Rabi flopping in semiconductors,” Phys. Rev. Lett. 73, 1178-1181 (1994).
[CrossRef] [PubMed]

Y. Z. Hu, R. Binder, S. W. Koch, S. T. Cundiff, H. Wang, and D. G. Steel, “Excitation and polarization effects in semiconductor four-wave-mixing spectroscopy,” Phys. Rev. B 49, 14382-14386 (1994).
[CrossRef]

H. Wang, K. B. Ferrio, D. G. Steel, P. R. Berman, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient four-wave-mixing line shapes: effects of excitation-induced dephasing,” Phys. Rev. A 49, R1551-R1554 (1994).
[CrossRef] [PubMed]

H. Wang, K. Ferrio, D. G. Steel, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient nonlinear optical response from excitation induced dephasing in GaAs,” Phys. Rev. Lett. 71, 1261-1264 (1993).
[CrossRef] [PubMed]

A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, “Theoretical study of resonant ultrashort-pulse propagation in semiconductors,” Phys. Rev. A 46, 7179-7186 (1992).
[CrossRef] [PubMed]

Kuhl, J.

K. Bott, O. Heller, D. Bennhardt, S. T. Cundiff, P. Thomas, E. J. Mayer, G. O. Smith, R. Eccleston, J. Kuhl, and K. Ploog, “Influence of exciton-exciton interactions on the coherent optical response in GaAs quantum wells,” Phys. Rev. B 48, 17418-17426 (1993).
[CrossRef]

Kuhn, T.

A. Leitenstorfer, A. Lohner, K. Rick, P. Leisching, T. Elsaesser, T. Kuhn, F. Rossi, W. Stolz, and K. Ploog, “Excitonic and free-carrier polarizations of bulk GaAs studied by femtosecond coherent spectroscopy,” Phys. Rev. B 49, 16372-16380 (1994).
[CrossRef]

Leisching, P.

A. Leitenstorfer, A. Lohner, K. Rick, P. Leisching, T. Elsaesser, T. Kuhn, F. Rossi, W. Stolz, and K. Ploog, “Excitonic and free-carrier polarizations of bulk GaAs studied by femtosecond coherent spectroscopy,” Phys. Rev. B 49, 16372-16380 (1994).
[CrossRef]

Leitenstorfer, A.

A. Leitenstorfer, A. Lohner, K. Rick, P. Leisching, T. Elsaesser, T. Kuhn, F. Rossi, W. Stolz, and K. Ploog, “Excitonic and free-carrier polarizations of bulk GaAs studied by femtosecond coherent spectroscopy,” Phys. Rev. B 49, 16372-16380 (1994).
[CrossRef]

Leo, K.

K. Leo, M. Wegener, J. Shah, D. S. Chemla, E. O. Go¨bel, T. C. Damen, S. Schmitt-Rink, and W. Scha¨fer, “Effects of coherent polarization interactions on time-resolved degenerate four-wave mixing,” Phys. Rev. Lett. 65, 1340-1343 (1990).
[CrossRef] [PubMed]

Lindberg, M.

A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, “Theoretical study of resonant ultrashort-pulse propagation in semiconductors,” Phys. Rev. A 46, 7179-7186 (1992).
[CrossRef] [PubMed]

Lohner, A.

A. Leitenstorfer, A. Lohner, K. Rick, P. Leisching, T. Elsaesser, T. Kuhn, F. Rossi, W. Stolz, and K. Ploog, “Excitonic and free-carrier polarizations of bulk GaAs studied by femtosecond coherent spectroscopy,” Phys. Rev. B 49, 16372-16380 (1994).
[CrossRef]

Lorenz, V. O.

S. T. Cundiff, J. M. Shacklette, and V. O. Lorenz, “Interaction effects in optically dense materials,” in Ultrafast Phenomena in Semiconductors V, H. Jiang, K. T. Tsen, J.-J. Song, eds., Proc. SPIE 4280, 138-148 (2001).
[CrossRef]

Lyssenko, V. G.

V. G. Lyssenko, J. Erland, I. Balslev, K.-H. Pantke, B. S. Razbirin, and J. M. Hvam, “Nature of nonlinear four-wave-mixing beats in semiconductors,” Phys. Rev. B 48, 5720–5723 (1993).
[CrossRef]

Maki, J. J.

J. J. Maki, M. S. Malcuit, J. E. Sipe, and R. W. Boyd, “Linear and nonlinear optical measurements of the Lorentz local field,” Phys. Rev. Lett. 67, 972-975 (1991).
[CrossRef] [PubMed]

Malcuit, M. S.

J. J. Maki, M. S. Malcuit, J. E. Sipe, and R. W. Boyd, “Linear and nonlinear optical measurements of the Lorentz local field,” Phys. Rev. Lett. 67, 972-975 (1991).
[CrossRef] [PubMed]

Mayer, E. J.

K. Bott, O. Heller, D. Bennhardt, S. T. Cundiff, P. Thomas, E. J. Mayer, G. O. Smith, R. Eccleston, J. Kuhl, and K. Ploog, “Influence of exciton-exciton interactions on the coherent optical response in GaAs quantum wells,” Phys. Rev. B 48, 17418-17426 (1993).
[CrossRef]

Mycek, M.-A.

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, “Collective effects in excitonic free induction decay: do semiconductors and atoms emit coherent light in different ways?,” Phys. Rev. Lett. 69, 2685-2688 (1992).
[CrossRef] [PubMed]

Nickel, H.

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, and H. Nickel, “Rabi flopping in semiconductors,” Phys. Rev. Lett. 73, 1178-1181 (1994).
[CrossRef] [PubMed]

O¨streich, T.

A. Knorr, T. O¨streich, K. Scho¨nhammer, R. Binder, and S. W. Koch, “Asymptotic analytic solution for Rabi oscillations in a system of weakly coupled excitons,” Phys. Rev. B 49, 14024-14027 (1994).
[CrossRef]

Pantke, K.-H.

V. G. Lyssenko, J. Erland, I. Balslev, K.-H. Pantke, B. S. Razbirin, and J. M. Hvam, “Nature of nonlinear four-wave-mixing beats in semiconductors,” Phys. Rev. B 48, 5720–5723 (1993).
[CrossRef]

Paul, A. E.

Pellegrino, J. G.

Ploog, K.

A. Leitenstorfer, A. Lohner, K. Rick, P. Leisching, T. Elsaesser, T. Kuhn, F. Rossi, W. Stolz, and K. Ploog, “Excitonic and free-carrier polarizations of bulk GaAs studied by femtosecond coherent spectroscopy,” Phys. Rev. B 49, 16372-16380 (1994).
[CrossRef]

K. Bott, O. Heller, D. Bennhardt, S. T. Cundiff, P. Thomas, E. J. Mayer, G. O. Smith, R. Eccleston, J. Kuhl, and K. Ploog, “Influence of exciton-exciton interactions on the coherent optical response in GaAs quantum wells,” Phys. Rev. B 48, 17418-17426 (1993).
[CrossRef]

Razbirin, B. S.

V. G. Lyssenko, J. Erland, I. Balslev, K.-H. Pantke, B. S. Razbirin, and J. M. Hvam, “Nature of nonlinear four-wave-mixing beats in semiconductors,” Phys. Rev. B 48, 5720–5723 (1993).
[CrossRef]

Rick, K.

A. Leitenstorfer, A. Lohner, K. Rick, P. Leisching, T. Elsaesser, T. Kuhn, F. Rossi, W. Stolz, and K. Ploog, “Excitonic and free-carrier polarizations of bulk GaAs studied by femtosecond coherent spectroscopy,” Phys. Rev. B 49, 16372-16380 (1994).
[CrossRef]

Rossi, F.

A. Leitenstorfer, A. Lohner, K. Rick, P. Leisching, T. Elsaesser, T. Kuhn, F. Rossi, W. Stolz, and K. Ploog, “Excitonic and free-carrier polarizations of bulk GaAs studied by femtosecond coherent spectroscopy,” Phys. Rev. B 49, 16372-16380 (1994).
[CrossRef]

Sautenkov, V. A.

V. A. Sautenkov, H. van Kampen, E. R. Eliel, and J. P. Woerdman, “Dipole-dipole broadened line shape in a partially excited dense atomic gas,” Phys. Rev. Lett. 77, 3327-3330 (1996).
[CrossRef] [PubMed]

Scha¨fer, W.

D.-S. Kim, J. Shah, T. C. Damen, W. Scha¨fer, F. Jahnke, S. Schmitt-Rink, and K. Ko¨hler, “Unusually slow temporal evolution of femtosecond four-wave-mixing signals in intrinsic GaAs quantum wells: direct evidence for the dominance of interaction effects,” Phys. Rev. Lett. 69, 2725-2728 (1992).
[CrossRef] [PubMed]

K. Leo, M. Wegener, J. Shah, D. S. Chemla, E. O. Go¨bel, T. C. Damen, S. Schmitt-Rink, and W. Scha¨fer, “Effects of coherent polarization interactions on time-resolved degenerate four-wave mixing,” Phys. Rev. Lett. 65, 1340-1343 (1990).
[CrossRef] [PubMed]

M. Wegener, D. S. Chemla, S. Schmitt-Rink, and W. Scha¨fer, “Line shape of time-resolved four-wave mixing,” Phys. Rev. A 42, 5675-5683 (1990).
[CrossRef] [PubMed]

Schmitt-Rink, S.

D.-S. Kim, J. Shah, T. C. Damen, W. Scha¨fer, F. Jahnke, S. Schmitt-Rink, and K. Ko¨hler, “Unusually slow temporal evolution of femtosecond four-wave-mixing signals in intrinsic GaAs quantum wells: direct evidence for the dominance of interaction effects,” Phys. Rev. Lett. 69, 2725-2728 (1992).
[CrossRef] [PubMed]

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, “Collective effects in excitonic free induction decay: do semiconductors and atoms emit coherent light in different ways?,” Phys. Rev. Lett. 69, 2685-2688 (1992).
[CrossRef] [PubMed]

K. Leo, M. Wegener, J. Shah, D. S. Chemla, E. O. Go¨bel, T. C. Damen, S. Schmitt-Rink, and W. Scha¨fer, “Effects of coherent polarization interactions on time-resolved degenerate four-wave mixing,” Phys. Rev. Lett. 65, 1340-1343 (1990).
[CrossRef] [PubMed]

M. Wegener, D. S. Chemla, S. Schmitt-Rink, and W. Scha¨fer, “Line shape of time-resolved four-wave mixing,” Phys. Rev. A 42, 5675-5683 (1990).
[CrossRef] [PubMed]

Scho¨nhammer, K.

A. Knorr, T. O¨streich, K. Scho¨nhammer, R. Binder, and S. W. Koch, “Asymptotic analytic solution for Rabi oscillations in a system of weakly coupled excitons,” Phys. Rev. B 49, 14024-14027 (1994).
[CrossRef]

Shacklette, J. M.

J. M. Shacklette and S. T. Cundiff, “Role of excitation induced shift in the coherent optical response of semiconductors,” Phys. Rev. B 66, 045309 (2002).
[CrossRef]

S. T. Cundiff, J. M. Shacklette, and V. O. Lorenz, “Interaction effects in optically dense materials,” in Ultrafast Phenomena in Semiconductors V, H. Jiang, K. T. Tsen, J.-J. Song, eds., Proc. SPIE 4280, 138-148 (2001).
[CrossRef]

Shah, J.

D.-S. Kim, J. Shah, T. C. Damen, W. Scha¨fer, F. Jahnke, S. Schmitt-Rink, and K. Ko¨hler, “Unusually slow temporal evolution of femtosecond four-wave-mixing signals in intrinsic GaAs quantum wells: direct evidence for the dominance of interaction effects,” Phys. Rev. Lett. 69, 2725-2728 (1992).
[CrossRef] [PubMed]

K. Leo, M. Wegener, J. Shah, D. S. Chemla, E. O. Go¨bel, T. C. Damen, S. Schmitt-Rink, and W. Scha¨fer, “Effects of coherent polarization interactions on time-resolved degenerate four-wave mixing,” Phys. Rev. Lett. 65, 1340-1343 (1990).
[CrossRef] [PubMed]

Sipe, J. E.

J. J. Maki, M. S. Malcuit, J. E. Sipe, and R. W. Boyd, “Linear and nonlinear optical measurements of the Lorentz local field,” Phys. Rev. Lett. 67, 972-975 (1991).
[CrossRef] [PubMed]

Smirl, A. L.

A. L. Smirl, W. J. Walecki, X. Y. Chen, and O. Buccafusca,“Dynamics of the amplitude, phase and polarization state of coherent emission from quantum wells,” Phys. Status Solidi B 204, 16-19 (1997).
[CrossRef]

A. E. Paul, I. A. Bolger, A. L. Smirl, and J. G. Pellegrino, “Time-resolved measurements of the polarization state of four-wave mixing signals from GaAs multiple quantum wells,” J. Opt. Soc. Am. B 13, 1016-1025 (1996).
[CrossRef]

Smith, G. O.

K. Bott, O. Heller, D. Bennhardt, S. T. Cundiff, P. Thomas, E. J. Mayer, G. O. Smith, R. Eccleston, J. Kuhl, and K. Ploog, “Influence of exciton-exciton interactions on the coherent optical response in GaAs quantum wells,” Phys. Rev. B 48, 17418-17426 (1993).
[CrossRef]

Stahl, A.

K. Victor, V. M. Axt, G. Bartels, A. Stahl, K. Bott, and P. Thomas, “Microscopic foundation of the phenomenological few-level approach to coherent semiconductor optics,” Z. Phys. B 99, 197-205 (1996).
[CrossRef]

Steel, D. G.

Y. Z. Hu, R. Binder, S. W. Koch, S. T. Cundiff, H. Wang, and D. G. Steel, “Excitation and polarization effects in semiconductor four-wave-mixing spectroscopy,” Phys. Rev. B 49, 14382-14386 (1994).
[CrossRef]

H. Wang, K. B. Ferrio, D. G. Steel, P. R. Berman, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient four-wave-mixing line shapes: effects of excitation-induced dephasing,” Phys. Rev. A 49, R1551-R1554 (1994).
[CrossRef] [PubMed]

H. Wang, K. Ferrio, D. G. Steel, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient nonlinear optical response from excitation induced dephasing in GaAs,” Phys. Rev. Lett. 71, 1261-1264 (1993).
[CrossRef] [PubMed]

M. D. Webb, S. T. Cundiff, and D. G. Steel, “Observation of time-resolved picosecond stimulated photon echoes and free polarization decay in GaAs/AlGaAs multiple quantum wells,” Phys. Rev. Lett. 66, 934-937 (1991).
[CrossRef] [PubMed]

Stolz, W.

A. Leitenstorfer, A. Lohner, K. Rick, P. Leisching, T. Elsaesser, T. Kuhn, F. Rossi, W. Stolz, and K. Ploog, “Excitonic and free-carrier polarizations of bulk GaAs studied by femtosecond coherent spectroscopy,” Phys. Rev. B 49, 16372-16380 (1994).
[CrossRef]

Taira, Y.

T. Yajima and 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]

Thomas, P.

K. Victor, V. M. Axt, G. Bartels, A. Stahl, K. Bott, and P. Thomas, “Microscopic foundation of the phenomenological few-level approach to coherent semiconductor optics,” Z. Phys. B 99, 197-205 (1996).
[CrossRef]

K. Bott, O. Heller, D. Bennhardt, S. T. Cundiff, P. Thomas, E. J. Mayer, G. O. Smith, R. Eccleston, J. Kuhl, and K. Ploog, “Influence of exciton-exciton interactions on the coherent optical response in GaAs quantum wells,” Phys. Rev. B 48, 17418-17426 (1993).
[CrossRef]

M. Koch, J. Feldmann, G. von Plessen, E. O. Go¨bel, P. Thomas, and K. Ko¨hler, “Quantum beats versus polarization interference: an experimental distinction,” Phys. Rev. Lett. 69, 3631-3634 (1992).
[CrossRef] [PubMed]

van Kampen, H.

V. A. Sautenkov, H. van Kampen, E. R. Eliel, and J. P. Woerdman, “Dipole-dipole broadened line shape in a partially excited dense atomic gas,” Phys. Rev. Lett. 77, 3327-3330 (1996).
[CrossRef] [PubMed]

Victor, K.

K. Victor, V. M. Axt, G. Bartels, A. Stahl, K. Bott, and P. Thomas, “Microscopic foundation of the phenomenological few-level approach to coherent semiconductor optics,” Z. Phys. B 99, 197-205 (1996).
[CrossRef]

von Plessen, G.

M. Koch, J. Feldmann, G. von Plessen, E. O. Go¨bel, P. Thomas, and K. Ko¨hler, “Quantum beats versus polarization interference: an experimental distinction,” Phys. Rev. Lett. 69, 3631-3634 (1992).
[CrossRef] [PubMed]

Walecki, W. J.

A. L. Smirl, W. J. Walecki, X. Y. Chen, and O. Buccafusca,“Dynamics of the amplitude, phase and polarization state of coherent emission from quantum wells,” Phys. Status Solidi B 204, 16-19 (1997).
[CrossRef]

Wang, H.

Y. Z. Hu, R. Binder, S. W. Koch, S. T. Cundiff, H. Wang, and D. G. Steel, “Excitation and polarization effects in semiconductor four-wave-mixing spectroscopy,” Phys. Rev. B 49, 14382-14386 (1994).
[CrossRef]

H. Wang, K. B. Ferrio, D. G. Steel, P. R. Berman, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient four-wave-mixing line shapes: effects of excitation-induced dephasing,” Phys. Rev. A 49, R1551-R1554 (1994).
[CrossRef] [PubMed]

H. Wang, K. Ferrio, D. G. Steel, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient nonlinear optical response from excitation induced dephasing in GaAs,” Phys. Rev. Lett. 71, 1261-1264 (1993).
[CrossRef] [PubMed]

Wang, P.

P. Wang, A. Gallagher, and J. Cooper, “Selective reflection by Rb,” Phys. Rev. A 56, 1598-1606 (1997).
[CrossRef]

Webb, M. D.

M. D. Webb, S. T. Cundiff, and D. G. Steel, “Observation of time-resolved picosecond stimulated photon echoes and free polarization decay in GaAs/AlGaAs multiple quantum wells,” Phys. Rev. Lett. 66, 934-937 (1991).
[CrossRef] [PubMed]

Wegener, M.

K. Leo, M. Wegener, J. Shah, D. S. Chemla, E. O. Go¨bel, T. C. Damen, S. Schmitt-Rink, and W. Scha¨fer, “Effects of coherent polarization interactions on time-resolved degenerate four-wave mixing,” Phys. Rev. Lett. 65, 1340-1343 (1990).
[CrossRef] [PubMed]

M. Wegener, D. S. Chemla, S. Schmitt-Rink, and W. Scha¨fer, “Line shape of time-resolved four-wave mixing,” Phys. Rev. A 42, 5675-5683 (1990).
[CrossRef] [PubMed]

Weiss, S.

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, “Collective effects in excitonic free induction decay: do semiconductors and atoms emit coherent light in different ways?,” Phys. Rev. Lett. 69, 2685-2688 (1992).
[CrossRef] [PubMed]

Woerdman, J. P.

V. A. Sautenkov, H. van Kampen, E. R. Eliel, and J. P. Woerdman, “Dipole-dipole broadened line shape in a partially excited dense atomic gas,” Phys. Rev. Lett. 77, 3327-3330 (1996).
[CrossRef] [PubMed]

Yajima, T.

T. Yajima and 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]

J. Chem. Phys.

D. A. Blank, L. J. Kaufman, and G. R. Fleming, “Fifth-order two-dimensional Raman spectra of CS2 are dominated by third-order cascades,” J. Chem. Phys. 111, 3105-3114 (1999).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. Soc. Jpn.

T. Yajima and 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]

Laser Phys.

S. T. Cundiff, “Time domain observation of the Lorentz-local field,” Laser Phys. 12, 1073-1078 (2002).

Opt. Commun.

J. Guo, A. Gallagher, and J. Cooper, “Lorentz-Lorenz shift in an inhomogeneously broadened medium,” Opt. Commun. 131, 219-222 (1996).
[CrossRef]

Phys. Rev. A

J. Guo, J. Cooper, and A. Gallagher, “Selective reflection from a dense atomic vapor,” Phys. Rev. A 53, 1130-1138 (1996).
[CrossRef] [PubMed]

M. Wegener, D. S. Chemla, S. Schmitt-Rink, and W. Scha¨fer, “Line shape of time-resolved four-wave mixing,” Phys. Rev. A 42, 5675-5683 (1990).
[CrossRef] [PubMed]

H. Wang, K. B. Ferrio, D. G. Steel, P. R. Berman, Y. Z. Hu, R. Binder, and S. W. Koch, “Transient four-wave-mixing line shapes: effects of excitation-induced dephasing,” Phys. Rev. A 49, R1551-R1554 (1994).
[CrossRef] [PubMed]

A. Knorr, R. Binder, M. Lindberg, and S. W. Koch, “Theoretical study of resonant ultrashort-pulse propagation in semiconductors,” Phys. Rev. A 46, 7179-7186 (1992).
[CrossRef] [PubMed]

P. Wang, A. Gallagher, and J. Cooper, “Selective reflection by Rb,” Phys. Rev. A 56, 1598-1606 (1997).
[CrossRef]

Phys. Rev. B

V. G. Lyssenko, J. Erland, I. Balslev, K.-H. Pantke, B. S. Razbirin, and J. M. Hvam, “Nature of nonlinear four-wave-mixing beats in semiconductors,” Phys. Rev. B 48, 5720–5723 (1993).
[CrossRef]

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[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic of a two-pulse TFWM experiment. The two pulses are incident with wave vectors k1 and k2 and separated by a delay τ. The signal is emitted in the direction 2 k2-k1. (b) Diagram of the paraxial expansion used in the numerical calculations for the electric field (indexed by s) and off-diagonal elements of the density matrix (indexed by p). The incident pulses are injected in s=0 and 1, while the signal corresponds to s=2.

Fig. 2
Fig. 2

Calculated signal strength as a function of pulse area of the incident pulses. The results for third-order perturbation theory is shown as a thin dashed curve. The other results are obtained numerically including no interactions (solid) or EID (dashed-dotted), EIS (dotted) or LFC (dashed) separately. These results are for τ=1 (units of the dephasing rate, γph).

Fig. 3
Fig. 3

Numerical results without interaction terms. (a) Calculated TR-TFWM and (b) SR-TFWM line shapes for pulse areas of 0.1 (solid), 0.01 (dashed), and 0.001 (dotted) π including no interaction terms and for a delay τ=1. Vertical axes are logarithmic, and time and frequency axes are in units of γph.

Fig. 4
Fig. 4

Numerical results including excitation-induced dephasing: (a), (c) Calculated TR-TFWM line shapes; (b), (d) SR-TFWM line shapes including two different strengths of EID for pulse areas of 0.1 (solid), 0.01 (dashed), and 0.001 (dotted) π and for a delay τ=1. For (a) and (b) Nγ=10, while for (c) and (d) Nγ=1000, which corresponds to stronger EID. Note the ordering of the curves in (c) and (d).

Fig. 5
Fig. 5

Numerical results including excitation-induced shift: (a), (c) Calculated TR-TFWM line shapes; (b) (d) SR-TFWM line shapes including EIS for pulse areas of 0.1 (solid), 0.01 (dashed), and 0.001 (dotted) π and for a delay τ=1. For (a) and (b) Nω=10, while for (c) and (d) Nω=1000, which corresponds to stronger EIS.

Fig. 6
Fig. 6

Numerical results including the local-field correction: (a) and (c) Calculated TR-TFWM line shapes; (b), (d) SR-TFWM line shapes including LFC for pulse areas of 0.1 (solid), 0.01 (dashed), and 0.001 (dotted) π and for a delay τ=1. For (a) and (b) Nη=1, while for (c) and (d) Nη=10, which corresponds to stronger LFC. Note that the normalized strength of the LFC is weaker compared with the EIS and EID used in Figs. 4 and 5.

Fig. 7
Fig. 7

Numerical results for TI-TFWM. The TI-TFWM signal as function of delay for several pulse areas is shown including (a) EID (Nγ=10) and (b) EIS (Nω=10).

Equations (8)

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ρ˙22=-γρ22+i [μ12(E+LP)](ρ12-ρ21),
ρ˙12=-(γph+γNρ22)ρ12+i(ωA+ωNρ22)ρ12+i [μ12(E+LP)](ρ22-ρ11),
P^12(3)(t)=i μ1243N8 E22E1*×[(1+C{1-exp[-γ(t-τ)]})×exp(-γpht)Θ(t-τ)Θ(τ)+C[1-exp(-γt)]×exp[-γph(t-2τ)]Θ(t)Θ(-τ)]×exp[+i(ωA-Ω-ηN)(t-2τ)]+c.c.,
Is(τ)=μ1286N2128I22I1γph1+2γNγ+2γphexp(-2γphτ)Θ(τ)+N2[γ2+(2η+ω)2](γ+2γph)(γ+γph) [exp(-2γphτ)Θ(τ)+exp(+4γphτ)Θ(-τ)],
E(r, t)=12 [(r, t)exp(+iωt)+*(r, t)exp(-iωt)],
(r, t)=ses(t)exp(-iKr)exp(-isΔkr),
ρ22=12pρ22(p)exp(-ipΔkr)+ρ^22(p)*exp(ipΔkr),
ρ^12=νρ^12(ν)exp(-ikr)exp(-iνΔkr),

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