Abstract

We propose and describe a new method of optical matrix–vector multiplication by using four-wave mixing in photorefractive media. Using a BaTiO3 crystal, we have demonstrated such a parallel multiplication. The results are presented and discussed.

© 1987 Optical Society of America

Full Article  |  PDF Article

Corrections

Pochi Yeh and Arthur E. T. Chiou, "Optical matrix-vector multiplication via four-wave mixing in photorefractive media: errata," Opt. Lett. 12, 373-373 (1987)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-12-5-373

References

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  1. R. A. Athale, in Proceedings of the Tenth International Optical Computing Conference, Catalog No. 83CH1880-4 (Institute of Electrical and Electronics Engineers, New York, 1983), pp. 24–31.
  2. R. A. Athale, W. C. Collins, Appl. Opt. 21, 2089 (1982), and references therein.
    [CrossRef] [PubMed]
  3. See also papers in the session on optical matrix processing in Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, D.C., 1985), pp. TuD1–TuD7.
  4. M. A. Monaham, K. Bromley, R. P. Bocker, Proc. IEEE 65, 121 (1977).
    [CrossRef]
  5. J. W. Goodman, A. R. Dias, L. M. Woody, Opt. Lett. 2, 1 (1978).
    [CrossRef] [PubMed]
  6. B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, Sov. Phys. JETP 15, 109 (1972).
  7. A. Yariv, IEEE J. Quantum Electron. QE14, 650 (1978).
    [CrossRef]
  8. C. R. Giuliano, Phys. Today 34(4), 27 (1981).
    [CrossRef]
  9. M. Ewbank, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng., 464, 2 (1984).
  10. M. Ewbank, P. Yeh, M. Khoshnevisan, J. Feinberg, Opt. Lett. 10, 282 (1985).
    [CrossRef] [PubMed]
  11. See, e.g., J. O. White, A. Yariv, Opt. Eng. 21, 224 (1982).
  12. A. E. Chiou, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 201 (1986).
  13. S. Kwong, G. A. Rakuljic, V. Leyva, A. Yariv, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 36 (1986).
  14. A. E. T. Chiou, P. Yeh, Opt. Lett. 11, 306 (1986).
    [CrossRef] [PubMed]
  15. S. K. Kwong, G. A. Rakuljic, A. Yariv, Appl. Lett. 48, 201 (1986).
    [CrossRef]
  16. Y. Fainman, C. C. Guest, S. H. Lee, in Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, D.C., 1985), paper TuA5.
  17. Sample of BaTiO3 purchased from Sanders Associates, Nashua, N.H. 03061.

1986 (4)

A. E. Chiou, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 201 (1986).

S. Kwong, G. A. Rakuljic, V. Leyva, A. Yariv, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 36 (1986).

A. E. T. Chiou, P. Yeh, Opt. Lett. 11, 306 (1986).
[CrossRef] [PubMed]

S. K. Kwong, G. A. Rakuljic, A. Yariv, Appl. Lett. 48, 201 (1986).
[CrossRef]

1985 (1)

1984 (1)

M. Ewbank, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng., 464, 2 (1984).

1982 (2)

1981 (1)

C. R. Giuliano, Phys. Today 34(4), 27 (1981).
[CrossRef]

1978 (2)

1977 (1)

M. A. Monaham, K. Bromley, R. P. Bocker, Proc. IEEE 65, 121 (1977).
[CrossRef]

1972 (1)

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, Sov. Phys. JETP 15, 109 (1972).

Athale, R. A.

R. A. Athale, W. C. Collins, Appl. Opt. 21, 2089 (1982), and references therein.
[CrossRef] [PubMed]

R. A. Athale, in Proceedings of the Tenth International Optical Computing Conference, Catalog No. 83CH1880-4 (Institute of Electrical and Electronics Engineers, New York, 1983), pp. 24–31.

Bocker, R. P.

M. A. Monaham, K. Bromley, R. P. Bocker, Proc. IEEE 65, 121 (1977).
[CrossRef]

Bromley, K.

M. A. Monaham, K. Bromley, R. P. Bocker, Proc. IEEE 65, 121 (1977).
[CrossRef]

Chiou, A. E.

A. E. Chiou, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 201 (1986).

Chiou, A. E. T.

Collins, W. C.

Dias, A. R.

Ewbank, M.

M. Ewbank, P. Yeh, M. Khoshnevisan, J. Feinberg, Opt. Lett. 10, 282 (1985).
[CrossRef] [PubMed]

M. Ewbank, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng., 464, 2 (1984).

Fainman, Y.

Y. Fainman, C. C. Guest, S. H. Lee, in Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, D.C., 1985), paper TuA5.

Faizullov, F. S.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, Sov. Phys. JETP 15, 109 (1972).

Feinberg, J.

Giuliano, C. R.

C. R. Giuliano, Phys. Today 34(4), 27 (1981).
[CrossRef]

Goodman, J. W.

Guest, C. C.

Y. Fainman, C. C. Guest, S. H. Lee, in Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, D.C., 1985), paper TuA5.

Khoshnevisan, M.

A. E. Chiou, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 201 (1986).

M. Ewbank, P. Yeh, M. Khoshnevisan, J. Feinberg, Opt. Lett. 10, 282 (1985).
[CrossRef] [PubMed]

M. Ewbank, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng., 464, 2 (1984).

Kwong, S.

S. Kwong, G. A. Rakuljic, V. Leyva, A. Yariv, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 36 (1986).

Kwong, S. K.

S. K. Kwong, G. A. Rakuljic, A. Yariv, Appl. Lett. 48, 201 (1986).
[CrossRef]

Lee, S. H.

Y. Fainman, C. C. Guest, S. H. Lee, in Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, D.C., 1985), paper TuA5.

Leyva, V.

S. Kwong, G. A. Rakuljic, V. Leyva, A. Yariv, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 36 (1986).

Monaham, M. A.

M. A. Monaham, K. Bromley, R. P. Bocker, Proc. IEEE 65, 121 (1977).
[CrossRef]

Popovichev, V. I.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, Sov. Phys. JETP 15, 109 (1972).

Ragul’skii, V. V.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, Sov. Phys. JETP 15, 109 (1972).

Rakuljic, G. A.

S. Kwong, G. A. Rakuljic, V. Leyva, A. Yariv, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 36 (1986).

S. K. Kwong, G. A. Rakuljic, A. Yariv, Appl. Lett. 48, 201 (1986).
[CrossRef]

White, J. O.

See, e.g., J. O. White, A. Yariv, Opt. Eng. 21, 224 (1982).

Woody, L. M.

Yariv, A.

S. K. Kwong, G. A. Rakuljic, A. Yariv, Appl. Lett. 48, 201 (1986).
[CrossRef]

S. Kwong, G. A. Rakuljic, V. Leyva, A. Yariv, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 36 (1986).

See, e.g., J. O. White, A. Yariv, Opt. Eng. 21, 224 (1982).

A. Yariv, IEEE J. Quantum Electron. QE14, 650 (1978).
[CrossRef]

Yeh, P.

A. E. Chiou, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 201 (1986).

A. E. T. Chiou, P. Yeh, Opt. Lett. 11, 306 (1986).
[CrossRef] [PubMed]

M. Ewbank, P. Yeh, M. Khoshnevisan, J. Feinberg, Opt. Lett. 10, 282 (1985).
[CrossRef] [PubMed]

M. Ewbank, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng., 464, 2 (1984).

Zel’dovich, B. Ya.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, Sov. Phys. JETP 15, 109 (1972).

Appl. Lett. (1)

S. K. Kwong, G. A. Rakuljic, A. Yariv, Appl. Lett. 48, 201 (1986).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

A. Yariv, IEEE J. Quantum Electron. QE14, 650 (1978).
[CrossRef]

Opt. Eng. (1)

See, e.g., J. O. White, A. Yariv, Opt. Eng. 21, 224 (1982).

Opt. Lett. (3)

Phys. Today (1)

C. R. Giuliano, Phys. Today 34(4), 27 (1981).
[CrossRef]

Proc. IEEE (1)

M. A. Monaham, K. Bromley, R. P. Bocker, Proc. IEEE 65, 121 (1977).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

A. E. Chiou, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 201 (1986).

S. Kwong, G. A. Rakuljic, V. Leyva, A. Yariv, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 36 (1986).

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

M. Ewbank, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng., 464, 2 (1984).

Sov. Phys. JETP (1)

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, Sov. Phys. JETP 15, 109 (1972).

Other (4)

R. A. Athale, in Proceedings of the Tenth International Optical Computing Conference, Catalog No. 83CH1880-4 (Institute of Electrical and Electronics Engineers, New York, 1983), pp. 24–31.

See also papers in the session on optical matrix processing in Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, D.C., 1985), pp. TuD1–TuD7.

Y. Fainman, C. C. Guest, S. H. Lee, in Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, D.C., 1985), paper TuA5.

Sample of BaTiO3 purchased from Sanders Associates, Nashua, N.H. 03061.

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Figures (3)

Fig. 1
Fig. 1

Schematic drawing of the basic principle of optical matrix–vector multiplication through four-wave mixing in nonlinear media.

Fig. 2
Fig. 2

Experimental setup used to demonstrate the optical matrix–vector multiplication.

Fig. 3
Fig. 3

Photographs showing the matrix and the vectors: (a) input matrix; (b) input vector, expanded into a matrix with five identical rows; (c) resultant phase-conjugate reflection matrix; (d) resultant vector of a matrix–vector multiplication after summation of (c) by a cylindrical lens.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

b ( i ) = j M ( i , j ) × a ( j ) ,
M = [ 1 1 1 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 ] ,             a = [ 1 0 1 1 1 ] .
b = M a = [ 1 1 1 0 1 1 1 1 0 0 1 0 0 1 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 1 ] = [ 3 2 0 1 4 ] .

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