Abstract

A coherent optical neural network is proposed that has the learning ability to achieve desirable phase values in the frequency domain. It is composed of multiple optical-path differences whose lengths are different from one another. The system learns a phase value at each discrete position in the frequency domain by obeying the complex-valued Hebbian rule. The learning curve also agrees with theoretical evolution.

© 2003 Optical Society of America

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References

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  1. D. Psaltis, A. A. Yamamura, K. Hsu, X. G. Gu, S. Lin, and D. Brady, IEEE Commun. Mag. 27(11), 37 (1989).
    [CrossRef]
  2. R. T. Weverka, K. Wagner, and M. Saffman, Opt. Lett. 16, 826 (1991).
    [CrossRef] [PubMed]
  3. E. C. Mos, J. J. H. B. Schleipen, and H. de Waardt, Appl. Opt. 36, 6654 (1997).
    [CrossRef]
  4. A. Hirose and R. Eckmiller, Appl. Opt. 35, 836 (1996).
    [CrossRef] [PubMed]
  5. A. Hirose and M. Kiuchi, IEEE Photon. Technol. Lett. 12, 564 (2000).
    [CrossRef]
  6. S. Kawata and A. Hirose, Opt. Eng. 42, 2670 (2003).
    [CrossRef]
  7. A. J. Noest, Europhys. Lett. 6, 469 (1988).
    [CrossRef]
  8. A. Hirose, Electron. Lett. 28, 1492 (1992).
    [CrossRef]
  9. A. Hirose, in Proceedings of International Conference on Artificial Neural Networks (ICANN) (Springer, New York, 1999), Vol. 2, p. 726.
    [CrossRef]
  10. T. Sato, Y. Ohtera, N. Ishino, K. Miura, and S. Kawakami, IEEE J. Quantum Electron. 38, 904 (2002).
    [CrossRef]

2003 (1)

S. Kawata and A. Hirose, Opt. Eng. 42, 2670 (2003).
[CrossRef]

2002 (1)

T. Sato, Y. Ohtera, N. Ishino, K. Miura, and S. Kawakami, IEEE J. Quantum Electron. 38, 904 (2002).
[CrossRef]

2000 (1)

A. Hirose and M. Kiuchi, IEEE Photon. Technol. Lett. 12, 564 (2000).
[CrossRef]

1999 (1)

A. Hirose, in Proceedings of International Conference on Artificial Neural Networks (ICANN) (Springer, New York, 1999), Vol. 2, p. 726.
[CrossRef]

1997 (1)

1996 (1)

1992 (1)

A. Hirose, Electron. Lett. 28, 1492 (1992).
[CrossRef]

1991 (1)

1989 (1)

D. Psaltis, A. A. Yamamura, K. Hsu, X. G. Gu, S. Lin, and D. Brady, IEEE Commun. Mag. 27(11), 37 (1989).
[CrossRef]

1988 (1)

A. J. Noest, Europhys. Lett. 6, 469 (1988).
[CrossRef]

Brady, D.

D. Psaltis, A. A. Yamamura, K. Hsu, X. G. Gu, S. Lin, and D. Brady, IEEE Commun. Mag. 27(11), 37 (1989).
[CrossRef]

de Waardt, H.

Eckmiller, R.

Gu, X. G.

D. Psaltis, A. A. Yamamura, K. Hsu, X. G. Gu, S. Lin, and D. Brady, IEEE Commun. Mag. 27(11), 37 (1989).
[CrossRef]

Hirose, A.

S. Kawata and A. Hirose, Opt. Eng. 42, 2670 (2003).
[CrossRef]

A. Hirose and M. Kiuchi, IEEE Photon. Technol. Lett. 12, 564 (2000).
[CrossRef]

A. Hirose, in Proceedings of International Conference on Artificial Neural Networks (ICANN) (Springer, New York, 1999), Vol. 2, p. 726.
[CrossRef]

A. Hirose and R. Eckmiller, Appl. Opt. 35, 836 (1996).
[CrossRef] [PubMed]

A. Hirose, Electron. Lett. 28, 1492 (1992).
[CrossRef]

Hsu, K.

D. Psaltis, A. A. Yamamura, K. Hsu, X. G. Gu, S. Lin, and D. Brady, IEEE Commun. Mag. 27(11), 37 (1989).
[CrossRef]

Ishino, N.

T. Sato, Y. Ohtera, N. Ishino, K. Miura, and S. Kawakami, IEEE J. Quantum Electron. 38, 904 (2002).
[CrossRef]

Kawakami, S.

T. Sato, Y. Ohtera, N. Ishino, K. Miura, and S. Kawakami, IEEE J. Quantum Electron. 38, 904 (2002).
[CrossRef]

Kawata, S.

S. Kawata and A. Hirose, Opt. Eng. 42, 2670 (2003).
[CrossRef]

Kiuchi, M.

A. Hirose and M. Kiuchi, IEEE Photon. Technol. Lett. 12, 564 (2000).
[CrossRef]

Lin, S.

D. Psaltis, A. A. Yamamura, K. Hsu, X. G. Gu, S. Lin, and D. Brady, IEEE Commun. Mag. 27(11), 37 (1989).
[CrossRef]

Miura, K.

T. Sato, Y. Ohtera, N. Ishino, K. Miura, and S. Kawakami, IEEE J. Quantum Electron. 38, 904 (2002).
[CrossRef]

Mos, E. C.

Noest, A. J.

A. J. Noest, Europhys. Lett. 6, 469 (1988).
[CrossRef]

Ohtera, Y.

T. Sato, Y. Ohtera, N. Ishino, K. Miura, and S. Kawakami, IEEE J. Quantum Electron. 38, 904 (2002).
[CrossRef]

Psaltis, D.

D. Psaltis, A. A. Yamamura, K. Hsu, X. G. Gu, S. Lin, and D. Brady, IEEE Commun. Mag. 27(11), 37 (1989).
[CrossRef]

Saffman, M.

Sato, T.

T. Sato, Y. Ohtera, N. Ishino, K. Miura, and S. Kawakami, IEEE J. Quantum Electron. 38, 904 (2002).
[CrossRef]

Schleipen, J. J. H. B.

Wagner, K.

Weverka, R. T.

Yamamura, A. A.

D. Psaltis, A. A. Yamamura, K. Hsu, X. G. Gu, S. Lin, and D. Brady, IEEE Commun. Mag. 27(11), 37 (1989).
[CrossRef]

Appl. Opt. (2)

Electron. Lett. (1)

A. Hirose, Electron. Lett. 28, 1492 (1992).
[CrossRef]

Europhys. Lett. (1)

A. J. Noest, Europhys. Lett. 6, 469 (1988).
[CrossRef]

IEEE Commun. Mag. (1)

D. Psaltis, A. A. Yamamura, K. Hsu, X. G. Gu, S. Lin, and D. Brady, IEEE Commun. Mag. 27(11), 37 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

T. Sato, Y. Ohtera, N. Ishino, K. Miura, and S. Kawakami, IEEE J. Quantum Electron. 38, 904 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Hirose and M. Kiuchi, IEEE Photon. Technol. Lett. 12, 564 (2000).
[CrossRef]

Opt. Eng. (1)

S. Kawata and A. Hirose, Opt. Eng. 42, 2670 (2003).
[CrossRef]

Opt. Lett. (1)

Other (1)

A. Hirose, in Proceedings of International Conference on Artificial Neural Networks (ICANN) (Springer, New York, 1999), Vol. 2, p. 726.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Conceptual illustration of (1) synthesis of multiple signals in the frequency domain and (2) a neuron with multiple weights.

Fig. 2
Fig. 2

Optical setup: LD, laser diode; M1–M3, mirrors; HM1–HM3, half-mirrors; ND filter, neutral-density filter; PC, personal computer. The light wave emitted from the laser diode is collimated and divided into signal and reference beams at HM1. The signal wave becomes three signal beams through the combination of HM2 and M3. The three beams’ phase values are separately modulated by PAL-SLM. Then the signal beams interfere with the reference adjusted by the neutral-beam filter at HM3. The interference fringe is captured by a CCD camera.

Fig. 3
Fig. 3

Signal assignments on PAL-SLM and CCD surfaces and an interference fringe image.

Fig. 4
Fig. 4

Simulation results when the teacher phase values are located at several different positions. (1) Generalization characteristics after 200 learning iterations. (2) Error functions: A=1.00, B=1.00, K=0.10, k=3.00, nmax=1, mmax=1, hmax=3, μmax=4, ΔL1=0.0151 m, ΔL2=0.0559 m, ΔL3=0.0865 m, f1=472.002 THz, f2=472.004 THz, f3=472.006 THz, and f4=472.008 THz. (3) Teacher values.

Fig. 5
Fig. 5

Experimental results: (1) generalization characteristics, (2) error function.

Equations (5)

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gzA tanhBzexpi argBz,    zC,
kdwmn,hdt=-wmn,h+Kymxn×cosβm-αn-argwmn,h,
kdτmn,hdt=K2πfymxnwmn,h×sinβm-αn-2πfτmn,h,
E12μyxˆμ-yˆμ2,

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