Abstract

A photorefractive resonator containing an optical delay line is shown to learn temporal information through a self-organization process. We present experiments in which a resonator mode selectively learns the most-frequently presented signals at the input. We also demonstrate the self-organized association of two different analog signals with two different resonator modes.

© 1994 Optical Society of America

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References

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  1. F. H. Mok, Opt. Lett. 18, 915 (1993).
    [CrossRef] [PubMed]
  2. D. Psaltis, D. Brady, K. Wagner, Appl. Opt. 27, 1752 (1988).
    [CrossRef]
  3. G. Zhou, D. Z. Anderson, Opt. Lett. 18, 167 (1993).
    [CrossRef] [PubMed]
  4. G. Zhou, D. Z. Anderson, Opt. Lett. 19, 655 (1994).
    [CrossRef] [PubMed]
  5. D. Z. Anderson, C. Benkert, V. Hebler, J.-S. Jang, D. Montgomery, M. Saffman, in Neural Information Processing Systems 4, J. E. Moody, S. J. Hanson, R. P. Lippman (Morgan Kaufmann, San Mateo, Calif., 1992), pp. 821–828.
  6. D. Z. Anderson, R. Saxena, J. Opt. Soc. Am. B 4, 164 (1987).
    [CrossRef]
  7. C. Benkert, D. Z. Anderson, Phys. Rev. A 44, 4633 (1991).
    [CrossRef] [PubMed]
  8. M. Saffman, C. Benkert, D. Z. Anderson, Opt. Lett. 16, 1993 (1991).
    [CrossRef] [PubMed]
  9. R. Futami, N. Hoshimiya, Syst. Comput. Jpn. 19, 102 (1988).
    [CrossRef]

1994

1993

1991

1988

D. Psaltis, D. Brady, K. Wagner, Appl. Opt. 27, 1752 (1988).
[CrossRef]

R. Futami, N. Hoshimiya, Syst. Comput. Jpn. 19, 102 (1988).
[CrossRef]

1987

Anderson, D. Z.

G. Zhou, D. Z. Anderson, Opt. Lett. 19, 655 (1994).
[CrossRef] [PubMed]

G. Zhou, D. Z. Anderson, Opt. Lett. 18, 167 (1993).
[CrossRef] [PubMed]

C. Benkert, D. Z. Anderson, Phys. Rev. A 44, 4633 (1991).
[CrossRef] [PubMed]

M. Saffman, C. Benkert, D. Z. Anderson, Opt. Lett. 16, 1993 (1991).
[CrossRef] [PubMed]

D. Z. Anderson, R. Saxena, J. Opt. Soc. Am. B 4, 164 (1987).
[CrossRef]

D. Z. Anderson, C. Benkert, V. Hebler, J.-S. Jang, D. Montgomery, M. Saffman, in Neural Information Processing Systems 4, J. E. Moody, S. J. Hanson, R. P. Lippman (Morgan Kaufmann, San Mateo, Calif., 1992), pp. 821–828.

Benkert, C.

C. Benkert, D. Z. Anderson, Phys. Rev. A 44, 4633 (1991).
[CrossRef] [PubMed]

M. Saffman, C. Benkert, D. Z. Anderson, Opt. Lett. 16, 1993 (1991).
[CrossRef] [PubMed]

D. Z. Anderson, C. Benkert, V. Hebler, J.-S. Jang, D. Montgomery, M. Saffman, in Neural Information Processing Systems 4, J. E. Moody, S. J. Hanson, R. P. Lippman (Morgan Kaufmann, San Mateo, Calif., 1992), pp. 821–828.

Brady, D.

Futami, R.

R. Futami, N. Hoshimiya, Syst. Comput. Jpn. 19, 102 (1988).
[CrossRef]

Hebler, V.

D. Z. Anderson, C. Benkert, V. Hebler, J.-S. Jang, D. Montgomery, M. Saffman, in Neural Information Processing Systems 4, J. E. Moody, S. J. Hanson, R. P. Lippman (Morgan Kaufmann, San Mateo, Calif., 1992), pp. 821–828.

Hoshimiya, N.

R. Futami, N. Hoshimiya, Syst. Comput. Jpn. 19, 102 (1988).
[CrossRef]

Jang, J.-S.

D. Z. Anderson, C. Benkert, V. Hebler, J.-S. Jang, D. Montgomery, M. Saffman, in Neural Information Processing Systems 4, J. E. Moody, S. J. Hanson, R. P. Lippman (Morgan Kaufmann, San Mateo, Calif., 1992), pp. 821–828.

Mok, F. H.

Montgomery, D.

D. Z. Anderson, C. Benkert, V. Hebler, J.-S. Jang, D. Montgomery, M. Saffman, in Neural Information Processing Systems 4, J. E. Moody, S. J. Hanson, R. P. Lippman (Morgan Kaufmann, San Mateo, Calif., 1992), pp. 821–828.

Psaltis, D.

Saffman, M.

M. Saffman, C. Benkert, D. Z. Anderson, Opt. Lett. 16, 1993 (1991).
[CrossRef] [PubMed]

D. Z. Anderson, C. Benkert, V. Hebler, J.-S. Jang, D. Montgomery, M. Saffman, in Neural Information Processing Systems 4, J. E. Moody, S. J. Hanson, R. P. Lippman (Morgan Kaufmann, San Mateo, Calif., 1992), pp. 821–828.

Saxena, R.

Wagner, K.

Zhou, G.

Appl. Opt.

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. A

C. Benkert, D. Z. Anderson, Phys. Rev. A 44, 4633 (1991).
[CrossRef] [PubMed]

Syst. Comput. Jpn.

R. Futami, N. Hoshimiya, Syst. Comput. Jpn. 19, 102 (1988).
[CrossRef]

Other

D. Z. Anderson, C. Benkert, V. Hebler, J.-S. Jang, D. Montgomery, M. Saffman, in Neural Information Processing Systems 4, J. E. Moody, S. J. Hanson, R. P. Lippman (Morgan Kaufmann, San Mateo, Calif., 1992), pp. 821–828.

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Figures (4)

Fig. 1
Fig. 1

Schematic of an optical resonator incorporating a delay line for learning temporal information.

Fig. 2
Fig. 2

Experimental setup. The oscillation is between mirror M1 and the rotating BaTiO3 crystal #1. Two chronomodes (differently dashed lines) are shown within the resonator. L, lens; BS, beam splitter.

Fig. 3
Fig. 3

Steady-state resonator response after presentation of two binary sequences S1 and S2 (see text for definitions): (a) S1 presented twice as often and learned, (b) S2 presented twice as often and learned. The lower trace indicates which input signal is on at a given time. Note that the system response grows from the beginning until the end of a signal, then it decays.

Fig. 4
Fig. 4

Association of two partially noisy time signals with two chronomodes. (a) Time-dependent amplitude of the two input signals presented alternately, (b) instantaneous intensity profile of the two modes after Signal 1 has just been applied, (c) same intensity profile with Signal 2 at the input. In each picture the lower chronomode is associated with Signal 1 and the upper with Signal 2. Images are taken by a CCD camera at the place of the detector in Fig. 2.

Equations (2)

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E j + 1 ( t ) = G j + 1 S ( t ) + μ E j ( t τ ) ( j = 1 , ... , n 1 ) ,
E j ( t ) = k = 1 j G k S ( t j τ + k τ ) μ j k ( j = 1 , , n ) .

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