Abstract

We demonstrate the operation of a parallel matrix–matrix multiplier that uses a photorefractive crystal in conjunction with an array of mutually incoherent laser sources. A complex set of gratings is written in parallel with the aid of the mutually incoherent laser source array whose spatial modulation is the desired matrix–matrix product.

© 1991 Optical Society of America

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References

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  1. P. Yeh, A. E. T. Chiou, Opt. Lett. 12, 138 (1987).
    [Crossref] [PubMed]
  2. J. W. Goodman, A. R. Dias, L. M. Woody, Opt. Lett. 2, 1 (1978).
    [Crossref] [PubMed]
  3. X. S. Yao, V. Dominic, J. Feinberg, J. Opt. Soc. Am. B 7, 2347 (1990).
    [Crossref]
  4. J. L. Jewell, A. Scherer, S. L. McCall, Y. H. Lee, S. Walker, J. P. Harbison, L. T. Florez, Electron. Lett. 25, 1123 (1989).
    [Crossref]
  5. J. Hong, P. Yeh, in Topical Meeting on Optical Computing, Vol. 6 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 160.
  6. J. Hong, T. Chang, Opt. Lett. 16, 333 (1991).
    [Crossref] [PubMed]

1991 (1)

1990 (1)

1989 (1)

J. L. Jewell, A. Scherer, S. L. McCall, Y. H. Lee, S. Walker, J. P. Harbison, L. T. Florez, Electron. Lett. 25, 1123 (1989).
[Crossref]

1987 (1)

1978 (1)

Chang, T.

Chiou, A. E. T.

Dias, A. R.

Dominic, V.

Feinberg, J.

Florez, L. T.

J. L. Jewell, A. Scherer, S. L. McCall, Y. H. Lee, S. Walker, J. P. Harbison, L. T. Florez, Electron. Lett. 25, 1123 (1989).
[Crossref]

Goodman, J. W.

Harbison, J. P.

J. L. Jewell, A. Scherer, S. L. McCall, Y. H. Lee, S. Walker, J. P. Harbison, L. T. Florez, Electron. Lett. 25, 1123 (1989).
[Crossref]

Hong, J.

J. Hong, T. Chang, Opt. Lett. 16, 333 (1991).
[Crossref] [PubMed]

J. Hong, P. Yeh, in Topical Meeting on Optical Computing, Vol. 6 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 160.

Jewell, J. L.

J. L. Jewell, A. Scherer, S. L. McCall, Y. H. Lee, S. Walker, J. P. Harbison, L. T. Florez, Electron. Lett. 25, 1123 (1989).
[Crossref]

Lee, Y. H.

J. L. Jewell, A. Scherer, S. L. McCall, Y. H. Lee, S. Walker, J. P. Harbison, L. T. Florez, Electron. Lett. 25, 1123 (1989).
[Crossref]

McCall, S. L.

J. L. Jewell, A. Scherer, S. L. McCall, Y. H. Lee, S. Walker, J. P. Harbison, L. T. Florez, Electron. Lett. 25, 1123 (1989).
[Crossref]

Scherer, A.

J. L. Jewell, A. Scherer, S. L. McCall, Y. H. Lee, S. Walker, J. P. Harbison, L. T. Florez, Electron. Lett. 25, 1123 (1989).
[Crossref]

Walker, S.

J. L. Jewell, A. Scherer, S. L. McCall, Y. H. Lee, S. Walker, J. P. Harbison, L. T. Florez, Electron. Lett. 25, 1123 (1989).
[Crossref]

Woody, L. M.

Yao, X. S.

Yeh, P.

P. Yeh, A. E. T. Chiou, Opt. Lett. 12, 138 (1987).
[Crossref] [PubMed]

J. Hong, P. Yeh, in Topical Meeting on Optical Computing, Vol. 6 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 160.

Electron. Lett. (1)

J. L. Jewell, A. Scherer, S. L. McCall, Y. H. Lee, S. Walker, J. P. Harbison, L. T. Florez, Electron. Lett. 25, 1123 (1989).
[Crossref]

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

Opt. Lett. (3)

Other (1)

J. Hong, P. Yeh, in Topical Meeting on Optical Computing, Vol. 6 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 160.

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Figures (6)

Fig. 1
Fig. 1

Photorefractive matrix–matrix multiplication concept.

Fig. 2
Fig. 2

Acousto-optic realization of a mutually incoherent laser array (the acousto-optic device is driven with a periodically chirped electrical signal).

Fig. 3
Fig. 3

Complete matrix–matrix multiplier system.

Fig. 4
Fig. 4

Validation of acousto-optic mutually incoherent linear array concept. (a) Diffracted beam from uniform grating written with single-tone drive signal (f0 = 70 MHz). (b) Illustration of nonuniform grating expected from two identical linear arrays oriented at 90°; only the diagonal portion, where the two distributions oscillate at the same frequency, records a grating. (c) Diffracted beam from grating written by chirped drive signal (f0 = 70 MHz, δf = 1 MHz, repetition rate = 10 kHz).

Fig. 5
Fig. 5

Experimental results with 1-mm-thick crystal: (a) input matrix B (see text), (b) input matrix A, (c) output matrix.

Fig. 6
Fig. 6

Experimental result with 2-mm-thick crystal.

Equations (4)

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E m n = a m n exp ( i ω m t ) ,
A n ( t ) = m a m n exp ( i ω m t ) , B l ( t ) = k b k l exp ( i ω k t )
Δ n A n ( t ) B l * ( t ) τ | A n ( t ) | 2 + | B l * ( t ) | 2 τ = m k a m n b k l * exp [ i ( ω m ω k ) t ] τ m | a m n | 2 + m | b m l | 2 = m b m l * a m n m | a m n | 2 + m | b m l | 2 ,
[ 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 ] × [ 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 ] = [ 0 3 0 3 0 2 0 2 0 2 0 3 0 3 0 2 0 2 0 2 0 3 0 3 0 ] ,

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