Abstract

Experimental results of a practical self-learning pulse-shaping system are presented. Real-time adaptive pulse shaping of uncharacterized pulses is achieved. A cross-correlation feedback measurement of the output pulses is used by a simulated-annealing algorithm to modify the pulses iteratively toward target shapes. This scheme can readily be used for coherent control of quantum dynamics.

© 1998 Optical Society of America

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References

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  1. A. M. Weiner and J. P. Heritage, Rev. Phys. Appl. 22, 1619 (1987).
    [CrossRef]
  2. D. H. Reitze, A. M. Weiner, and D. E. Leaird, Appl. Phys. Lett. 61, 1260 (1992).
    [CrossRef]
  3. A. Efimov, C. Schaffer, and D. H. Reitze, J. Opt. Soc. Am. B 12, 1968 (1995).
    [CrossRef]
  4. A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, Opt. Lett. 15, 326 (1990).
    [CrossRef]
  5. C. W. Hillegas, J. X. Tull, D. Goswami, D. Strickland, and W. S. Warren, Opt. Lett. 19, 737 (1994).
    [CrossRef] [PubMed]
  6. R. S. Judson and H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992).
    [CrossRef] [PubMed]
  7. W. S. Warren, H. Rabitz, and M. Dahleh, Science 259, 1581 (1993).
    [CrossRef] [PubMed]
  8. A. M. Weiner, Prog. Quantum. Electron. 19, 161 (1995).
    [CrossRef]
  9. D. Meshulach, D. Yelin, and Y. Silberberg, Opt. Commun. 138, 345 (1997).
    [CrossRef]
  10. D. Meshulach, D. Yelin, and Y. Silberberg, “Adaptive compression of femtosecond pulses,” presented at Ultrafast Optics 1997 Meeting of the Optical Society of America, Monterey, Calif., session WPD-1, August 4–7, 1997; D. Yelin, D. Meshulach, and Y. Silberberg, Opt. Lett. 22, 1793 (1997).
    [CrossRef]
  11. S. Shi and H. Rabitz, J. Chem. Phys. 92, 364 (1990).
    [CrossRef]
  12. M. M. Wefers and K. A. Nelson, Opt. Lett. 20, 1047 (1995).
    [CrossRef]
  13. A. M. Weiner, S. Oudin, D. E. Leaird, and D. H. Reitze, J. Opt. Soc. Am. A 10, 1112 (1993).
    [CrossRef]
  14. D. Kane, “Real-time inversion of frequency-resolved optical gating (FROG) spectrograms: A femtosecond oscilloscope,” presented at Ultrafast Optics 1997 Meeting of the Optical Society of America, Monterey, Calif., session MA-3, August 4–7, 1997.
  15. D. N. Fittinghoff, J. L. Bowie, N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walsmley, Opt. Lett. 21, 884 (1996).
    [CrossRef] [PubMed]

1997 (1)

D. Meshulach, D. Yelin, and Y. Silberberg, Opt. Commun. 138, 345 (1997).
[CrossRef]

1996 (1)

1995 (3)

1994 (1)

1993 (2)

1992 (2)

R. S. Judson and H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992).
[CrossRef] [PubMed]

D. H. Reitze, A. M. Weiner, and D. E. Leaird, Appl. Phys. Lett. 61, 1260 (1992).
[CrossRef]

1990 (2)

1987 (1)

A. M. Weiner and J. P. Heritage, Rev. Phys. Appl. 22, 1619 (1987).
[CrossRef]

Bowie, J. L.

Dahleh, M.

W. S. Warren, H. Rabitz, and M. Dahleh, Science 259, 1581 (1993).
[CrossRef] [PubMed]

DeLong, K. W.

Efimov, A.

Fittinghoff, D. N.

Goswami, D.

Heritage, J. P.

A. M. Weiner and J. P. Heritage, Rev. Phys. Appl. 22, 1619 (1987).
[CrossRef]

Hillegas, C. W.

Jennings, R. T.

Judson, R. S.

R. S. Judson and H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992).
[CrossRef] [PubMed]

Krumbügel, M. A.

Leaird, D. E.

Meshulach, D.

D. Meshulach, D. Yelin, and Y. Silberberg, Opt. Commun. 138, 345 (1997).
[CrossRef]

Nelson, K. A.

Oudin, S.

Patel, J. S.

Rabitz, H.

W. S. Warren, H. Rabitz, and M. Dahleh, Science 259, 1581 (1993).
[CrossRef] [PubMed]

R. S. Judson and H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992).
[CrossRef] [PubMed]

S. Shi and H. Rabitz, J. Chem. Phys. 92, 364 (1990).
[CrossRef]

Reitze, D. H.

Schaffer, C.

Shi, S.

S. Shi and H. Rabitz, J. Chem. Phys. 92, 364 (1990).
[CrossRef]

Silberberg, Y.

D. Meshulach, D. Yelin, and Y. Silberberg, Opt. Commun. 138, 345 (1997).
[CrossRef]

Strickland, D.

Sweetser, N.

Trebino, R.

Tull, J. X.

Walsmley, I. A.

Warren, W. S.

Wefers, M. M.

Weiner, A. M.

A. M. Weiner, Prog. Quantum. Electron. 19, 161 (1995).
[CrossRef]

A. M. Weiner, S. Oudin, D. E. Leaird, and D. H. Reitze, J. Opt. Soc. Am. A 10, 1112 (1993).
[CrossRef]

D. H. Reitze, A. M. Weiner, and D. E. Leaird, Appl. Phys. Lett. 61, 1260 (1992).
[CrossRef]

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, Opt. Lett. 15, 326 (1990).
[CrossRef]

A. M. Weiner and J. P. Heritage, Rev. Phys. Appl. 22, 1619 (1987).
[CrossRef]

Wullert, J. R.

Yelin, D.

D. Meshulach, D. Yelin, and Y. Silberberg, Opt. Commun. 138, 345 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

D. H. Reitze, A. M. Weiner, and D. E. Leaird, Appl. Phys. Lett. 61, 1260 (1992).
[CrossRef]

J. Chem. Phys. (1)

S. Shi and H. Rabitz, J. Chem. Phys. 92, 364 (1990).
[CrossRef]

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

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

Opt. Commun. (1)

D. Meshulach, D. Yelin, and Y. Silberberg, Opt. Commun. 138, 345 (1997).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

R. S. Judson and H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992).
[CrossRef] [PubMed]

Prog. Quantum. Electron. (1)

A. M. Weiner, Prog. Quantum. Electron. 19, 161 (1995).
[CrossRef]

Rev. Phys. Appl. (1)

A. M. Weiner and J. P. Heritage, Rev. Phys. Appl. 22, 1619 (1987).
[CrossRef]

Science (1)

W. S. Warren, H. Rabitz, and M. Dahleh, Science 259, 1581 (1993).
[CrossRef] [PubMed]

Other (2)

D. Meshulach, D. Yelin, and Y. Silberberg, “Adaptive compression of femtosecond pulses,” presented at Ultrafast Optics 1997 Meeting of the Optical Society of America, Monterey, Calif., session WPD-1, August 4–7, 1997; D. Yelin, D. Meshulach, and Y. Silberberg, Opt. Lett. 22, 1793 (1997).
[CrossRef]

D. Kane, “Real-time inversion of frequency-resolved optical gating (FROG) spectrograms: A femtosecond oscilloscope,” presented at Ultrafast Optics 1997 Meeting of the Optical Society of America, Monterey, Calif., session MA-3, August 4–7, 1997.

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Figures (5)

Fig. 1
Fig. 1

Optimization procedure for adaptive pulse shaping. The dashed boxes describe operations that are performed by the experimental optical setup. In each iteration a random phase change vector is generated and added to the current phase vector to form a trial phase filter, which is applied to the SLM. The output shaped pulse is measured, a cost is calculated, and the change is accepted if the cost is smaller than that of the last accepted change, and rejected otherwise.

Fig. 2
Fig. 2

Experimental setup for adaptive pulse shaping. The setup consists of a 4-f pulse shaper, a programmable liquid-crystal SLM, a background-free intensity cross-correlation arrangement, a digital oscilloscope, and a computer. The computer was used for acquiring the cross-correlation measurement, for calculating the cost function, and for updating the spectral filter of the SLM accordingly.

Fig. 3
Fig. 3

Experimental cross-correlation signals of the shaped pulses (solid) and the target signals (dashed): (a) A sequence of few nonidentical features. (b) A pulse doublet, each pulse of 54-fs-long duration, separated by 450 fs. (c) A square pulse of 190-fs-long duration. The results were obtained by a simulated-annealing algorithm after 1000 iterations.

Fig. 4
Fig. 4

Calculated cross-correlation signals of the shaped pulses (solid) and the target signals (dashed), corresponding to the experimental results shown in Figs. 3(a)–3(c).

Fig. 5
Fig. 5

Convergence of the cost function for the case of adaptive shaping, where the final shaped pulse is shown in Fig. 3(a).

Equations (5)

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δΦ=α1-iNr,
G(i)(τ)=Iout(i)(t)Iref(t+τ)dt,
C(i)=|G(i)(τ)-Gtar(τ)|dτ.
C(i)=min|δτ|<T|G(i)(τ+δτ)-Gtar(τ)|dτ,
C(i)=||G(i)(ω)|-|Gtar(ω)||dω,

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