Abstract

In numerical computing systems with a tightly coupled large-scale multiprocessor architecture (MIMD or multiple SIMD), the interconnection network among the system elements is of considerable importance. Such a network may be built by nodes and channels made with optical components presently available. In this work two types of optical reversible node are discussed: the symmetrical exchange box and the complete node, and two examples of optical interconnection networks of the multistage nonblocking type are considered: two-sided, based on the symmetrical interchange box, and one-sided, based on the complete node. These networks may be used either in digital optical computer architectures or in traditional multiprocessor systems and may function both in guided transmission and free transmission of optical information.

© 1988 Optical Society of America

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References

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  2. H. J. Siegel, Interconnection Networks for Large-Scale Parallel Processing (D. C. Heath, Lexington, MA, 1985).
  3. M. A. Franklin, “VLSI Performance Comparison of Banyan and Crossbar Communications Networks,” IEEE Trans. Comput. C-30, 283 (1981).
    [CrossRef]
  4. K. G. Shin, J. C. Lin, “A Cost-Effective Multistage Interconnection Network with Network Overlapping and Memory Interleaving,” IEEE Trans. Comput. C-34, 1088 (1985).
    [CrossRef]
  5. A. P. Reeves, “Parallel Computer Architectures for Image Processing,” Comput. Vision Graphics Image Process. 25, 68 (1984).
    [CrossRef]
  6. K. J. Thurber, “Interconnection Networks—A Survey and Assessment,” in Proceedings, National Computer Conference (1974), p. 904.
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    [CrossRef]
  8. H. J. Siegel, “Theory Underlying the Partitioning of Permutation Networks,” IEEE Trans. Comput. C-29, 791 (1980).
    [CrossRef]
  9. J. Tanida, Y. Ichioka, “Optical Logic Array Processor Using Shadowgrams,” J. Opt. Soc. Am. 73, 800 (1983).
    [CrossRef]
  10. Y. Ichioka, J. Tanida, “Optical Parallel Logic Gates Using a Shadow-Castings System for Optical Digital Computing,” Proc. IEEE 72, 787 (1984).
    [CrossRef]
  11. J. Tanida, Y. Ichioka, “Optical-Logic-Array Processor Using Shadowgrams. III. Parallel Neighborhood Operations and an Architecture of an Optical Digital-Computing System,” J. Opt. Soc. Am. A 2, 1245 (1985).
    [CrossRef]
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  15. A. W. Lohmann, “What Classical Optics Can Do for the Digital Optical Computer,” Appl. Opt. 25, 1543 (1986).
    [CrossRef] [PubMed]
  16. A. W. Lohmann, “Optical Bus Network,” Optik 74, 30 (1986).
  17. H-I. Jeon, A. A. Sawchuk, “Optical Crossbar Interconnections Using Variable Grating Mode Devices,” Appl. Opt. 26, 261 (1987).
    [CrossRef] [PubMed]
  18. J. Shamir, H. J. Caulfield, “High-Efficiency Rapidly Programmable Optical Interconnections,” Appl. Opt. 26, 1032 (1987).
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  19. A. W. Lohmann, W. Stork, G. Stucke, “Optical Perfect Shuffle,” Appl. Opt. 25, 1530 (1986).
    [CrossRef] [PubMed]
  20. G. Eichmann, Y. Li, “Compact Optical Generalized Perfect Shuffle,” Appl. Opt. 26, 1167 (1987).
    [CrossRef]
  21. M. A. Franklin, S. Dhar, “Interconnection Networks: Physical Design and Performance Analysis,” J. Parallel Distributed Comput. 3, 352 (1986).
    [CrossRef]
  22. C. Salvatore, “Studio di una Architettura Parallela per l’elaborazione delle Immagini Astronomiche,” Thesis of Laurea in Mathematics, U. Rome la Sapienza (1987), in Italian.
  23. A. W. Lohmann, “Parallel Interfacing of Integrated Optics with Free-Space Optics,” Optik 76, 53 (1987).

1987

1986

1985

K. G. Shin, J. C. Lin, “A Cost-Effective Multistage Interconnection Network with Network Overlapping and Memory Interleaving,” IEEE Trans. Comput. C-34, 1088 (1985).
[CrossRef]

J. Tanida, Y. Ichioka, “Optical-Logic-Array Processor Using Shadowgrams. III. Parallel Neighborhood Operations and an Architecture of an Optical Digital-Computing System,” J. Opt. Soc. Am. A 2, 1245 (1985).
[CrossRef]

1984

Y. Ichioka, J. Tanida, “Optical Parallel Logic Gates Using a Shadow-Castings System for Optical Digital Computing,” Proc. IEEE 72, 787 (1984).
[CrossRef]

A. P. Reeves, “Parallel Computer Architectures for Image Processing,” Comput. Vision Graphics Image Process. 25, 68 (1984).
[CrossRef]

1983

1981

M. A. Franklin, “VLSI Performance Comparison of Banyan and Crossbar Communications Networks,” IEEE Trans. Comput. C-30, 283 (1981).
[CrossRef]

T. Y. Feng, “A Survey of Interconnection Networks,” Computer 14, 12 (Dec.1981).
[CrossRef]

1980

H. J. Siegel, “Theory Underlying the Partitioning of Permutation Networks,” IEEE Trans. Comput. C-29, 791 (1980).
[CrossRef]

Caulfield, H. J.

Dhar, S.

M. A. Franklin, S. Dhar, “Interconnection Networks: Physical Design and Performance Analysis,” J. Parallel Distributed Comput. 3, 352 (1986).
[CrossRef]

Eichmann, G.

Feng, T. Y.

T. Y. Feng, “A Survey of Interconnection Networks,” Computer 14, 12 (Dec.1981).
[CrossRef]

Franklin, M. A.

M. A. Franklin, S. Dhar, “Interconnection Networks: Physical Design and Performance Analysis,” J. Parallel Distributed Comput. 3, 352 (1986).
[CrossRef]

M. A. Franklin, “VLSI Performance Comparison of Banyan and Crossbar Communications Networks,” IEEE Trans. Comput. C-30, 283 (1981).
[CrossRef]

Hockney, R. W.

R. W. Hockney, C. R. Jesshope, Parallel Computers (Adam Hilger, Bristol, 1983).

Ichioka, Y.

Jeon, H-I.

Jesshope, C. R.

R. W. Hockney, C. R. Jesshope, Parallel Computers (Adam Hilger, Bristol, 1983).

Li, Y.

Lin, J. C.

K. G. Shin, J. C. Lin, “A Cost-Effective Multistage Interconnection Network with Network Overlapping and Memory Interleaving,” IEEE Trans. Comput. C-34, 1088 (1985).
[CrossRef]

Lohmann, A. W.

A. W. Lohmann, “Parallel Interfacing of Integrated Optics with Free-Space Optics,” Optik 76, 53 (1987).

A. W. Lohmann, “What Classical Optics Can Do for the Digital Optical Computer,” Appl. Opt. 25, 1543 (1986).
[CrossRef] [PubMed]

A. W. Lohmann, “Optical Bus Network,” Optik 74, 30 (1986).

A. W. Lohmann, W. Stork, G. Stucke, “Optical Perfect Shuffle,” Appl. Opt. 25, 1530 (1986).
[CrossRef] [PubMed]

Minemoto, T.

Miyamoto, K.

Numata, S.

Reeves, A. P.

A. P. Reeves, “Parallel Computer Architectures for Image Processing,” Comput. Vision Graphics Image Process. 25, 68 (1984).
[CrossRef]

Salvatore, C.

C. Salvatore, “Studio di una Architettura Parallela per l’elaborazione delle Immagini Astronomiche,” Thesis of Laurea in Mathematics, U. Rome la Sapienza (1987), in Italian.

Sawchuk, A. A.

Shamir, J.

Shin, K. G.

K. G. Shin, J. C. Lin, “A Cost-Effective Multistage Interconnection Network with Network Overlapping and Memory Interleaving,” IEEE Trans. Comput. C-34, 1088 (1985).
[CrossRef]

Siegel, H. J.

H. J. Siegel, “Theory Underlying the Partitioning of Permutation Networks,” IEEE Trans. Comput. C-29, 791 (1980).
[CrossRef]

H. J. Siegel, Interconnection Networks for Large-Scale Parallel Processing (D. C. Heath, Lexington, MA, 1985).

Stork, W.

Stucke, G.

Tanida, J.

Thurber, K. J.

K. J. Thurber, “Interconnection Networks—A Survey and Assessment,” in Proceedings, National Computer Conference (1974), p. 904.

Appl. Opt.

Comput. Vision Graphics Image Process.

A. P. Reeves, “Parallel Computer Architectures for Image Processing,” Comput. Vision Graphics Image Process. 25, 68 (1984).
[CrossRef]

Computer

T. Y. Feng, “A Survey of Interconnection Networks,” Computer 14, 12 (Dec.1981).
[CrossRef]

IEEE Trans. Comput.

H. J. Siegel, “Theory Underlying the Partitioning of Permutation Networks,” IEEE Trans. Comput. C-29, 791 (1980).
[CrossRef]

M. A. Franklin, “VLSI Performance Comparison of Banyan and Crossbar Communications Networks,” IEEE Trans. Comput. C-30, 283 (1981).
[CrossRef]

K. G. Shin, J. C. Lin, “A Cost-Effective Multistage Interconnection Network with Network Overlapping and Memory Interleaving,” IEEE Trans. Comput. C-34, 1088 (1985).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Parallel Distributed Comput.

M. A. Franklin, S. Dhar, “Interconnection Networks: Physical Design and Performance Analysis,” J. Parallel Distributed Comput. 3, 352 (1986).
[CrossRef]

Optik

A. W. Lohmann, “Optical Bus Network,” Optik 74, 30 (1986).

A. W. Lohmann, “Parallel Interfacing of Integrated Optics with Free-Space Optics,” Optik 76, 53 (1987).

Proc. IEEE

Y. Ichioka, J. Tanida, “Optical Parallel Logic Gates Using a Shadow-Castings System for Optical Digital Computing,” Proc. IEEE 72, 787 (1984).
[CrossRef]

Other

R. W. Hockney, C. R. Jesshope, Parallel Computers (Adam Hilger, Bristol, 1983).

H. J. Siegel, Interconnection Networks for Large-Scale Parallel Processing (D. C. Heath, Lexington, MA, 1985).

C. Salvatore, “Studio di una Architettura Parallela per l’elaborazione delle Immagini Astronomiche,” Thesis of Laurea in Mathematics, U. Rome la Sapienza (1987), in Italian.

K. J. Thurber, “Interconnection Networks—A Survey and Assessment,” in Proceedings, National Computer Conference (1974), p. 904.

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Figures (6)

Fig. 1
Fig. 1

(a) Electrical switch, (b) Optical switch for the two states of plate polarization (see the Appendix), (c) Symmetrical optical switch; all the halfwave plates have the same state, and the output and input beams have the same polarization (see Table I). A practical realization of this device can be made by one plate only. The black halfwave plates ▮ are active, and ⊙ and ↕ indicate orthogonal states of polarization.

Fig. 2
Fig. 2

Optical binary trees made with (a) the optical switch of Fig. 1(b) and (b) the optical 1(b) and (b) the optical symmetrical switch of Fig. 1(c). The black halfwave plates ▮ are active.

Fig. 3
Fig. 3

Reversible optical nodes, (a) The symmetrical interchange box node: functions definition and optical realization with polarizing beam splitter cubes and halfwave plates (the plates at the two ends have the same state, see Table II). (b) The complete node (three functions node): functions definition and optical realization by polarizing beam splitter cubes and halfwave plates (see TableIII).

Fig. 4
Fig. 4

Indirect Benes network (two-sided) for N = 16, built by the optical symmetrical interchange box of Fig. 3(a) (see Table IV).

Fig. 5
Fig. 5

Indirect Benes network (one-sided) for N = 16, made by the complete optical node shown in Fig. 3(b) (see Table IV).

Fig. 6
Fig. 6

(a) Functions of the switch of Fig. 1(b) (see Table V). (b) Functions of the same switch used as an interchange box node (see Table VI).

Tables (6)

Tables Icon

Table I Reversible States of the Switch In Fig. 1(c)

Tables Icon

Table II Reversible States of the Node In Fig. 3(a)

Tables Icon

Table III Reversible States of the Node in Fig. 3(b)

Tables Icon

Table IV Networks Connections

Tables Icon

Table V States of the Switch In Fig. 6(a)

Tables Icon

Table VI States of the Node In Fig. 6(b)

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