Abstract

We demonstrate that a dual-beam version of spectral interferometry together with a well-characterized reference pulse can be used to measure accurately the temporal dynamics of the polarization state of weak ultrafast four-wave mixing emission from semiconductor multiple quantum wells. We completely determine the electric field, including its vectorial nature, by measuring the amplitude and the phase dynamics of two orthogonal components of the field. This technique directly measures quantities in the spectral domain, and the temporal information is obtained only after considerable processing. Nevertheless, we establish the accuracy of the technique by comparing the spectral interferometric results with the corresponding data obtained by direct time-resolved ellipsometry. The data reveal that the four-wave mixing polarization state changes its ellipticity and its orientation dramatically during a single emission. The latter attribute indicates the usefulness of this technique for studying manybody effects, because without them a constant linear polarization state would be expected.

© 1998 Optical Society of America

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References

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  1. S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford U. Press, Oxford, UK, 1995).
  2. R. T. Phillips, ed., Coherent Optical Interactions in Semiconductors (Plenum, New York, 1994), and references therein.
  3. D. S. Chemla, J. Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schäfer, “Ultrafast phase dynamics of coherent emission from excitons in GaAs quantum wells,” Phys. Rev. B 50, 8439–8453 (1994).
    [CrossRef]
  4. K. W. DeLong, R. Trebino, and D. J. Kane, “Comparison of ultrashort-pulse frequency-resolved-optical-gating traces for three common geometries,” J. Opt. Soc. Am. B 11, 1595–1608 (1994), and references therein.
    [CrossRef]
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    [CrossRef] [PubMed]
  6. K. C. Chu, J. P. Heritage, R. S. Grant, K. X. Liu, A. Dienes, W. E. White, and A. Sullivan, “Direct measurement of the spectral phase of femtosecond pulses,” Opt. Lett. 20, 904–906 (1991).
    [CrossRef]
  7. L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12, 2467–2474 (1995).
    [CrossRef]
  8. D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
    [CrossRef] [PubMed]
  9. W. J. Walecki, D. N. Fittinghoff, and A. L. Smirl, “Time resolved amplitude and phase of coherent four wave mixing emission from GaAs quantum wells,” in Quantum Electronics, Vol. 9 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 15–17.
  10. J. P. Likforman, M. Joffre, and V. Thierry-Mieg, “Measurement of photon echoes using femtosecond Fourier-transform spectral interferometry,” Opt. Lett. (to be published).
  11. X. Chen, W. J. Walecki, O. Buccafusca, D. N. Fittinghoff, and A. L. Smirl, “Temporally and spectrally resolved amplitude and phase of coherent four-wave-mixing emission from GaAs quantum wells,” Phys. Rev. B (to be published).
  12. A. E. Paul, J. A. Bolger, A. L. Smirl, and J. G. Pelligrino, “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]
  13. J. A. Bolger, A. E. Paul, and A. L. Smirl, “Ultrafast ellipsometry of coherent processes and exciton–exciton interactions in quantum wells at negative delays,” Phys. Rev. B 54, 11, 666–11, 671 (1996).
    [CrossRef]
  14. W. J. Walecki, D. N. Fittinghoff, A. L. Smirl, and R. Trebino, “Characterization of the polarization state of weak ultrashort coherent signals by dual-channel spectral interferometry,” Opt. Lett. 22, 81–83 (1997).
    [CrossRef] [PubMed]
  15. K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11, 2206–2215 (1994), and references therein.
    [CrossRef]
  16. M. Kujawinska, in Interferogram Analysis, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 141–193.

1997 (1)

1996 (3)

1995 (1)

1994 (3)

1991 (2)

Bigot, J. Y.

D. S. Chemla, J. Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schäfer, “Ultrafast phase dynamics of coherent emission from excitons in GaAs quantum wells,” Phys. Rev. B 50, 8439–8453 (1994).
[CrossRef]

Bolger, J. A.

J. A. Bolger, A. E. Paul, and A. L. Smirl, “Ultrafast ellipsometry of coherent processes and exciton–exciton interactions in quantum wells at negative delays,” Phys. Rev. B 54, 11, 666–11, 671 (1996).
[CrossRef]

A. E. Paul, J. A. Bolger, A. L. Smirl, and J. G. Pelligrino, “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]

Bowie, J. L.

Chemla, D. S.

D. S. Chemla, J. Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schäfer, “Ultrafast phase dynamics of coherent emission from excitons in GaAs quantum wells,” Phys. Rev. B 50, 8439–8453 (1994).
[CrossRef]

Chériaux, G.

Chilla, J. L. A.

Chu, K. C.

DeLong, K. W.

Dienes, A.

Fittinghoff, D. N.

Grant, R. S.

Heritage, J. P.

Hunter, J.

Jennings, R. T.

Joffre, M.

Kane, D. J.

Krumbügel, M. A.

Lepetit, L.

Liu, K. X.

Martinez, O. E.

Mycek, M.-A.

D. S. Chemla, J. Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schäfer, “Ultrafast phase dynamics of coherent emission from excitons in GaAs quantum wells,” Phys. Rev. B 50, 8439–8453 (1994).
[CrossRef]

Paul, A. E.

J. A. Bolger, A. E. Paul, and A. L. Smirl, “Ultrafast ellipsometry of coherent processes and exciton–exciton interactions in quantum wells at negative delays,” Phys. Rev. B 54, 11, 666–11, 671 (1996).
[CrossRef]

A. E. Paul, J. A. Bolger, A. L. Smirl, and J. G. Pelligrino, “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]

Pelligrino, J. G.

Schäfer, W.

D. S. Chemla, J. Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schäfer, “Ultrafast phase dynamics of coherent emission from excitons in GaAs quantum wells,” Phys. Rev. B 50, 8439–8453 (1994).
[CrossRef]

Smirl, A. L.

Sullivan, A.

Sweetser, J. N.

Trebino, R.

Walecki, W. J.

Walmsley, I. A.

Weiss, S.

D. S. Chemla, J. Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schäfer, “Ultrafast phase dynamics of coherent emission from excitons in GaAs quantum wells,” Phys. Rev. B 50, 8439–8453 (1994).
[CrossRef]

White, W. E.

J. Opt. Soc. Am. B (4)

Opt. Lett. (4)

Phys. Rev. B (2)

D. S. Chemla, J. Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schäfer, “Ultrafast phase dynamics of coherent emission from excitons in GaAs quantum wells,” Phys. Rev. B 50, 8439–8453 (1994).
[CrossRef]

J. A. Bolger, A. E. Paul, and A. L. Smirl, “Ultrafast ellipsometry of coherent processes and exciton–exciton interactions in quantum wells at negative delays,” Phys. Rev. B 54, 11, 666–11, 671 (1996).
[CrossRef]

Other (6)

M. Kujawinska, in Interferogram Analysis, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 141–193.

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

R. T. Phillips, ed., Coherent Optical Interactions in Semiconductors (Plenum, New York, 1994), and references therein.

W. J. Walecki, D. N. Fittinghoff, and A. L. Smirl, “Time resolved amplitude and phase of coherent four wave mixing emission from GaAs quantum wells,” in Quantum Electronics, Vol. 9 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 15–17.

J. P. Likforman, M. Joffre, and V. Thierry-Mieg, “Measurement of photon echoes using femtosecond Fourier-transform spectral interferometry,” Opt. Lett. (to be published).

X. Chen, W. J. Walecki, O. Buccafusca, D. N. Fittinghoff, and A. L. Smirl, “Temporally and spectrally resolved amplitude and phase of coherent four-wave-mixing emission from GaAs quantum wells,” Phys. Rev. B (to be published).

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Figures (5)

Fig. 1
Fig. 1

Schematic representation of experimental geometry used for the dual-beam spectral interferometric measurement of the intensity, the phase, and the polarization state of the coherent ultrashort FWM emission from a MQW. Typical spectral interferograms for the x and the y components of the FWM signal are shown in the inset.

Fig. 2
Fig. 2

Spectral intensities (solid curves) and spectral phases (dotted curves) for (a) the x component and (b) the y component of the FWM signal for an angle of 60° between the two linear input polarizations.

Fig. 3
Fig. 3

Data of Fig. 2 replotted as the real (solid curves) and the imaginary (dotted curves) parts of the complex spectral field for (a) the x component and (b) the y component of the FWM signal.

Fig. 4
Fig. 4

Total time-dependent intensity (dotted curves and open triangles), the x component of the intensity (solid curves and filled squares), the y component of the intensity (dotted–dashed curves and filled circles), and the difference between the temporal phases of the x and the y components of the intensity (dashed curves and filled diamonds). The data in (a) are obtained by inverse Fourier transformation of the spectral data of Fig. 2 (or Fig. 3), and the data in (b) are extracted from direct time-resolved ellipsometric measurements.

Fig. 5
Fig. 5

(a) Total intensity S0(t) (solid curve), azimuthal angle θsig(t) (dotted–dashed curve), and ellipticity angle ε(t) (dashed curve) that temporally characterize the complete polarization state corresponding to the data of Fig. 4(a), (b) sketches of the polarization ellipses corresponding to the data in (a) for selected time delays.

Equations (1)

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ISIi(ω)=IFWMi(ω)+Irefi(ω)+2IFWMi(ω)Irefi(ω)× cos[ϕFWMi(ω)-ϕrefi(ω)-ωτ],

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