Abstract

Major issues in optoelectronic system design include timing, synchronization, and control. Designing free-space optical computing architectures is difficult because of the high degree of system complexity, parallelism, and concurrency in conjunction with the high cost and lack of availability of devices. Current simulation tools lack the expressiveness to model the system structure and behavior of parallel and concurrent architectures, thus making them inefficient and ineffective. We show that Petri nets, compared with other system-modeling methodologies, are more efficient and effective at expressing the functional, behavioral, and structural properties of parallel and concurrent architectures. We show how an extended version of the standard Petri net, a timed–colored Petri net, is used to model and simulate free-space optoelectronic computing architectures. We also present methods for analysis of system timing, synchronization, and control behavior.

© 1998 Optical Society of America

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References

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  1. W. T. Cathey, “Promises and prospects of optoelectronic computing,” in LEOS Conference Proceedings IEEE Lasers and Electro-Optics Society Annual Meeting (IEEE, New York, 1993), pp. 69–70.
  2. L. Ji, V. P. Heuring, “The impact of gate fan-in and fan-out limits on optoelectronic digital circuits,” Appl. Opt. 36, 3937–3940 (1997).
    [CrossRef]
  3. J. A. Neff, “Optoelectronic arrays for hybrid optical/electronic computing,” in Digital Optical Computing II, R. Arrathoon, ed., Proc. SPIE1215, 44–54 (1990).
    [CrossRef]
  4. H. S. Hinton, T. J. Cloonan, F. B. McCormick, F. A. P. Tooley, A. L. Lentine, “Free-space digital optical systems,” Proc. IEEE—Special Issue on Optical Computing 82, 1632–1649 (1994).
  5. J. N. Lee, Design Issues in Optical Processing (Cambridge U. Press, Cambridge, 1995), pp. 84–131.
  6. A. Louri, J. Na, “Modeling and simulation methodology for digital optical computing systems,” Appl. Opt. 33, 1549–1558 (1994).
    [CrossRef] [PubMed]
  7. J. M. Xu, D. S. Ellis, “oeUT-spice: A CAD tool for design and simulation of OEIC,” in Optoelectronic Integrated Circuits, Y.-S. Park, R. V. Ramaswamy, eds., Proc. SPIE3006, 406–417 (1977).
    [CrossRef]
  8. J. J. Morikuni, S.-M. Kang, Computer-Aided Design of Optoelectronic Integrated Circuits and Systems (Prentice-Hall, Englewood Cliffs, N.J., 1997).
  9. S. Koh, L. Ye, “Modeling and simulation of optoelectronic multichip modules using vhdl,” in Optoelectronic Integrated Circuits, Y.-S. Park, R. V. Ramaswamy, eds., Proc. SPIE3006, 418–428 (1977).
    [CrossRef]
  10. D. Gajski, N. Dutt, A. Wu, S. Lin, “Design representation and transformation,” in High-Level Synthesis—Introduction to Chip and System Design (Kluwer, Dordrecht, The Netherlands, 1992).
  11. R. Waxman, J.-M. Bergé, O. Levia, J. Rouillard, High-Level System Modeling: Specification and Design Methodologies (Kluwer, Dordrecht, The Netherlands, 1996).
    [CrossRef]
  12. R. David, H. Alla, Petri Nets and Grafcet—Tools for Modeling Discrete Event Systems (Prentice-Hall, Englewood Cliffs, N.J., 1992).
  13. T. Murata, “Petri nets: properties, analysis and applications,” Proc. IEEE 77, 541–580 (1989).
    [CrossRef]
  14. K. Jensen, G. Rosenberg, High-Level Petri Nets: Theory and Applications (Springer-Verlag, Berlin, Heidelberg, 1991).
  15. W. M. Zuberek, “Timed Petri nets definitions, properties, and applications,” Microelectron. Reliab. 31, 627–644 (1991).
    [CrossRef]
  16. V. P. Heuring, L. H. Ji, R. J. Feuerstein, V. Morozov, “Toward a free-space parallel optoelectronic computer: a 300-MHz optoelectronic counter using holographic interconnects,” Appl. Opt. 33, 7579–7587 (1994).
    [CrossRef] [PubMed]
  17. L. Ferrarini, “An incremental approach to logic controller design with Petri nets,” IEEE Trans. Syst. Man Cybern. 22, 461–473 (1992).
    [CrossRef]
  18. V. Heuring, V. Morozov, “Synchronizing and controlling fast digital optical processors,” in Optical Computing, Vol. 7 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 188–191.
  19. J. P. Pratt, V. P. Heuring, “Delay synchronization in time-of-flight optical systems,” Appl. Opt. 31, 2430–2437 (1992).
    [CrossRef] [PubMed]
  20. M. J. Denham, Advanced Computing Concepts and Techniques in Control Engineering, Vol. F47 of NATO ASI Series (Springer-Verlag, Berlin, 1988), pp. 191–214.
    [CrossRef]
  21. W.-K. Chen, Theory of Nets: Flows in Networks (Wiley, New York, 1990).

1997 (1)

L. Ji, V. P. Heuring, “The impact of gate fan-in and fan-out limits on optoelectronic digital circuits,” Appl. Opt. 36, 3937–3940 (1997).
[CrossRef]

1994 (3)

1992 (2)

L. Ferrarini, “An incremental approach to logic controller design with Petri nets,” IEEE Trans. Syst. Man Cybern. 22, 461–473 (1992).
[CrossRef]

J. P. Pratt, V. P. Heuring, “Delay synchronization in time-of-flight optical systems,” Appl. Opt. 31, 2430–2437 (1992).
[CrossRef] [PubMed]

1991 (1)

W. M. Zuberek, “Timed Petri nets definitions, properties, and applications,” Microelectron. Reliab. 31, 627–644 (1991).
[CrossRef]

1989 (1)

T. Murata, “Petri nets: properties, analysis and applications,” Proc. IEEE 77, 541–580 (1989).
[CrossRef]

Alla, H.

R. David, H. Alla, Petri Nets and Grafcet—Tools for Modeling Discrete Event Systems (Prentice-Hall, Englewood Cliffs, N.J., 1992).

Bergé, J.-M.

R. Waxman, J.-M. Bergé, O. Levia, J. Rouillard, High-Level System Modeling: Specification and Design Methodologies (Kluwer, Dordrecht, The Netherlands, 1996).
[CrossRef]

Cathey, W. T.

W. T. Cathey, “Promises and prospects of optoelectronic computing,” in LEOS Conference Proceedings IEEE Lasers and Electro-Optics Society Annual Meeting (IEEE, New York, 1993), pp. 69–70.

Chen, W.-K.

W.-K. Chen, Theory of Nets: Flows in Networks (Wiley, New York, 1990).

Cloonan, T. J.

H. S. Hinton, T. J. Cloonan, F. B. McCormick, F. A. P. Tooley, A. L. Lentine, “Free-space digital optical systems,” Proc. IEEE—Special Issue on Optical Computing 82, 1632–1649 (1994).

David, R.

R. David, H. Alla, Petri Nets and Grafcet—Tools for Modeling Discrete Event Systems (Prentice-Hall, Englewood Cliffs, N.J., 1992).

Denham, M. J.

M. J. Denham, Advanced Computing Concepts and Techniques in Control Engineering, Vol. F47 of NATO ASI Series (Springer-Verlag, Berlin, 1988), pp. 191–214.
[CrossRef]

Dutt, N.

D. Gajski, N. Dutt, A. Wu, S. Lin, “Design representation and transformation,” in High-Level Synthesis—Introduction to Chip and System Design (Kluwer, Dordrecht, The Netherlands, 1992).

Ellis, D. S.

J. M. Xu, D. S. Ellis, “oeUT-spice: A CAD tool for design and simulation of OEIC,” in Optoelectronic Integrated Circuits, Y.-S. Park, R. V. Ramaswamy, eds., Proc. SPIE3006, 406–417 (1977).
[CrossRef]

Ferrarini, L.

L. Ferrarini, “An incremental approach to logic controller design with Petri nets,” IEEE Trans. Syst. Man Cybern. 22, 461–473 (1992).
[CrossRef]

Feuerstein, R. J.

Gajski, D.

D. Gajski, N. Dutt, A. Wu, S. Lin, “Design representation and transformation,” in High-Level Synthesis—Introduction to Chip and System Design (Kluwer, Dordrecht, The Netherlands, 1992).

Heuring, V.

V. Heuring, V. Morozov, “Synchronizing and controlling fast digital optical processors,” in Optical Computing, Vol. 7 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 188–191.

Heuring, V. P.

Hinton, H. S.

H. S. Hinton, T. J. Cloonan, F. B. McCormick, F. A. P. Tooley, A. L. Lentine, “Free-space digital optical systems,” Proc. IEEE—Special Issue on Optical Computing 82, 1632–1649 (1994).

Jensen, K.

K. Jensen, G. Rosenberg, High-Level Petri Nets: Theory and Applications (Springer-Verlag, Berlin, Heidelberg, 1991).

Ji, L.

L. Ji, V. P. Heuring, “The impact of gate fan-in and fan-out limits on optoelectronic digital circuits,” Appl. Opt. 36, 3937–3940 (1997).
[CrossRef]

Ji, L. H.

Kang, S.-M.

J. J. Morikuni, S.-M. Kang, Computer-Aided Design of Optoelectronic Integrated Circuits and Systems (Prentice-Hall, Englewood Cliffs, N.J., 1997).

Koh, S.

S. Koh, L. Ye, “Modeling and simulation of optoelectronic multichip modules using vhdl,” in Optoelectronic Integrated Circuits, Y.-S. Park, R. V. Ramaswamy, eds., Proc. SPIE3006, 418–428 (1977).
[CrossRef]

Lee, J. N.

J. N. Lee, Design Issues in Optical Processing (Cambridge U. Press, Cambridge, 1995), pp. 84–131.

Lentine, A. L.

H. S. Hinton, T. J. Cloonan, F. B. McCormick, F. A. P. Tooley, A. L. Lentine, “Free-space digital optical systems,” Proc. IEEE—Special Issue on Optical Computing 82, 1632–1649 (1994).

Levia, O.

R. Waxman, J.-M. Bergé, O. Levia, J. Rouillard, High-Level System Modeling: Specification and Design Methodologies (Kluwer, Dordrecht, The Netherlands, 1996).
[CrossRef]

Lin, S.

D. Gajski, N. Dutt, A. Wu, S. Lin, “Design representation and transformation,” in High-Level Synthesis—Introduction to Chip and System Design (Kluwer, Dordrecht, The Netherlands, 1992).

Louri, A.

McCormick, F. B.

H. S. Hinton, T. J. Cloonan, F. B. McCormick, F. A. P. Tooley, A. L. Lentine, “Free-space digital optical systems,” Proc. IEEE—Special Issue on Optical Computing 82, 1632–1649 (1994).

Morikuni, J. J.

J. J. Morikuni, S.-M. Kang, Computer-Aided Design of Optoelectronic Integrated Circuits and Systems (Prentice-Hall, Englewood Cliffs, N.J., 1997).

Morozov, V.

V. P. Heuring, L. H. Ji, R. J. Feuerstein, V. Morozov, “Toward a free-space parallel optoelectronic computer: a 300-MHz optoelectronic counter using holographic interconnects,” Appl. Opt. 33, 7579–7587 (1994).
[CrossRef] [PubMed]

V. Heuring, V. Morozov, “Synchronizing and controlling fast digital optical processors,” in Optical Computing, Vol. 7 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 188–191.

Murata, T.

T. Murata, “Petri nets: properties, analysis and applications,” Proc. IEEE 77, 541–580 (1989).
[CrossRef]

Na, J.

Neff, J. A.

J. A. Neff, “Optoelectronic arrays for hybrid optical/electronic computing,” in Digital Optical Computing II, R. Arrathoon, ed., Proc. SPIE1215, 44–54 (1990).
[CrossRef]

Pratt, J. P.

Rosenberg, G.

K. Jensen, G. Rosenberg, High-Level Petri Nets: Theory and Applications (Springer-Verlag, Berlin, Heidelberg, 1991).

Rouillard, J.

R. Waxman, J.-M. Bergé, O. Levia, J. Rouillard, High-Level System Modeling: Specification and Design Methodologies (Kluwer, Dordrecht, The Netherlands, 1996).
[CrossRef]

Tooley, F. A. P.

H. S. Hinton, T. J. Cloonan, F. B. McCormick, F. A. P. Tooley, A. L. Lentine, “Free-space digital optical systems,” Proc. IEEE—Special Issue on Optical Computing 82, 1632–1649 (1994).

Waxman, R.

R. Waxman, J.-M. Bergé, O. Levia, J. Rouillard, High-Level System Modeling: Specification and Design Methodologies (Kluwer, Dordrecht, The Netherlands, 1996).
[CrossRef]

Wu, A.

D. Gajski, N. Dutt, A. Wu, S. Lin, “Design representation and transformation,” in High-Level Synthesis—Introduction to Chip and System Design (Kluwer, Dordrecht, The Netherlands, 1992).

Xu, J. M.

J. M. Xu, D. S. Ellis, “oeUT-spice: A CAD tool for design and simulation of OEIC,” in Optoelectronic Integrated Circuits, Y.-S. Park, R. V. Ramaswamy, eds., Proc. SPIE3006, 406–417 (1977).
[CrossRef]

Ye, L.

S. Koh, L. Ye, “Modeling and simulation of optoelectronic multichip modules using vhdl,” in Optoelectronic Integrated Circuits, Y.-S. Park, R. V. Ramaswamy, eds., Proc. SPIE3006, 418–428 (1977).
[CrossRef]

Zuberek, W. M.

W. M. Zuberek, “Timed Petri nets definitions, properties, and applications,” Microelectron. Reliab. 31, 627–644 (1991).
[CrossRef]

Appl. Opt. (4)

IEEE Trans. Syst. Man Cybern. (1)

L. Ferrarini, “An incremental approach to logic controller design with Petri nets,” IEEE Trans. Syst. Man Cybern. 22, 461–473 (1992).
[CrossRef]

Microelectron. Reliab. (1)

W. M. Zuberek, “Timed Petri nets definitions, properties, and applications,” Microelectron. Reliab. 31, 627–644 (1991).
[CrossRef]

Proc. IEEE (2)

T. Murata, “Petri nets: properties, analysis and applications,” Proc. IEEE 77, 541–580 (1989).
[CrossRef]

H. S. Hinton, T. J. Cloonan, F. B. McCormick, F. A. P. Tooley, A. L. Lentine, “Free-space digital optical systems,” Proc. IEEE—Special Issue on Optical Computing 82, 1632–1649 (1994).

Other (13)

J. N. Lee, Design Issues in Optical Processing (Cambridge U. Press, Cambridge, 1995), pp. 84–131.

J. A. Neff, “Optoelectronic arrays for hybrid optical/electronic computing,” in Digital Optical Computing II, R. Arrathoon, ed., Proc. SPIE1215, 44–54 (1990).
[CrossRef]

J. M. Xu, D. S. Ellis, “oeUT-spice: A CAD tool for design and simulation of OEIC,” in Optoelectronic Integrated Circuits, Y.-S. Park, R. V. Ramaswamy, eds., Proc. SPIE3006, 406–417 (1977).
[CrossRef]

J. J. Morikuni, S.-M. Kang, Computer-Aided Design of Optoelectronic Integrated Circuits and Systems (Prentice-Hall, Englewood Cliffs, N.J., 1997).

S. Koh, L. Ye, “Modeling and simulation of optoelectronic multichip modules using vhdl,” in Optoelectronic Integrated Circuits, Y.-S. Park, R. V. Ramaswamy, eds., Proc. SPIE3006, 418–428 (1977).
[CrossRef]

D. Gajski, N. Dutt, A. Wu, S. Lin, “Design representation and transformation,” in High-Level Synthesis—Introduction to Chip and System Design (Kluwer, Dordrecht, The Netherlands, 1992).

R. Waxman, J.-M. Bergé, O. Levia, J. Rouillard, High-Level System Modeling: Specification and Design Methodologies (Kluwer, Dordrecht, The Netherlands, 1996).
[CrossRef]

R. David, H. Alla, Petri Nets and Grafcet—Tools for Modeling Discrete Event Systems (Prentice-Hall, Englewood Cliffs, N.J., 1992).

K. Jensen, G. Rosenberg, High-Level Petri Nets: Theory and Applications (Springer-Verlag, Berlin, Heidelberg, 1991).

W. T. Cathey, “Promises and prospects of optoelectronic computing,” in LEOS Conference Proceedings IEEE Lasers and Electro-Optics Society Annual Meeting (IEEE, New York, 1993), pp. 69–70.

V. Heuring, V. Morozov, “Synchronizing and controlling fast digital optical processors,” in Optical Computing, Vol. 7 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 188–191.

M. J. Denham, Advanced Computing Concepts and Techniques in Control Engineering, Vol. F47 of NATO ASI Series (Springer-Verlag, Berlin, 1988), pp. 191–214.
[CrossRef]

W.-K. Chen, Theory of Nets: Flows in Networks (Wiley, New York, 1990).

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Figures (10)

Fig. 1
Fig. 1

Two-stage free-space optoelectronic architecture with 2-D smart-pixel arrays and holographic interconnects.

Fig. 2
Fig. 2

Example PN illustrating a transition (firing) rule: (a) The marking before firing the enabled transition t 3. (b) The marking after firing t 3.

Fig. 4
Fig. 4

Optical and optoelectronic device models.

Fig. 5
Fig. 5

Device data structure.

Fig. 6
Fig. 6

Token data structure.

Fig. 7
Fig. 7

Model of a smart pixel (an optoelectronic logical nor gate).

Fig. 8
Fig. 8

Models for a simple optoelectronic oscillator: (a) two-dimensional projection of an optoelectronic circuit and (b) PN model showing an initial marking (place p 2) and the enabled transitions {t 2}.

Fig. 9
Fig. 9

(a) PN simulation of a simple optoelectronic oscillator. Each diagram shows the current marking obtained from the firing of transitions in the proceding net and the transitions enabled by the current marking. (b) Oscillator timing analysis. The occurrence and the sequence of events is indicated by the marking of the net.

Fig. 10
Fig. 10

(a) Two-dimensional projection of optoelectronic model of a signal stretch circuit. (b) Signal-stretch circuit by the PN model. (c) Signal-stretch circuit timing analysis.

Tables (1)

Tables Icon

Table 1 Comparison of System-Design Models

Equations (2)

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τ = output _ device _ latency + OPL c + T b + input _ device _ latency ,
Repeat {     Find the set of enabled transitions .     Fire all transitions concurrently . } .

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