Abstract

Using Fourier-transform spectral interferometry, we demonstrate the measurement of both amplitude and phase of photon echoes in GaAs multiple-quantum-well structures. The complete measurement of the electric field thus achieved makes possible the determination of the corresponding Wigner spectrograms.

© 1997 Optical Society of America

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References

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  1. S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford U. Press, London, 1995).
  2. S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, Phys. Rev. Lett. 69, 2685 (1992).
    [CrossRef] [PubMed]
  3. D.-S. Kim, J. Shah, T. C. Damen, W. Schäfer, F. Jahnke, S. Schmitt-Rink, and K. Köhler, Phys. Rev. Lett. 69, 2725 (1992).
    [CrossRef] [PubMed]
  4. M. S. Pshenichnikov, K. Duppen, and D. A. Wiersma, Phys. Rev. Lett. 74, 674 (1995).
    [CrossRef] [PubMed]
  5. L. Lepetit, G. Chériaux, and M. Joffre, J. Opt. Soc. Am. B 12, 2467 (1995).
    [CrossRef]
  6. F. Reynaud, F. Salin, and A. Barthelemy, Opt. Lett. 14, 275 (1989).
    [CrossRef] [PubMed]
  7. E. Tokunaga, A. Terasaki, and T. Kobayashi, Opt. Lett. 18, 370 (1993).
    [CrossRef] [PubMed]
  8. J.-P. Geindre, P. Audebert, A. Rousse, F. Falliès, J. C. Gauthier, A. Mysyrowicz, A. Dos Santos, G. Hamoniaux, and A. Antonetti, Opt. Lett. 19, 1997 (1994).
    [CrossRef] [PubMed]
  9. M. Emde, M. S. Pshenichnikov, W. P. de Boeij, and D. A. Wiersma, presented at Lasers and Electro-Optics/Electronics and Quantum Electronics Conference ’96, Hamburg, Germany, September 10–12, 1996; M. F. Emde, W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, submitted to Optics Letters.
  10. M. S. Pshenichnikov, W. P. de Boiej, and D. A. Wiersma, Phys. Rev. Lett. 76, 4701 (1996).
    [CrossRef] [PubMed]
  11. M. Ramaswamy, M. Ulman, J. Paye, and J. G. Fujimoto, Opt. Lett. 18, 1822 (1993).
    [CrossRef] [PubMed]
  12. M. S. Pshenichnikov, W. P. de Boeij, and D. A. Wiersma, Opt. Lett. 19, 572 (1994).
    [CrossRef] [PubMed]
  13. T. Yajima and T. Taira, J. Phys. Soc. Jpn. 47, 1620 (1979).
    [CrossRef]
  14. D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbugel, K. W. DeLong, R. Trebino, and I. A. Walmsley, Opt. Lett. 21, 884 (1996).
    [CrossRef] [PubMed]
  15. L. Lepetit and M. Joffre, Opt. Lett. 21, 564 (1996).
    [CrossRef] [PubMed]
  16. J. Paye, IEEE J. Quantum Electron. 28, 2262 (1992).
    [CrossRef]
  17. S. Mukamel, C. Ciordas-Ciurdariu, and V. Khidekel, IEEE J. Quantum Electron. 32, 1278 (1996).
    [CrossRef]
  18. The Wigner spectrogram obtained in the inhomogeneous sample (not shown) exhibits a simple Gaussian shape reflecting the distribution of exciton transition frequencies.
  19. T. Meier and S. Mukamel, Phys. Rev. Lett. 77, 3471 (1996).
    [CrossRef] [PubMed]
  20. The full movie (set of time delays), of which Fig.  3 is on a single frame, can be viewed at the following addresses:  http://yvette.ensta.fr/~joffre/echo and http://www.polytechnique.fr/poly/~joffre/echo .
  21. W. J. Walecki, D. N. Fittinghoff, and A. L. Smirl, in Quantum Optoelectronics, Vol.  9 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 15–17.

1996 (5)

M. S. Pshenichnikov, W. P. de Boiej, and D. A. Wiersma, Phys. Rev. Lett. 76, 4701 (1996).
[CrossRef] [PubMed]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbugel, K. W. DeLong, R. Trebino, and I. A. Walmsley, Opt. Lett. 21, 884 (1996).
[CrossRef] [PubMed]

L. Lepetit and M. Joffre, Opt. Lett. 21, 564 (1996).
[CrossRef] [PubMed]

S. Mukamel, C. Ciordas-Ciurdariu, and V. Khidekel, IEEE J. Quantum Electron. 32, 1278 (1996).
[CrossRef]

T. Meier and S. Mukamel, Phys. Rev. Lett. 77, 3471 (1996).
[CrossRef] [PubMed]

1995 (2)

M. S. Pshenichnikov, K. Duppen, and D. A. Wiersma, Phys. Rev. Lett. 74, 674 (1995).
[CrossRef] [PubMed]

L. Lepetit, G. Chériaux, and M. Joffre, J. Opt. Soc. Am. B 12, 2467 (1995).
[CrossRef]

1994 (2)

1993 (2)

1992 (3)

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, Phys. Rev. Lett. 69, 2685 (1992).
[CrossRef] [PubMed]

D.-S. Kim, J. Shah, T. C. Damen, W. Schäfer, F. Jahnke, S. Schmitt-Rink, and K. Köhler, Phys. Rev. Lett. 69, 2725 (1992).
[CrossRef] [PubMed]

J. Paye, IEEE J. Quantum Electron. 28, 2262 (1992).
[CrossRef]

1989 (1)

1979 (1)

T. Yajima and T. Taira, J. Phys. Soc. Jpn. 47, 1620 (1979).
[CrossRef]

Antonetti, A.

Audebert, P.

Barthelemy, A.

Bigot, J.-Y.

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, Phys. Rev. Lett. 69, 2685 (1992).
[CrossRef] [PubMed]

Bowie, J. L.

Chemla, D. S.

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, Phys. Rev. Lett. 69, 2685 (1992).
[CrossRef] [PubMed]

Chériaux, G.

Ciordas-Ciurdariu, C.

S. Mukamel, C. Ciordas-Ciurdariu, and V. Khidekel, IEEE J. Quantum Electron. 32, 1278 (1996).
[CrossRef]

Damen, T. C.

D.-S. Kim, J. Shah, T. C. Damen, W. Schäfer, F. Jahnke, S. Schmitt-Rink, and K. Köhler, Phys. Rev. Lett. 69, 2725 (1992).
[CrossRef] [PubMed]

de Boeij, W. P.

M. S. Pshenichnikov, W. P. de Boeij, and D. A. Wiersma, Opt. Lett. 19, 572 (1994).
[CrossRef] [PubMed]

M. Emde, M. S. Pshenichnikov, W. P. de Boeij, and D. A. Wiersma, presented at Lasers and Electro-Optics/Electronics and Quantum Electronics Conference ’96, Hamburg, Germany, September 10–12, 1996; M. F. Emde, W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, submitted to Optics Letters.

de Boiej, W. P.

M. S. Pshenichnikov, W. P. de Boiej, and D. A. Wiersma, Phys. Rev. Lett. 76, 4701 (1996).
[CrossRef] [PubMed]

DeLong, K. W.

Dos Santos, A.

Duppen, K.

M. S. Pshenichnikov, K. Duppen, and D. A. Wiersma, Phys. Rev. Lett. 74, 674 (1995).
[CrossRef] [PubMed]

Emde, M.

M. Emde, M. S. Pshenichnikov, W. P. de Boeij, and D. A. Wiersma, presented at Lasers and Electro-Optics/Electronics and Quantum Electronics Conference ’96, Hamburg, Germany, September 10–12, 1996; M. F. Emde, W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, submitted to Optics Letters.

Falliès, F.

Fittinghoff, D. N.

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbugel, K. W. DeLong, R. Trebino, and I. A. Walmsley, Opt. Lett. 21, 884 (1996).
[CrossRef] [PubMed]

W. J. Walecki, D. N. Fittinghoff, and A. L. Smirl, in Quantum Optoelectronics, Vol.  9 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 15–17.

Fujimoto, J. G.

Gauthier, J. C.

Geindre, J.-P.

Hamoniaux, G.

Jahnke, F.

D.-S. Kim, J. Shah, T. C. Damen, W. Schäfer, F. Jahnke, S. Schmitt-Rink, and K. Köhler, Phys. Rev. Lett. 69, 2725 (1992).
[CrossRef] [PubMed]

Jennings, R. T.

Joffre, M.

Khidekel, V.

S. Mukamel, C. Ciordas-Ciurdariu, and V. Khidekel, IEEE J. Quantum Electron. 32, 1278 (1996).
[CrossRef]

Kim, D.-S.

D.-S. Kim, J. Shah, T. C. Damen, W. Schäfer, F. Jahnke, S. Schmitt-Rink, and K. Köhler, Phys. Rev. Lett. 69, 2725 (1992).
[CrossRef] [PubMed]

Kobayashi, T.

Köhler, K.

D.-S. Kim, J. Shah, T. C. Damen, W. Schäfer, F. Jahnke, S. Schmitt-Rink, and K. Köhler, Phys. Rev. Lett. 69, 2725 (1992).
[CrossRef] [PubMed]

Krumbugel, M. A.

Lepetit, L.

Meier, T.

T. Meier and S. Mukamel, Phys. Rev. Lett. 77, 3471 (1996).
[CrossRef] [PubMed]

Mukamel, S.

T. Meier and S. Mukamel, Phys. Rev. Lett. 77, 3471 (1996).
[CrossRef] [PubMed]

S. Mukamel, C. Ciordas-Ciurdariu, and V. Khidekel, IEEE J. Quantum Electron. 32, 1278 (1996).
[CrossRef]

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

Mycek, M.-A.

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, Phys. Rev. Lett. 69, 2685 (1992).
[CrossRef] [PubMed]

Mysyrowicz, A.

Paye, J.

Pshenichnikov, M. S.

M. S. Pshenichnikov, W. P. de Boiej, and D. A. Wiersma, Phys. Rev. Lett. 76, 4701 (1996).
[CrossRef] [PubMed]

M. S. Pshenichnikov, K. Duppen, and D. A. Wiersma, Phys. Rev. Lett. 74, 674 (1995).
[CrossRef] [PubMed]

M. S. Pshenichnikov, W. P. de Boeij, and D. A. Wiersma, Opt. Lett. 19, 572 (1994).
[CrossRef] [PubMed]

M. Emde, M. S. Pshenichnikov, W. P. de Boeij, and D. A. Wiersma, presented at Lasers and Electro-Optics/Electronics and Quantum Electronics Conference ’96, Hamburg, Germany, September 10–12, 1996; M. F. Emde, W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, submitted to Optics Letters.

Ramaswamy, M.

Reynaud, F.

Rousse, A.

Salin, F.

Schäfer, W.

D.-S. Kim, J. Shah, T. C. Damen, W. Schäfer, F. Jahnke, S. Schmitt-Rink, and K. Köhler, Phys. Rev. Lett. 69, 2725 (1992).
[CrossRef] [PubMed]

Schmitt-Rink, S.

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, Phys. Rev. Lett. 69, 2685 (1992).
[CrossRef] [PubMed]

D.-S. Kim, J. Shah, T. C. Damen, W. Schäfer, F. Jahnke, S. Schmitt-Rink, and K. Köhler, Phys. Rev. Lett. 69, 2725 (1992).
[CrossRef] [PubMed]

Shah, J.

D.-S. Kim, J. Shah, T. C. Damen, W. Schäfer, F. Jahnke, S. Schmitt-Rink, and K. Köhler, Phys. Rev. Lett. 69, 2725 (1992).
[CrossRef] [PubMed]

Smirl, A. L.

W. J. Walecki, D. N. Fittinghoff, and A. L. Smirl, in Quantum Optoelectronics, Vol.  9 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 15–17.

Sweetser, J. N.

Taira, T.

T. Yajima and T. Taira, J. Phys. Soc. Jpn. 47, 1620 (1979).
[CrossRef]

Terasaki, A.

Tokunaga, E.

Trebino, R.

Ulman, M.

Walecki, W. J.

W. J. Walecki, D. N. Fittinghoff, and A. L. Smirl, in Quantum Optoelectronics, Vol.  9 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 15–17.

Walmsley, I. A.

Weiss, S.

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, Phys. Rev. Lett. 69, 2685 (1992).
[CrossRef] [PubMed]

Wiersma, D. A.

M. S. Pshenichnikov, W. P. de Boiej, and D. A. Wiersma, Phys. Rev. Lett. 76, 4701 (1996).
[CrossRef] [PubMed]

M. S. Pshenichnikov, K. Duppen, and D. A. Wiersma, Phys. Rev. Lett. 74, 674 (1995).
[CrossRef] [PubMed]

M. S. Pshenichnikov, W. P. de Boeij, and D. A. Wiersma, Opt. Lett. 19, 572 (1994).
[CrossRef] [PubMed]

M. Emde, M. S. Pshenichnikov, W. P. de Boeij, and D. A. Wiersma, presented at Lasers and Electro-Optics/Electronics and Quantum Electronics Conference ’96, Hamburg, Germany, September 10–12, 1996; M. F. Emde, W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, submitted to Optics Letters.

Yajima, T.

T. Yajima and T. Taira, J. Phys. Soc. Jpn. 47, 1620 (1979).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. Paye, IEEE J. Quantum Electron. 28, 2262 (1992).
[CrossRef]

S. Mukamel, C. Ciordas-Ciurdariu, and V. Khidekel, IEEE J. Quantum Electron. 32, 1278 (1996).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. Soc. Jpn. (1)

T. Yajima and T. Taira, J. Phys. Soc. Jpn. 47, 1620 (1979).
[CrossRef]

Opt. Lett. (7)

Phys. Rev. Lett. (5)

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, Phys. Rev. Lett. 69, 2685 (1992).
[CrossRef] [PubMed]

D.-S. Kim, J. Shah, T. C. Damen, W. Schäfer, F. Jahnke, S. Schmitt-Rink, and K. Köhler, Phys. Rev. Lett. 69, 2725 (1992).
[CrossRef] [PubMed]

M. S. Pshenichnikov, K. Duppen, and D. A. Wiersma, Phys. Rev. Lett. 74, 674 (1995).
[CrossRef] [PubMed]

M. S. Pshenichnikov, W. P. de Boiej, and D. A. Wiersma, Phys. Rev. Lett. 76, 4701 (1996).
[CrossRef] [PubMed]

T. Meier and S. Mukamel, Phys. Rev. Lett. 77, 3471 (1996).
[CrossRef] [PubMed]

Other (5)

The full movie (set of time delays), of which Fig.  3 is on a single frame, can be viewed at the following addresses:  http://yvette.ensta.fr/~joffre/echo and http://www.polytechnique.fr/poly/~joffre/echo .

W. J. Walecki, D. N. Fittinghoff, and A. L. Smirl, in Quantum Optoelectronics, Vol.  9 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 15–17.

The Wigner spectrogram obtained in the inhomogeneous sample (not shown) exhibits a simple Gaussian shape reflecting the distribution of exciton transition frequencies.

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

M. Emde, M. S. Pshenichnikov, W. P. de Boeij, and D. A. Wiersma, presented at Lasers and Electro-Optics/Electronics and Quantum Electronics Conference ’96, Hamburg, Germany, September 10–12, 1996; M. F. Emde, W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, submitted to Optics Letters.

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Figures (3)

Fig. 1
Fig. 1

Experimental setup. The pulses delivered by a cavity-dumped Ti:sapphire laser are split into two parts, the reference beam and a beam that is split again into two beams, thereby exciting the sample in a standard FWM geometry. The FWM emission is recombined with the reference beam by a beam splitter. The spectral interferences between the two beams are recorded with a spectrometer (SP) and a multichannel analyzer (CCD). The inset shows the background-free autocorrelation of the laser pulses (filled squares) compared with the autocorrelation computed from the laser spectrum (solid curve), assuming a constant spectral phase.

Fig. 2
Fig. 2

(a) Spectral interferences between the reference pulse and the photon-echo emission recorded for several time delays between the two exciting pulses. (b) Magnitude of the Fourier transform of the interferograms, after an acquisition time per curve of 60  s and subtraction of the exciting-pulse scattering, yielding the time dependence of the photon echo for a series of time delays. The arrows show the positions of the two exciting pulses. They are deduced from an exact determination of the phase origin as obtained from the scattered spectral interferences between the exciting pulses and the reference, also visible in (a). The open circles show a data set obtained with a shorter acquisition time of only 2.5  s.

Fig. 3
Fig. 3

(a) Wigner function Wt, ω of the FWM emission as obtained in a homogeneous multiple-quantum-well structure held at room temperature (10  nm GaAs; 20  nm GaAlAs). Both exciting pulses are centered on t=0. The Wigner function is coded in gray levels from negative (white) to positive values (black). (b) Theoretical Wigner representation of the FWM emission in a two-level Bloch model with T2=250 fs.

Equations (1)

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Wt, ω=-+E*t-t/2Et+t/2expiωtdt.

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