Abstract

We present an optical time-delay line based on photorefractive beam coupling in a rotating crystal. The delay line can be tapped continuously or at selected positions. We demonstrate a 64-channel device with a BaTiO3 crystal rotating at 1.5 rpm, which gives approximately a 167-Hz bandwidth and 0.5 s of time delay for each channel.

© 1993 Optical Society of America

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References

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  1. J. J. Hopfield, T. W. Tank, in Neural Models of Plasticity, J. H. Byrne, ed. (Academic, New York, 1989), pp. 363–377.
  2. K. P. Unnikrishnan, J. J. Hopfield, T. W. Tank, Neural Comput. 4, 108 (1992).
    [Crossref]
  3. A. Waibel, T. Hanazawa, G. Hinton, K. Shikano, K. J. Lang, IEEE Trans. Acoust. Speech Signal Process. 37, 328 (1989).
    [Crossref]
  4. See, e.g., P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications I: Fundamental Phenomena (Springer-Verlag, New York, 1988).
    [Crossref]
  5. D. Psaltis, M. A. Neifeld, A. Yamamura, Opt. Lett. 14, 429 (1989).
    [Crossref] [PubMed]
  6. A. L. Mikaelian, V. A. Barachevsky, Proc. Soc. Photo-Opt. Instrum. Eng. 1559, 246 (1991).
  7. D. Z. Anderson, J. Feinberg, IEEE J. Quantum Electron. 25, 635(1989).
    [Crossref]
  8. D. Z. Anderson, R. Saxena, J. Opt. Soc. Am. B 4, 164 (1987).
    [Crossref]
  9. The derivation of Eq. (3) uses the Laplace transform technique. Interested readers can see Ref. 7 for an example of using the technique to derive the transfer function of an optical novelty filter.
  10. A. Hermanns, C. Benkert, D. M. Lininger, D. Z. Anderson, IEEE J. Quantum Electron. 28, 750 (1992).
    [Crossref]

1992 (2)

K. P. Unnikrishnan, J. J. Hopfield, T. W. Tank, Neural Comput. 4, 108 (1992).
[Crossref]

A. Hermanns, C. Benkert, D. M. Lininger, D. Z. Anderson, IEEE J. Quantum Electron. 28, 750 (1992).
[Crossref]

1991 (1)

A. L. Mikaelian, V. A. Barachevsky, Proc. Soc. Photo-Opt. Instrum. Eng. 1559, 246 (1991).

1989 (3)

D. Z. Anderson, J. Feinberg, IEEE J. Quantum Electron. 25, 635(1989).
[Crossref]

A. Waibel, T. Hanazawa, G. Hinton, K. Shikano, K. J. Lang, IEEE Trans. Acoust. Speech Signal Process. 37, 328 (1989).
[Crossref]

D. Psaltis, M. A. Neifeld, A. Yamamura, Opt. Lett. 14, 429 (1989).
[Crossref] [PubMed]

1987 (1)

Anderson, D. Z.

A. Hermanns, C. Benkert, D. M. Lininger, D. Z. Anderson, IEEE J. Quantum Electron. 28, 750 (1992).
[Crossref]

D. Z. Anderson, J. Feinberg, IEEE J. Quantum Electron. 25, 635(1989).
[Crossref]

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

Barachevsky, V. A.

A. L. Mikaelian, V. A. Barachevsky, Proc. Soc. Photo-Opt. Instrum. Eng. 1559, 246 (1991).

Benkert, C.

A. Hermanns, C. Benkert, D. M. Lininger, D. Z. Anderson, IEEE J. Quantum Electron. 28, 750 (1992).
[Crossref]

Feinberg, J.

D. Z. Anderson, J. Feinberg, IEEE J. Quantum Electron. 25, 635(1989).
[Crossref]

Günter, P.

See, e.g., P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications I: Fundamental Phenomena (Springer-Verlag, New York, 1988).
[Crossref]

Hanazawa, T.

A. Waibel, T. Hanazawa, G. Hinton, K. Shikano, K. J. Lang, IEEE Trans. Acoust. Speech Signal Process. 37, 328 (1989).
[Crossref]

Hermanns, A.

A. Hermanns, C. Benkert, D. M. Lininger, D. Z. Anderson, IEEE J. Quantum Electron. 28, 750 (1992).
[Crossref]

Hinton, G.

A. Waibel, T. Hanazawa, G. Hinton, K. Shikano, K. J. Lang, IEEE Trans. Acoust. Speech Signal Process. 37, 328 (1989).
[Crossref]

Hopfield, J. J.

K. P. Unnikrishnan, J. J. Hopfield, T. W. Tank, Neural Comput. 4, 108 (1992).
[Crossref]

J. J. Hopfield, T. W. Tank, in Neural Models of Plasticity, J. H. Byrne, ed. (Academic, New York, 1989), pp. 363–377.

Huignard, J.-P.

See, e.g., P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications I: Fundamental Phenomena (Springer-Verlag, New York, 1988).
[Crossref]

Lang, K. J.

A. Waibel, T. Hanazawa, G. Hinton, K. Shikano, K. J. Lang, IEEE Trans. Acoust. Speech Signal Process. 37, 328 (1989).
[Crossref]

Lininger, D. M.

A. Hermanns, C. Benkert, D. M. Lininger, D. Z. Anderson, IEEE J. Quantum Electron. 28, 750 (1992).
[Crossref]

Mikaelian, A. L.

A. L. Mikaelian, V. A. Barachevsky, Proc. Soc. Photo-Opt. Instrum. Eng. 1559, 246 (1991).

Neifeld, M. A.

Psaltis, D.

Saxena, R.

Shikano, K.

A. Waibel, T. Hanazawa, G. Hinton, K. Shikano, K. J. Lang, IEEE Trans. Acoust. Speech Signal Process. 37, 328 (1989).
[Crossref]

Tank, T. W.

K. P. Unnikrishnan, J. J. Hopfield, T. W. Tank, Neural Comput. 4, 108 (1992).
[Crossref]

J. J. Hopfield, T. W. Tank, in Neural Models of Plasticity, J. H. Byrne, ed. (Academic, New York, 1989), pp. 363–377.

Unnikrishnan, K. P.

K. P. Unnikrishnan, J. J. Hopfield, T. W. Tank, Neural Comput. 4, 108 (1992).
[Crossref]

Waibel, A.

A. Waibel, T. Hanazawa, G. Hinton, K. Shikano, K. J. Lang, IEEE Trans. Acoust. Speech Signal Process. 37, 328 (1989).
[Crossref]

Yamamura, A.

IEEE J. Quantum Electron. (2)

D. Z. Anderson, J. Feinberg, IEEE J. Quantum Electron. 25, 635(1989).
[Crossref]

A. Hermanns, C. Benkert, D. M. Lininger, D. Z. Anderson, IEEE J. Quantum Electron. 28, 750 (1992).
[Crossref]

IEEE Trans. Acoust. Speech Signal Process. (1)

A. Waibel, T. Hanazawa, G. Hinton, K. Shikano, K. J. Lang, IEEE Trans. Acoust. Speech Signal Process. 37, 328 (1989).
[Crossref]

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

Neural Comput. (1)

K. P. Unnikrishnan, J. J. Hopfield, T. W. Tank, Neural Comput. 4, 108 (1992).
[Crossref]

Opt. Lett. (1)

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

A. L. Mikaelian, V. A. Barachevsky, Proc. Soc. Photo-Opt. Instrum. Eng. 1559, 246 (1991).

Other (3)

The derivation of Eq. (3) uses the Laplace transform technique. Interested readers can see Ref. 7 for an example of using the technique to derive the transfer function of an optical novelty filter.

J. J. Hopfield, T. W. Tank, in Neural Models of Plasticity, J. H. Byrne, ed. (Academic, New York, 1989), pp. 363–377.

See, e.g., P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications I: Fundamental Phenomena (Springer-Verlag, New York, 1988).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

Schematic of the photorefractive delay line.

Fig. 2
Fig. 2

k-vector diagram of the pump beam (kp), the diffracted signal beam (kθ), and the holographic grating (kg). The Bragg-match condition is satisfied when the rotation is along the kp axis.

Fig. 3
Fig. 3

Experimental setup to demonstrate photorefractive pirouette display for an array of signal inputs. BS and PBS, beam splitter and polarizing beam splitter, respectively; M, mirror; L, lens; λ/2 and λ/4, half-wave and quarter-wave plates, respectively; LCTV, liquid-crystal television.

Fig. 4
Fig. 4

Output of the pirouette display at a given instant. The input has one signal channel modulated in intensity by (a) a square wave with frequency 167 Hz and (b) a periodically chirped square wave with frequencies from 10 to 80 Hz. Camera speed: 1/1000.

Fig. 5
Fig. 5

Output of the pirouette display at two successive moments for an array of 64 input-signal channels. The lower picture is the output at an earlier time. Camera speed: 1/125.

Equations (4)

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E pump ( t , r ) = E p exp ( i ω t + i k p r ) ,
E signal ( t , r ) = A ( t , θ , z ) exp ( i ω t + i k θ r ) d θ ,
A ( t , θ , l ) = d θ f ( θ θ ) E s ( t θ / Ω ) × exp ( θ / Ω τ ) ξ I 1 ( 2 ξ θ ) 2 ξ θ ,
A ( t , θ , l ) = E 0 exp [ i ω m ( t θ / Ω ) ] × sin c [ ω m λ / Ω d sin ( ϕ ) ] × exp ( θ / Ω τ ) ξ I 1 ( 2 ξ θ ) 2 ξ θ .

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