Abstract

A formalism is presented for determining the amount of symmetry of optical interconnects in terms of their required number of degrees of freedom. The formalism is based on matrix representation of optical interconnects and shows that the relevant property of the interconnect matrix is its rank. On the basis of this formalism, an optical arrangement is proposed for the implementation of general interconnects. This arrangement exploits the symmetry of the interconnects to increase the space–bandwidth-product capabilities, up to the limit imposed by information theory. Some examples that illustrate the effectiveness of our approach are also given.

© 1993 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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1992 (4)

1991 (1)

1989 (4)

1988 (1)

G. E. Lohman, A. W. Lohmann, “Optical interconnection networks utilizing diffraction gratings,” Opt. Eng. 27, 893–900 (1988).
[Crossref]

1987 (1)

1986 (3)

1985 (1)

1984 (1)

1982 (1)

J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proc. Natl. Acad. Sci: USA 79, 2554–2558 (1982).
[Crossref]

1961 (1)

D. Gabor, “Light and information,” Prog. Opt. 1, 109–153 (1961).
[Crossref]

Barakat, R.

Brenner, K. H.

G. E. Lohman, K. H. Brenner, “Space-variance in optical computing systems,” Optik 89, 123–134 (1992).

Chavel, P.

Davidson, N.

Domany, E.

I. Shariv, T. Grossman, E. Domany, A. A. Friesem, “All-optical implementation of the inverted neural network model,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 194–195 (1990).
[Crossref]

Drabik, T. J.

Esener, S. C.

Farhat, N.

Feldman, M. R.

Forchheimer, R.

Friesem, A. A.

Gabor, D.

D. Gabor, “Light and information,” Prog. Opt. 1, 109–153 (1961).
[Crossref]

Goodman, J. W.

J. W. Goodman, “Linear space-variant optical data processing,” in Optical Information Processing, S. H. Lee, ed. (Springer-Verlag, Berlin, 1981).
[Crossref]

Grossman, T.

I. Shariv, T. Grossman, E. Domany, A. A. Friesem, “All-optical implementation of the inverted neural network model,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 194–195 (1990).
[Crossref]

Guest, C. G.

Hasman, E.

Hong, J.

Hopfield, J. J.

J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proc. Natl. Acad. Sci: USA 79, 2554–2558 (1982).
[Crossref]

Jenkins, B. K.

Kyuma, K.

Lohman, G. E.

G. E. Lohman, K. H. Brenner, “Space-variance in optical computing systems,” Optik 89, 123–134 (1992).

G. E. Lohman, A. W. Lohmann, “Optical interconnection networks utilizing diffraction gratings,” Opt. Eng. 27, 893–900 (1988).
[Crossref]

Lohmann, A. W.

Mitsunaga, K.

Nitta, Y.

Noguchi, K.

Ohta, J.

Psaltis, D.

Reif, J.

Sawchuck, A. A.

Shariv, I.

I. Shariv, A. A. Friesem, “All-optical neural network with inhibitory neurons,” Opt. Lett. 14, 485–487 (1989).
[Crossref] [PubMed]

I. Shariv, T. Grossman, E. Domany, A. A. Friesem, “All-optical implementation of the inverted neural network model,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 194–195 (1990).
[Crossref]

Stork, W.

Strand, T. C.

Stucke, G.

Tai, S.

Takahashi, M.

Wolfram, S.

S. Wolfram, Theory and Applications of Cellular Automata (World Scientific, Singapore, 1986).

Appl. Opt. (9)

B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuck, T. C. Strand, “Architectural implications of a digital optical processor,” Appl. Opt. 23, 3465–3474 (1984).
[Crossref] [PubMed]

R. Barakat, J. Reif, “Lower bounds on the computational efficiency of optical computing systems,” Appl. Opt. 26, 1015–1018 (1987).
[Crossref] [PubMed]

M. R. Feldman, C. G. Guest, “Interconnect density capabilities of computer generated holograms for optical interconnect of very large scale integrated circuits,” Appl. Opt. 28, 3134–3137 (1989).
[Crossref] [PubMed]

M. R. Feldman, C. G. Guest, T. J. Drabik, S. C. Esener, “Comparison between optical and electrical interconnects for fine grain processor arrays based on interconnect density capabilities,” Appl. Opt. 28, 3820–3829 (1989).
[Crossref] [PubMed]

N. Davidson, A. A. Friesem, E. Hasman, “Realization of perfect shuffle and inverse perfect shuffle transforms with holographic elements,” Appl. Opt. 31, 1810–1812 (1992).
[Crossref] [PubMed]

A. W. Lohmann, “What classical optics can do for the digital optical computer,” Appl. Opt. 25, 1543–1549 (1986).
[Crossref] [PubMed]

N. Davidson, A. A. Friesem, E. Hasman, “Optical coordinate transformations,” Appl. Opt. 31, 1067–1073 (1992).
[Crossref] [PubMed]

N. Davidson, A. A. Friesem, E. Hasman, “On the limits of optical interconnects,” Appl. Opt. 31, 5426–5430 (1992).
[Crossref] [PubMed]

A. W. Lohmann, W. Stork, G. Stucke, “Optical perfect shuffle,” Appl. Opt. 25, 1530–1531 (1986).
[Crossref] [PubMed]

Opt. Eng. (1)

G. E. Lohman, A. W. Lohmann, “Optical interconnection networks utilizing diffraction gratings,” Opt. Eng. 27, 893–900 (1988).
[Crossref]

Opt. Lett. (5)

Optik (1)

G. E. Lohman, K. H. Brenner, “Space-variance in optical computing systems,” Optik 89, 123–134 (1992).

Proc. Natl. Acad. Sci: USA (1)

J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proc. Natl. Acad. Sci: USA 79, 2554–2558 (1982).
[Crossref]

Prog. Opt. (1)

D. Gabor, “Light and information,” Prog. Opt. 1, 109–153 (1961).
[Crossref]

Other (3)

J. W. Goodman, “Linear space-variant optical data processing,” in Optical Information Processing, S. H. Lee, ed. (Springer-Verlag, Berlin, 1981).
[Crossref]

S. Wolfram, Theory and Applications of Cellular Automata (World Scientific, Singapore, 1986).

I. Shariv, T. Grossman, E. Domany, A. A. Friesem, “All-optical implementation of the inverted neural network model,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 194–195 (1990).
[Crossref]

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Figures (2)

Fig. 1
Fig. 1

Optical interconnect geometry between one-dimensional arrays. Tij denotes the fraction of the light that is transmitted from the ith pixel in the input to the jth pixel in the output.

Fig. 2
Fig. 2

Two-stage optical arrangement for the implementation of optical interconnects based on outer-product decomposition. DOE1 is a diffractive optical element adjacent to the input, with N facets and fan-out of R; DOE2 is a diffractive optical element located at the Fourier plane, with R facets and fan-out of N; SLM? is a spatial light modulator that may be tentatively located at the Fourier plane.

Equations (8)

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F = A Ω / λ 2 ,
F = M × N ,
y = Tx ,
y = ( A B ) x = A x ,
λ f p D R ,
N = D p D λ f # R F R ,
Y j = i = 1 N T i j X i = i = 1 N T i , i - j X i = i = 1 N r = 1 R A i r B r , i - j X i ,
T i j = μ = 1 M ξ i μ ξ j μ .

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