Abstract

Ultrashort-laser-pulse retrieval in frequency-resolved optical gating has previously required an iterative algorithm. Here, however, we show that a computational neural network can directly and rapidly recover the intensity and phase of a pulse.

© 1996 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  5. D. E. Rumelhart, J. L. McClelland, Parallel Distributed Processing (MIT Press, Cambridge, Mass., 1986), Vols. 1 and 2.
  6. R. Hecht-Nielsen, in Proceedings of International Conference on Neural Networks III (Institute of Electrical and Electronics Engineers, New York, 1987), p. 11.
  7. V. Kurková, Neural Networks 5, 501 (1992).
    [CrossRef]
  8. A. L. Perrone, P. Castiglione, G. Basti, R. Messi, Proc. Soc. Photo-Opt. Instrum. Eng. 2243, 540 (1994).
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    [CrossRef]
  10. S. E. Fahlman, “Faster-learning variations on back-propagation: an empirical study,” in Proceedings of the 1988 Connectionist Models Summer School (Morgan Kaufman, San Mateo, Calif., 1988), p. 38.
  11. K. W. DeLong, C. L. Ladera, R. Trebino, Opt. Lett. 20, 486 (1995).
    [CrossRef] [PubMed]

1995 (1)

1994 (2)

A. L. Perrone, P. Castiglione, G. Basti, R. Messi, Proc. Soc. Photo-Opt. Instrum. Eng. 2243, 540 (1994).

K. W. DeLong, R. Trebino, D. J. Kane, J. Opt. Soc. Am. B 11, 1595 (1994).
[CrossRef]

1993 (1)

1992 (1)

V. Kurková, Neural Networks 5, 501 (1992).
[CrossRef]

1991 (1)

1985 (1)

1980 (1)

Basti, G.

A. L. Perrone, P. Castiglione, G. Basti, R. Messi, Proc. Soc. Photo-Opt. Instrum. Eng. 2243, 540 (1994).

Castiglione, P.

A. L. Perrone, P. Castiglione, G. Basti, R. Messi, Proc. Soc. Photo-Opt. Instrum. Eng. 2243, 540 (1994).

Chilla, J. L. A.

DeLong, K. W.

Diels, J.-C. M.

Fahlman, S. E.

S. E. Fahlman, “Faster-learning variations on back-propagation: an empirical study,” in Proceedings of the 1988 Connectionist Models Summer School (Morgan Kaufman, San Mateo, Calif., 1988), p. 38.

Fontain, J. J.

Hecht-Nielsen, R.

R. Hecht-Nielsen, in Proceedings of International Conference on Neural Networks III (Institute of Electrical and Electronics Engineers, New York, 1987), p. 11.

Kane, D. J.

Kurková, V.

V. Kurková, Neural Networks 5, 501 (1992).
[CrossRef]

Ladera, C. L.

Martinez, O. E.

McClelland, J. L.

D. E. Rumelhart, J. L. McClelland, Parallel Distributed Processing (MIT Press, Cambridge, Mass., 1986), Vols. 1 and 2.

McMichael, I. C.

Messi, R.

A. L. Perrone, P. Castiglione, G. Basti, R. Messi, Proc. Soc. Photo-Opt. Instrum. Eng. 2243, 540 (1994).

Perrone, A. L.

A. L. Perrone, P. Castiglione, G. Basti, R. Messi, Proc. Soc. Photo-Opt. Instrum. Eng. 2243, 540 (1994).

Rumelhart, D. E.

D. E. Rumelhart, J. L. McClelland, Parallel Distributed Processing (MIT Press, Cambridge, Mass., 1986), Vols. 1 and 2.

Simoni, F.

Teague, M. R.

Trebino, R.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

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

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

Neural Networks (1)

V. Kurková, Neural Networks 5, 501 (1992).
[CrossRef]

Opt. Lett. (2)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

A. L. Perrone, P. Castiglione, G. Basti, R. Messi, Proc. Soc. Photo-Opt. Instrum. Eng. 2243, 540 (1994).

Other (3)

D. E. Rumelhart, J. L. McClelland, Parallel Distributed Processing (MIT Press, Cambridge, Mass., 1986), Vols. 1 and 2.

R. Hecht-Nielsen, in Proceedings of International Conference on Neural Networks III (Institute of Electrical and Electronics Engineers, New York, 1987), p. 11.

S. E. Fahlman, “Faster-learning variations on back-propagation: an empirical study,” in Proceedings of the 1988 Connectionist Models Summer School (Morgan Kaufman, San Mateo, Calif., 1988), p. 38.

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Figures (6)

Fig. 1
Fig. 1

Neural network for retrieval of ultrashort laser pulses from FROG traces.

Fig. 2
Fig. 2

Intensity (solid curves) and phase (dashed curves) of four pulses typical of those used to train the neural net. The insets in the upper left show the pulses versus frequency; the insets in the upper right show the corresponding FROG traces (frequency versus time).

Fig. 3
Fig. 3

Measured FROG trace.

Fig. 4
Fig. 4

Intensity and phase of the trace shown in Fig. 3, retrieved by the neural net (circles and diamonds) and the iterative FROG algorithm (solid curves) in the time domain and in the frequency domain (inset).

Fig. 5
Fig. 5

Intensity and phase of a typical test pulse (solid and dashed curves) and those reconstructed by the neural network in the presence of 5% noise (circles and diamonds).

Fig. 6
Fig. 6

FROG trace of the pulse shown in Fig. 5. The actual and retrieved traces are visually identical, so only one is shown.

Tables (1)

Tables Icon

Table 1 Ranges of Values for the Four Parameters Used in the Training of the Neural Neta

Equations (3)

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I FROG ( ω , τ ) = | E ( t ) | E ( t τ ) | 2 exp ( i ω t ) d t | 2 ,
E ( ω ) = exp [ 2 ln 2 ( ω ω 0 ) 2 Δ ω 2 ] exp [ i β ( ω ω 0 Δ ω ) 2 + i γ ( ω ω 0 Δ ω ) 3 + i δ ( ω ω 0 Δ ω ) 4 ] .
M p q 1 N 2 I FROG ( ω , τ ) ω p τ q d ω d τ ,

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