Abstract

The concept of self-similar grid patterns is introduced. These patterns are proposed as an alternative to rectangular grids for arraying the optoelectronic sources and detectors of smart pixels used in free-space shuffle–exchange networks. For large processing element arrays, in medium- and coarse-grained parallel computing applications the required smart pixel arrays will likely cover several optoelectronic chips. In this case, self-similar grid patterns are shown to provide a better match to the geometry of multichip modules, thereby overcoming the packaging constraints associated with rectangular grids.

© 1993 Optical Society of America

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References

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  1. A. Lohmann, W. Stork, G. Stucke, in Digest of Conference on Optical Computing (Optical Society of America, Washington, D.C., 1985), paper WA3.
  2. A. Lohmann, Appl. Opt. 25, 1543 (1986).
    [CrossRef] [PubMed]
  3. S. H. Lin, T. F. Krile, J. F. Walkup, Proc. Soc. Photo-Opt. Instrum. Eng.209 (1987).
  4. C. Stirk, R. Athale, M. Haney, Appl. Opt. 27, 202 (1988).
    [CrossRef] [PubMed]
  5. H. S. Stone, IEEE Trans. Comput. C-20, 153 (1971).
    [CrossRef]
  6. A. Sawchuk, I. Glaser, Proc. Soc. Photo-Opt. Instrum. Eng. 963, 270 (1988).
  7. M. W. Haney, Opt. Lett. 17, 282 (1992).
    [CrossRef] [PubMed]
  8. C. E. Bauer, presented at Twenty-Fifth International Symposium on Microelectronics, San Francisco, Calif., October 1992.
  9. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, Calif., 1983).

1992

1988

A. Sawchuk, I. Glaser, Proc. Soc. Photo-Opt. Instrum. Eng. 963, 270 (1988).

C. Stirk, R. Athale, M. Haney, Appl. Opt. 27, 202 (1988).
[CrossRef] [PubMed]

1987

S. H. Lin, T. F. Krile, J. F. Walkup, Proc. Soc. Photo-Opt. Instrum. Eng.209 (1987).

1986

1971

H. S. Stone, IEEE Trans. Comput. C-20, 153 (1971).
[CrossRef]

Athale, R.

Bauer, C. E.

C. E. Bauer, presented at Twenty-Fifth International Symposium on Microelectronics, San Francisco, Calif., October 1992.

Glaser, I.

A. Sawchuk, I. Glaser, Proc. Soc. Photo-Opt. Instrum. Eng. 963, 270 (1988).

Haney, M.

Haney, M. W.

Krile, T. F.

S. H. Lin, T. F. Krile, J. F. Walkup, Proc. Soc. Photo-Opt. Instrum. Eng.209 (1987).

Lin, S. H.

S. H. Lin, T. F. Krile, J. F. Walkup, Proc. Soc. Photo-Opt. Instrum. Eng.209 (1987).

Lohmann, A.

A. Lohmann, Appl. Opt. 25, 1543 (1986).
[CrossRef] [PubMed]

A. Lohmann, W. Stork, G. Stucke, in Digest of Conference on Optical Computing (Optical Society of America, Washington, D.C., 1985), paper WA3.

Mandelbrot, B.

B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, Calif., 1983).

Sawchuk, A.

A. Sawchuk, I. Glaser, Proc. Soc. Photo-Opt. Instrum. Eng. 963, 270 (1988).

Stirk, C.

Stone, H. S.

H. S. Stone, IEEE Trans. Comput. C-20, 153 (1971).
[CrossRef]

Stork, W.

A. Lohmann, W. Stork, G. Stucke, in Digest of Conference on Optical Computing (Optical Society of America, Washington, D.C., 1985), paper WA3.

Stucke, G.

A. Lohmann, W. Stork, G. Stucke, in Digest of Conference on Optical Computing (Optical Society of America, Washington, D.C., 1985), paper WA3.

Walkup, J. F.

S. H. Lin, T. F. Krile, J. F. Walkup, Proc. Soc. Photo-Opt. Instrum. Eng.209 (1987).

Appl. Opt.

IEEE Trans. Comput.

H. S. Stone, IEEE Trans. Comput. C-20, 153 (1971).
[CrossRef]

Opt. Lett.

Proc. Soc. Photo-Opt. Instrum. Eng.

A. Sawchuk, I. Glaser, Proc. Soc. Photo-Opt. Instrum. Eng. 963, 270 (1988).

S. H. Lin, T. F. Krile, J. F. Walkup, Proc. Soc. Photo-Opt. Instrum. Eng.209 (1987).

Other

A. Lohmann, W. Stork, G. Stucke, in Digest of Conference on Optical Computing (Optical Society of America, Washington, D.C., 1985), paper WA3.

C. E. Bauer, presented at Twenty-Fifth International Symposium on Microelectronics, San Francisco, Calif., October 1992.

B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, Calif., 1983).

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Figures (4)

Fig. 1
Fig. 1

Side view of a 2-D separable shuffle or folded PS. The auxiliary lenses over the input plane improve the optical efficiency by centering each pixel’s beam on its imaging lenses.

Fig. 2
Fig. 2

Illustration of the pixel OE I/O circuitry placement based on a self-similar grid pattern.

Fig. 3
Fig. 3

Side view of the improved PS scheme based on a self-similar grid pattern with η = 1/3.

Fig. 4
Fig. 4

Example of a MCM chip layout with a self-similar OE I/O pattern, with η = 1/3, for 256 smart pixels. In this case, the integrated circuits (IC) along the axes of the MCM substrate contain no OE I/O circuitry.

Equations (3)

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x pix = D [ ( 1 η ) / 2 ] ( ± 1 ± η ± η 2 ± ± η n 1 ) ,
x lens = ± D [ ( 1 η ) ( 1 η n ) / 2 ( 1 + η ) ] .
D = [ N ( η γ 1 ) / k p min ] 2 ,

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