Abstract

Multistage interconnection architectures can provide an arbitrary pattern of one-to-one connections between N input and N output channels. We show that bitonic multistage architectures, such as the Banyan architecture, result in the fundamentally least possible growth of system size with increasing N.

© 1993 Optical Society of America

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  1. H. M. Ozaktas, Y. Amitai, J. W. Goodman, Opt. Commun. 82, 225 (1991).
    [CrossRef]
  2. H. M. Ozaktas, J. W. Goodman, J. Opt. Soc. Am. A 7, 2100 (1990).
    [CrossRef]
  3. A. L. Rosenberg, J. Comput. Mach. 30, 397 (1983).
    [CrossRef]
  4. S. K. Case, P. R. Haugen, O. J. Løberge, Appl. Opt. 20, 2670 (1981).
    [CrossRef] [PubMed]
  5. R. K. Kostuk, J. W. Goodman, L. Hesselink, Appl. Opt. 24, 2851 (1985).
    [CrossRef] [PubMed]
  6. R. Kostuk, J. W. Goodman, L. Hesselink, Appl. Opt. 26, 3947 (1987).
    [CrossRef] [PubMed]
  7. M. R. Feldman, C. C. Guest, T. J. Drabik, S. C. Esener, Appl. Opt. 28, 3820 (1989).
    [CrossRef] [PubMed]
  8. M. R. Feldman, C. C. Guest, Appl. Opt. 28, 3134 (1989).
    [CrossRef] [PubMed]
  9. G. E. Lohman, A. W. Lohmann, Opt. Eng. 27, 893 (1988).
  10. G. E. Lohman, K.-H. Brenner, Optik 89, 123 (1992).
  11. D. Mendlovic, H. M. Ozaktas, “Optical coordinate transformation methods and optical interconnection architectures—analogy and comparison,” submitted to Appl. Opt.
    [PubMed]
  12. H. M. Ozaktas, Y. Amitai, J. W. Goodman, Opt. Commun. 85, 1 (1991).
    [CrossRef]
  13. A. W. Lohmann, Appl. Opt. 25, 1543 (1986).
    [CrossRef] [PubMed]
  14. A. W. Lohmann, F. Sauer, Appl. Opt. 27, 3003 (1988).
    [CrossRef] [PubMed]
  15. J. Jahns, M. J. Murdocca, Appl. Opt. 27, 3155 (1988).
    [CrossRef] [PubMed]
  16. J. Jahns, Opt. Commun. 76, 321 (1990).
    [CrossRef]
  17. A. W. Lohmann, W. Stork, G. Stucke, Appl. Opt. 25, 1530 (1986).
    [CrossRef] [PubMed]
  18. K.-H. Brenner, A. Huang, Appl. Opt. 27, 135 (1988).
    [CrossRef] [PubMed]
  19. N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, Proc. IEEE 77, 1954 (1989).
    [CrossRef]
  20. D. S. Wise, in VLSI Systems and Computations, H. T. Kung, B. Sproull, G. Steele, eds. (Computer Science Press, Rockville, Md., 1981), pp. 186–195.
    [CrossRef]

1992 (1)

G. E. Lohman, K.-H. Brenner, Optik 89, 123 (1992).

1991 (2)

H. M. Ozaktas, Y. Amitai, J. W. Goodman, Opt. Commun. 85, 1 (1991).
[CrossRef]

H. M. Ozaktas, Y. Amitai, J. W. Goodman, Opt. Commun. 82, 225 (1991).
[CrossRef]

1990 (2)

1989 (3)

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, Proc. IEEE 77, 1954 (1989).
[CrossRef]

M. R. Feldman, C. C. Guest, T. J. Drabik, S. C. Esener, Appl. Opt. 28, 3820 (1989).
[CrossRef] [PubMed]

M. R. Feldman, C. C. Guest, Appl. Opt. 28, 3134 (1989).
[CrossRef] [PubMed]

1988 (4)

1987 (1)

1986 (2)

1985 (1)

1983 (1)

A. L. Rosenberg, J. Comput. Mach. 30, 397 (1983).
[CrossRef]

1981 (1)

Amitai, Y.

H. M. Ozaktas, Y. Amitai, J. W. Goodman, Opt. Commun. 82, 225 (1991).
[CrossRef]

H. M. Ozaktas, Y. Amitai, J. W. Goodman, Opt. Commun. 85, 1 (1991).
[CrossRef]

Brenner, K.-H.

G. E. Lohman, K.-H. Brenner, Optik 89, 123 (1992).

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, Proc. IEEE 77, 1954 (1989).
[CrossRef]

K.-H. Brenner, A. Huang, Appl. Opt. 27, 135 (1988).
[CrossRef] [PubMed]

Case, S. K.

Drabik, T. J.

Esener, S. C.

Feldman, M. R.

Goodman, J. W.

Guest, C. C.

Haugen, P. R.

Hesselink, L.

Huang, A.

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, Proc. IEEE 77, 1954 (1989).
[CrossRef]

K.-H. Brenner, A. Huang, Appl. Opt. 27, 135 (1988).
[CrossRef] [PubMed]

Jahns, J.

J. Jahns, Opt. Commun. 76, 321 (1990).
[CrossRef]

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, Proc. IEEE 77, 1954 (1989).
[CrossRef]

J. Jahns, M. J. Murdocca, Appl. Opt. 27, 3155 (1988).
[CrossRef] [PubMed]

Jewell, J.

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, Proc. IEEE 77, 1954 (1989).
[CrossRef]

Kostuk, R.

Kostuk, R. K.

Løberge, O. J.

Lohman, G. E.

G. E. Lohman, K.-H. Brenner, Optik 89, 123 (1992).

G. E. Lohman, A. W. Lohmann, Opt. Eng. 27, 893 (1988).

Lohmann, A. W.

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, Proc. IEEE 77, 1954 (1989).
[CrossRef]

G. E. Lohman, A. W. Lohmann, Opt. Eng. 27, 893 (1988).

A. W. Lohmann, F. Sauer, Appl. Opt. 27, 3003 (1988).
[CrossRef] [PubMed]

A. W. Lohmann, W. Stork, G. Stucke, Appl. Opt. 25, 1530 (1986).
[CrossRef] [PubMed]

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

Mendlovic, D.

D. Mendlovic, H. M. Ozaktas, “Optical coordinate transformation methods and optical interconnection architectures—analogy and comparison,” submitted to Appl. Opt.
[PubMed]

Miller, D. A. B.

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, Proc. IEEE 77, 1954 (1989).
[CrossRef]

Murdocca, M.

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, Proc. IEEE 77, 1954 (1989).
[CrossRef]

Murdocca, M. J.

Ozaktas, H. M.

H. M. Ozaktas, Y. Amitai, J. W. Goodman, Opt. Commun. 85, 1 (1991).
[CrossRef]

H. M. Ozaktas, Y. Amitai, J. W. Goodman, Opt. Commun. 82, 225 (1991).
[CrossRef]

H. M. Ozaktas, J. W. Goodman, J. Opt. Soc. Am. A 7, 2100 (1990).
[CrossRef]

D. Mendlovic, H. M. Ozaktas, “Optical coordinate transformation methods and optical interconnection architectures—analogy and comparison,” submitted to Appl. Opt.
[PubMed]

Prise, M. E.

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, Proc. IEEE 77, 1954 (1989).
[CrossRef]

Rosenberg, A. L.

A. L. Rosenberg, J. Comput. Mach. 30, 397 (1983).
[CrossRef]

Sauer, F.

Sizer, T.

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, Proc. IEEE 77, 1954 (1989).
[CrossRef]

Stork, W.

Streibl, N.

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, Proc. IEEE 77, 1954 (1989).
[CrossRef]

Stucke, G.

Wise, D. S.

D. S. Wise, in VLSI Systems and Computations, H. T. Kung, B. Sproull, G. Steele, eds. (Computer Science Press, Rockville, Md., 1981), pp. 186–195.
[CrossRef]

Appl. Opt. (10)

J. Comput. Mach. (1)

A. L. Rosenberg, J. Comput. Mach. 30, 397 (1983).
[CrossRef]

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

Opt. Commun. (3)

H. M. Ozaktas, Y. Amitai, J. W. Goodman, Opt. Commun. 82, 225 (1991).
[CrossRef]

H. M. Ozaktas, Y. Amitai, J. W. Goodman, Opt. Commun. 85, 1 (1991).
[CrossRef]

J. Jahns, Opt. Commun. 76, 321 (1990).
[CrossRef]

Opt. Eng. (1)

G. E. Lohman, A. W. Lohmann, Opt. Eng. 27, 893 (1988).

Optik (1)

G. E. Lohman, K.-H. Brenner, Optik 89, 123 (1992).

Proc. IEEE (1)

N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. E. Prise, T. Sizer, Proc. IEEE 77, 1954 (1989).
[CrossRef]

Other (2)

D. S. Wise, in VLSI Systems and Computations, H. T. Kung, B. Sproull, G. Steele, eds. (Computer Science Press, Rockville, Md., 1981), pp. 186–195.
[CrossRef]

D. Mendlovic, H. M. Ozaktas, “Optical coordinate transformation methods and optical interconnection architectures—analogy and comparison,” submitted to Appl. Opt.
[PubMed]

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Figures (2)

Fig. 1
Fig. 1

(a) Perfect shuffle, (b) crossover, and (c) Banyan networks with 16 inputs and outputs; (c) is drawn such that the slopes of the slanted connections are equal.

Fig. 2
Fig. 2

Side view of the general partially space-variant system used to derive the transverse and axial extent of the optical implementation of the Banyan network. The system looks the same from the top.

Equations (2)

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

L t = SW 1 / 2 f # λ = 3 N 1 / 2 f # λ = 6 f # N 1 / 2 λ .
L a = 2 × 2 f = 24 f # N 1 / 2 λ .

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