Abstract

Decreasing the system volume for optoelectronic (OE) planar systems is achieved by advancing computer-aided design of OE multichip modules (MCM’s). It is shown that in order to minimize the volume in an OE MCM, it is necessary to minimize the maximum interconnect distance. To achieve this, we have developed placement algorithms based on the constraints of a given irregular interconnect pattern. Results are given for a twin-butterfly network for two general physical models: a transmissive MCM and a reflective MCM. We then show three different types of hologram design that can be used to implement the interconnect array. These elements are for reconstruction in the near field and are fabricated by direct-write electron-beam lithography. Both simulated and experimental reconstructions are demonstrated.

© 1994 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. H. Wu, L. A. Bergman, A. R. Johnson, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron. Dev. ED-34, 706–714 (1987).
    [CrossRef]
  2. D. Z. Tsang, D. L. Smthe, A. Chu, J. J. Lambert, “A technology for optical interconnections based on multichip integration,” Opt. Eng. 25, 1127–1131 (1986).
  3. C. A. Armiento, A. J. Negri, M. J. Tabasky, R. A. Boudreau, M. A. Rothman, T. W. Fitzgerald, P. O. Haugsjaa, “Gigabit transmitter array modules on silicon waferboard,” IEEE Trans. Comp. Hybrid Manuf. Technol. 15, 1072–1079 (1992).
    [CrossRef]
  4. J. W. Goodman, F. J. Leonberger, S. Y. Kang, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1989).
    [CrossRef]
  5. J. Jahns, A. Huang, “Planar integration of free-space optical components,” Appl. Opt. 28, 1602–1604 (1989).
    [CrossRef] [PubMed]
  6. K. Iga, M. Oikawa, S. Misawa, J. Banno, Y. Kokubun, “Stacked planar optics: an application of the planar microlens,” Appl. Opt. 21, 3456–3460 (1982).
    [CrossRef] [PubMed]
  7. K. S. Urquhart, P. Marchand, Y. Fainman, S. H. Lee, “Design of free-space optical interconnection modules utilizing diffractive optics,” submitted to Appl. Opt.
  8. W. Daschner, R. Stein, S. H. Lee, “Alignment and assembly of diffractive optical elements for optical system packaging,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 183.
  9. M. Nakkar, J. Stack, W. H. Welch, M. R. Feldman, “Computer generated holograms for large deflection angle optical interconnects,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 189.
  10. F. Kiamilev, J. Fan, B. Catanzaro, S. Esener, S. H. Lee, “The architecture of an integrated computer aided design system for optoelectronics,” in Microelectronic Interconnects and Packages: System and Process Integration, J. R. Carruthers, S. K. Tewksbury, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1390, 311–329 (1990).
  11. C. Sechen, A. Sangiovanni-Vincentelli, “The Timber-Wolf placement and routing package,” in Proceedings of the 1984 Custom Integrated Circuits Conference (Institute of Electrical and Electronics Engineers, New York, 1984), pp. 522–527.
  12. J. Fan, D. Zaleta, C. K. Cheng, S. H. Lee, “Physical layout for computer generated holograms for optoelectronic multichip modules,” in Proceedings of the IEEE Conference on Multichip Modules (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 198–203.
    [CrossRef]
  13. D. Zaleta, J. Fan, C. K. Cheng, S. H. Lee, “Simulated annealing applied to placement of processing elements in optoelectronic multichip modules interconnected by computer generated holograms,” in Optical Computing, Vol. 7 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 196–199.
  14. J. Fan, D. Zaleta, C. K. Cheng, S. H. Lee, “Requirements and physical layout algorithms for optoelectronic MCM,” submitted to IEEE Design Test.
  15. J. Edmonds, D. R. Fulkerson, “Bottleneck extrema,” J. Combin. Theory 8, 299–306 (1989).
  16. E. L. Lawler, Combinatorial Optimization: Networks and Matroids (Holt, Rinehart and Winston, New York, 1976), Sec. 5.7.
  17. C. Gelatt, S. Kirkpatrick, M. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
    [CrossRef] [PubMed]
  18. T. Leighton, B. Maggs, “Expander might be practical: fast algorithms for routing around faults on multibutterflies,” in Proceedings of the IEEE Symposium on the Foundation of Computer Science (Institute of Electrical and Electronics Engineers, New York, 1989), pp. 384–389.
  19. D. T. Lu, R. Paturi, S. Fainman, S. H. Lee, “Smart pixels for twin-butterfly interconnection network,” in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 199.
  20. B. Kress, D. E. Zaleta, S. H. Lee, “Iterative design of CGH for free-space optical interconnections,” in Optical Computing, Vol. 7 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 22–25.
  21. K. S. Urquhart, S. H. Lee, “Phase-only encoding method for complex wavefronts,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1555, 13–22 (1991).
  22. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  23. K. S. Urquhart, R. Stein, S. H. Lee, “Computer-generated holograms fabricated by direct write of positive electron-beam resist,” Opt. Lett. 18, 308–310 (1993).
    [CrossRef] [PubMed]

1993 (1)

1992 (1)

C. A. Armiento, A. J. Negri, M. J. Tabasky, R. A. Boudreau, M. A. Rothman, T. W. Fitzgerald, P. O. Haugsjaa, “Gigabit transmitter array modules on silicon waferboard,” IEEE Trans. Comp. Hybrid Manuf. Technol. 15, 1072–1079 (1992).
[CrossRef]

1989 (3)

J. W. Goodman, F. J. Leonberger, S. Y. Kang, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1989).
[CrossRef]

J. Jahns, A. Huang, “Planar integration of free-space optical components,” Appl. Opt. 28, 1602–1604 (1989).
[CrossRef] [PubMed]

J. Edmonds, D. R. Fulkerson, “Bottleneck extrema,” J. Combin. Theory 8, 299–306 (1989).

1987 (1)

W. H. Wu, L. A. Bergman, A. R. Johnson, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron. Dev. ED-34, 706–714 (1987).
[CrossRef]

1986 (1)

D. Z. Tsang, D. L. Smthe, A. Chu, J. J. Lambert, “A technology for optical interconnections based on multichip integration,” Opt. Eng. 25, 1127–1131 (1986).

1983 (1)

C. Gelatt, S. Kirkpatrick, M. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

1982 (1)

1972 (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Armiento, C. A.

C. A. Armiento, A. J. Negri, M. J. Tabasky, R. A. Boudreau, M. A. Rothman, T. W. Fitzgerald, P. O. Haugsjaa, “Gigabit transmitter array modules on silicon waferboard,” IEEE Trans. Comp. Hybrid Manuf. Technol. 15, 1072–1079 (1992).
[CrossRef]

Athale, R. A.

J. W. Goodman, F. J. Leonberger, S. Y. Kang, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1989).
[CrossRef]

Banno, J.

Bergman, L. A.

W. H. Wu, L. A. Bergman, A. R. Johnson, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron. Dev. ED-34, 706–714 (1987).
[CrossRef]

Boudreau, R. A.

C. A. Armiento, A. J. Negri, M. J. Tabasky, R. A. Boudreau, M. A. Rothman, T. W. Fitzgerald, P. O. Haugsjaa, “Gigabit transmitter array modules on silicon waferboard,” IEEE Trans. Comp. Hybrid Manuf. Technol. 15, 1072–1079 (1992).
[CrossRef]

Catanzaro, B.

F. Kiamilev, J. Fan, B. Catanzaro, S. Esener, S. H. Lee, “The architecture of an integrated computer aided design system for optoelectronics,” in Microelectronic Interconnects and Packages: System and Process Integration, J. R. Carruthers, S. K. Tewksbury, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1390, 311–329 (1990).

Cheng, C. K.

J. Fan, D. Zaleta, C. K. Cheng, S. H. Lee, “Physical layout for computer generated holograms for optoelectronic multichip modules,” in Proceedings of the IEEE Conference on Multichip Modules (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 198–203.
[CrossRef]

D. Zaleta, J. Fan, C. K. Cheng, S. H. Lee, “Simulated annealing applied to placement of processing elements in optoelectronic multichip modules interconnected by computer generated holograms,” in Optical Computing, Vol. 7 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 196–199.

J. Fan, D. Zaleta, C. K. Cheng, S. H. Lee, “Requirements and physical layout algorithms for optoelectronic MCM,” submitted to IEEE Design Test.

Chu, A.

D. Z. Tsang, D. L. Smthe, A. Chu, J. J. Lambert, “A technology for optical interconnections based on multichip integration,” Opt. Eng. 25, 1127–1131 (1986).

Daschner, W.

W. Daschner, R. Stein, S. H. Lee, “Alignment and assembly of diffractive optical elements for optical system packaging,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 183.

Edmonds, J.

J. Edmonds, D. R. Fulkerson, “Bottleneck extrema,” J. Combin. Theory 8, 299–306 (1989).

Esener, S.

F. Kiamilev, J. Fan, B. Catanzaro, S. Esener, S. H. Lee, “The architecture of an integrated computer aided design system for optoelectronics,” in Microelectronic Interconnects and Packages: System and Process Integration, J. R. Carruthers, S. K. Tewksbury, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1390, 311–329 (1990).

Esener, S. C.

W. H. Wu, L. A. Bergman, A. R. Johnson, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron. Dev. ED-34, 706–714 (1987).
[CrossRef]

Fainman, S.

D. T. Lu, R. Paturi, S. Fainman, S. H. Lee, “Smart pixels for twin-butterfly interconnection network,” in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 199.

Fainman, Y.

K. S. Urquhart, P. Marchand, Y. Fainman, S. H. Lee, “Design of free-space optical interconnection modules utilizing diffractive optics,” submitted to Appl. Opt.

Fan, J.

J. Fan, D. Zaleta, C. K. Cheng, S. H. Lee, “Requirements and physical layout algorithms for optoelectronic MCM,” submitted to IEEE Design Test.

J. Fan, D. Zaleta, C. K. Cheng, S. H. Lee, “Physical layout for computer generated holograms for optoelectronic multichip modules,” in Proceedings of the IEEE Conference on Multichip Modules (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 198–203.
[CrossRef]

F. Kiamilev, J. Fan, B. Catanzaro, S. Esener, S. H. Lee, “The architecture of an integrated computer aided design system for optoelectronics,” in Microelectronic Interconnects and Packages: System and Process Integration, J. R. Carruthers, S. K. Tewksbury, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1390, 311–329 (1990).

D. Zaleta, J. Fan, C. K. Cheng, S. H. Lee, “Simulated annealing applied to placement of processing elements in optoelectronic multichip modules interconnected by computer generated holograms,” in Optical Computing, Vol. 7 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 196–199.

Feldman, M. R.

W. H. Wu, L. A. Bergman, A. R. Johnson, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron. Dev. ED-34, 706–714 (1987).
[CrossRef]

M. Nakkar, J. Stack, W. H. Welch, M. R. Feldman, “Computer generated holograms for large deflection angle optical interconnects,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 189.

Fitzgerald, T. W.

C. A. Armiento, A. J. Negri, M. J. Tabasky, R. A. Boudreau, M. A. Rothman, T. W. Fitzgerald, P. O. Haugsjaa, “Gigabit transmitter array modules on silicon waferboard,” IEEE Trans. Comp. Hybrid Manuf. Technol. 15, 1072–1079 (1992).
[CrossRef]

Fulkerson, D. R.

J. Edmonds, D. R. Fulkerson, “Bottleneck extrema,” J. Combin. Theory 8, 299–306 (1989).

Gelatt, C.

C. Gelatt, S. Kirkpatrick, M. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Goodman, J. W.

J. W. Goodman, F. J. Leonberger, S. Y. Kang, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1989).
[CrossRef]

Guest, C. C.

W. H. Wu, L. A. Bergman, A. R. Johnson, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron. Dev. ED-34, 706–714 (1987).
[CrossRef]

Haugsjaa, P. O.

C. A. Armiento, A. J. Negri, M. J. Tabasky, R. A. Boudreau, M. A. Rothman, T. W. Fitzgerald, P. O. Haugsjaa, “Gigabit transmitter array modules on silicon waferboard,” IEEE Trans. Comp. Hybrid Manuf. Technol. 15, 1072–1079 (1992).
[CrossRef]

Huang, A.

Iga, K.

Jahns, J.

Johnson, A. R.

W. H. Wu, L. A. Bergman, A. R. Johnson, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron. Dev. ED-34, 706–714 (1987).
[CrossRef]

Kang, S. Y.

J. W. Goodman, F. J. Leonberger, S. Y. Kang, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1989).
[CrossRef]

Kiamilev, F.

F. Kiamilev, J. Fan, B. Catanzaro, S. Esener, S. H. Lee, “The architecture of an integrated computer aided design system for optoelectronics,” in Microelectronic Interconnects and Packages: System and Process Integration, J. R. Carruthers, S. K. Tewksbury, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1390, 311–329 (1990).

Kirkpatrick, S.

C. Gelatt, S. Kirkpatrick, M. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Kokubun, Y.

Kress, B.

B. Kress, D. E. Zaleta, S. H. Lee, “Iterative design of CGH for free-space optical interconnections,” in Optical Computing, Vol. 7 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 22–25.

Lambert, J. J.

D. Z. Tsang, D. L. Smthe, A. Chu, J. J. Lambert, “A technology for optical interconnections based on multichip integration,” Opt. Eng. 25, 1127–1131 (1986).

Lawler, E. L.

E. L. Lawler, Combinatorial Optimization: Networks and Matroids (Holt, Rinehart and Winston, New York, 1976), Sec. 5.7.

Lee, S. H.

K. S. Urquhart, R. Stein, S. H. Lee, “Computer-generated holograms fabricated by direct write of positive electron-beam resist,” Opt. Lett. 18, 308–310 (1993).
[CrossRef] [PubMed]

W. H. Wu, L. A. Bergman, A. R. Johnson, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron. Dev. ED-34, 706–714 (1987).
[CrossRef]

K. S. Urquhart, P. Marchand, Y. Fainman, S. H. Lee, “Design of free-space optical interconnection modules utilizing diffractive optics,” submitted to Appl. Opt.

J. Fan, D. Zaleta, C. K. Cheng, S. H. Lee, “Requirements and physical layout algorithms for optoelectronic MCM,” submitted to IEEE Design Test.

D. Zaleta, J. Fan, C. K. Cheng, S. H. Lee, “Simulated annealing applied to placement of processing elements in optoelectronic multichip modules interconnected by computer generated holograms,” in Optical Computing, Vol. 7 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 196–199.

D. T. Lu, R. Paturi, S. Fainman, S. H. Lee, “Smart pixels for twin-butterfly interconnection network,” in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 199.

J. Fan, D. Zaleta, C. K. Cheng, S. H. Lee, “Physical layout for computer generated holograms for optoelectronic multichip modules,” in Proceedings of the IEEE Conference on Multichip Modules (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 198–203.
[CrossRef]

F. Kiamilev, J. Fan, B. Catanzaro, S. Esener, S. H. Lee, “The architecture of an integrated computer aided design system for optoelectronics,” in Microelectronic Interconnects and Packages: System and Process Integration, J. R. Carruthers, S. K. Tewksbury, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1390, 311–329 (1990).

W. Daschner, R. Stein, S. H. Lee, “Alignment and assembly of diffractive optical elements for optical system packaging,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 183.

B. Kress, D. E. Zaleta, S. H. Lee, “Iterative design of CGH for free-space optical interconnections,” in Optical Computing, Vol. 7 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 22–25.

K. S. Urquhart, S. H. Lee, “Phase-only encoding method for complex wavefronts,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1555, 13–22 (1991).

Leighton, T.

T. Leighton, B. Maggs, “Expander might be practical: fast algorithms for routing around faults on multibutterflies,” in Proceedings of the IEEE Symposium on the Foundation of Computer Science (Institute of Electrical and Electronics Engineers, New York, 1989), pp. 384–389.

Leonberger, F. J.

J. W. Goodman, F. J. Leonberger, S. Y. Kang, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1989).
[CrossRef]

Lu, D. T.

D. T. Lu, R. Paturi, S. Fainman, S. H. Lee, “Smart pixels for twin-butterfly interconnection network,” in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 199.

Maggs, B.

T. Leighton, B. Maggs, “Expander might be practical: fast algorithms for routing around faults on multibutterflies,” in Proceedings of the IEEE Symposium on the Foundation of Computer Science (Institute of Electrical and Electronics Engineers, New York, 1989), pp. 384–389.

Marchand, P.

K. S. Urquhart, P. Marchand, Y. Fainman, S. H. Lee, “Design of free-space optical interconnection modules utilizing diffractive optics,” submitted to Appl. Opt.

Misawa, S.

Nakkar, M.

M. Nakkar, J. Stack, W. H. Welch, M. R. Feldman, “Computer generated holograms for large deflection angle optical interconnects,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 189.

Negri, A. J.

C. A. Armiento, A. J. Negri, M. J. Tabasky, R. A. Boudreau, M. A. Rothman, T. W. Fitzgerald, P. O. Haugsjaa, “Gigabit transmitter array modules on silicon waferboard,” IEEE Trans. Comp. Hybrid Manuf. Technol. 15, 1072–1079 (1992).
[CrossRef]

Oikawa, M.

Paturi, R.

D. T. Lu, R. Paturi, S. Fainman, S. H. Lee, “Smart pixels for twin-butterfly interconnection network,” in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 199.

Rothman, M. A.

C. A. Armiento, A. J. Negri, M. J. Tabasky, R. A. Boudreau, M. A. Rothman, T. W. Fitzgerald, P. O. Haugsjaa, “Gigabit transmitter array modules on silicon waferboard,” IEEE Trans. Comp. Hybrid Manuf. Technol. 15, 1072–1079 (1992).
[CrossRef]

Sangiovanni-Vincentelli, A.

C. Sechen, A. Sangiovanni-Vincentelli, “The Timber-Wolf placement and routing package,” in Proceedings of the 1984 Custom Integrated Circuits Conference (Institute of Electrical and Electronics Engineers, New York, 1984), pp. 522–527.

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Sechen, C.

C. Sechen, A. Sangiovanni-Vincentelli, “The Timber-Wolf placement and routing package,” in Proceedings of the 1984 Custom Integrated Circuits Conference (Institute of Electrical and Electronics Engineers, New York, 1984), pp. 522–527.

Smthe, D. L.

D. Z. Tsang, D. L. Smthe, A. Chu, J. J. Lambert, “A technology for optical interconnections based on multichip integration,” Opt. Eng. 25, 1127–1131 (1986).

Stack, J.

M. Nakkar, J. Stack, W. H. Welch, M. R. Feldman, “Computer generated holograms for large deflection angle optical interconnects,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 189.

Stein, R.

K. S. Urquhart, R. Stein, S. H. Lee, “Computer-generated holograms fabricated by direct write of positive electron-beam resist,” Opt. Lett. 18, 308–310 (1993).
[CrossRef] [PubMed]

W. Daschner, R. Stein, S. H. Lee, “Alignment and assembly of diffractive optical elements for optical system packaging,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 183.

Tabasky, M. J.

C. A. Armiento, A. J. Negri, M. J. Tabasky, R. A. Boudreau, M. A. Rothman, T. W. Fitzgerald, P. O. Haugsjaa, “Gigabit transmitter array modules on silicon waferboard,” IEEE Trans. Comp. Hybrid Manuf. Technol. 15, 1072–1079 (1992).
[CrossRef]

Tsang, D. Z.

D. Z. Tsang, D. L. Smthe, A. Chu, J. J. Lambert, “A technology for optical interconnections based on multichip integration,” Opt. Eng. 25, 1127–1131 (1986).

Urquhart, K. S.

K. S. Urquhart, R. Stein, S. H. Lee, “Computer-generated holograms fabricated by direct write of positive electron-beam resist,” Opt. Lett. 18, 308–310 (1993).
[CrossRef] [PubMed]

K. S. Urquhart, S. H. Lee, “Phase-only encoding method for complex wavefronts,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1555, 13–22 (1991).

K. S. Urquhart, P. Marchand, Y. Fainman, S. H. Lee, “Design of free-space optical interconnection modules utilizing diffractive optics,” submitted to Appl. Opt.

Vecchi, M.

C. Gelatt, S. Kirkpatrick, M. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Welch, W. H.

M. Nakkar, J. Stack, W. H. Welch, M. R. Feldman, “Computer generated holograms for large deflection angle optical interconnects,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 189.

Wu, W. H.

W. H. Wu, L. A. Bergman, A. R. Johnson, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron. Dev. ED-34, 706–714 (1987).
[CrossRef]

Yu, P. K. L.

W. H. Wu, L. A. Bergman, A. R. Johnson, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron. Dev. ED-34, 706–714 (1987).
[CrossRef]

Zaleta, D.

D. Zaleta, J. Fan, C. K. Cheng, S. H. Lee, “Simulated annealing applied to placement of processing elements in optoelectronic multichip modules interconnected by computer generated holograms,” in Optical Computing, Vol. 7 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 196–199.

J. Fan, D. Zaleta, C. K. Cheng, S. H. Lee, “Physical layout for computer generated holograms for optoelectronic multichip modules,” in Proceedings of the IEEE Conference on Multichip Modules (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 198–203.
[CrossRef]

J. Fan, D. Zaleta, C. K. Cheng, S. H. Lee, “Requirements and physical layout algorithms for optoelectronic MCM,” submitted to IEEE Design Test.

Zaleta, D. E.

B. Kress, D. E. Zaleta, S. H. Lee, “Iterative design of CGH for free-space optical interconnections,” in Optical Computing, Vol. 7 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 22–25.

Appl. Opt. (2)

IEEE Trans. Comp. Hybrid Manuf. Technol. (1)

C. A. Armiento, A. J. Negri, M. J. Tabasky, R. A. Boudreau, M. A. Rothman, T. W. Fitzgerald, P. O. Haugsjaa, “Gigabit transmitter array modules on silicon waferboard,” IEEE Trans. Comp. Hybrid Manuf. Technol. 15, 1072–1079 (1992).
[CrossRef]

IEEE Trans. Electron. Dev. (1)

W. H. Wu, L. A. Bergman, A. R. Johnson, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron. Dev. ED-34, 706–714 (1987).
[CrossRef]

J. Combin. Theory (1)

J. Edmonds, D. R. Fulkerson, “Bottleneck extrema,” J. Combin. Theory 8, 299–306 (1989).

Opt. Eng. (1)

D. Z. Tsang, D. L. Smthe, A. Chu, J. J. Lambert, “A technology for optical interconnections based on multichip integration,” Opt. Eng. 25, 1127–1131 (1986).

Opt. Lett. (1)

Optik (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Proc. IEEE (1)

J. W. Goodman, F. J. Leonberger, S. Y. Kang, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1989).
[CrossRef]

Science (1)

C. Gelatt, S. Kirkpatrick, M. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Other (13)

T. Leighton, B. Maggs, “Expander might be practical: fast algorithms for routing around faults on multibutterflies,” in Proceedings of the IEEE Symposium on the Foundation of Computer Science (Institute of Electrical and Electronics Engineers, New York, 1989), pp. 384–389.

D. T. Lu, R. Paturi, S. Fainman, S. H. Lee, “Smart pixels for twin-butterfly interconnection network,” in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 199.

B. Kress, D. E. Zaleta, S. H. Lee, “Iterative design of CGH for free-space optical interconnections,” in Optical Computing, Vol. 7 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 22–25.

K. S. Urquhart, S. H. Lee, “Phase-only encoding method for complex wavefronts,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1555, 13–22 (1991).

K. S. Urquhart, P. Marchand, Y. Fainman, S. H. Lee, “Design of free-space optical interconnection modules utilizing diffractive optics,” submitted to Appl. Opt.

W. Daschner, R. Stein, S. H. Lee, “Alignment and assembly of diffractive optical elements for optical system packaging,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 183.

M. Nakkar, J. Stack, W. H. Welch, M. R. Feldman, “Computer generated holograms for large deflection angle optical interconnects,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 189.

F. Kiamilev, J. Fan, B. Catanzaro, S. Esener, S. H. Lee, “The architecture of an integrated computer aided design system for optoelectronics,” in Microelectronic Interconnects and Packages: System and Process Integration, J. R. Carruthers, S. K. Tewksbury, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1390, 311–329 (1990).

C. Sechen, A. Sangiovanni-Vincentelli, “The Timber-Wolf placement and routing package,” in Proceedings of the 1984 Custom Integrated Circuits Conference (Institute of Electrical and Electronics Engineers, New York, 1984), pp. 522–527.

J. Fan, D. Zaleta, C. K. Cheng, S. H. Lee, “Physical layout for computer generated holograms for optoelectronic multichip modules,” in Proceedings of the IEEE Conference on Multichip Modules (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 198–203.
[CrossRef]

D. Zaleta, J. Fan, C. K. Cheng, S. H. Lee, “Simulated annealing applied to placement of processing elements in optoelectronic multichip modules interconnected by computer generated holograms,” in Optical Computing, Vol. 7 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 196–199.

J. Fan, D. Zaleta, C. K. Cheng, S. H. Lee, “Requirements and physical layout algorithms for optoelectronic MCM,” submitted to IEEE Design Test.

E. L. Lawler, Combinatorial Optimization: Networks and Matroids (Holt, Rinehart and Winston, New York, 1976), Sec. 5.7.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (18)

Fig. 1
Fig. 1

Optical interconnect model used to provide justification for the placement algorithm’s cost function being based on the MID. SLM, spatial light modulator; CGH, computer-generated hologram.

Fig. 2
Fig. 2

Relationship between the minimum features size Δr and the angle θ for f = 2.5 mm, D = 250 μm, λ = 0.8 μm, and n = 4.

Fig. 3
Fig. 3

Two OE MCM physical models: (a) transmissive MCM, (b) reflective MCM.

Fig. 4
Fig. 4

Multistage interconnection network logical model used to formulate the 2-D placement problem for the transmissive and the reflective MCM cases.

Fig. 5
Fig. 5

Interconnect netlist for the first stage of 64-PE’s/stage twin-butterfly network. Every node has a fan-out of 4. Two of the four connections (columns 1 and 3) follow the standard butterfly network. The other two are chosen with a uniform random distribution (columns 2 and 4) from the top and the bottom halves of the twin butterfly.

Fig. 6
Fig. 6

Comparison between (a) SFP and (b) placement by matching algorithm. Only the first stage is shown here. For the SFP the other stages are identical. The worst-case interconnect distance for SFP is 8.602, which occurs from PE 23 on plane P 0 to PE 56 on plane P 1 (outlined box). The worst-case interconnect distance for the matching algorithm is 4.24, which occurs from PE 49 on plane P 0 to PE 49 on plane P 1 (also marked).

Fig. 7
Fig. 7

Histogram of all the interconnect distances for the placement of a 64 PE’s/stage, six-stage twin butterfly with SFP, matching placement, and simulated annealing placement.

Fig. 8
Fig. 8

Mask for the CGH Fresnel lens interconnect array based on (a) the SFP [which corresponds to the holograms required for the 4 PE’s in plane P 0 marked in Fig. 6(a)], (b) the matching algorithm placement [corresponds to the hologram array required for the 4 PE’s in plane P 0 marked in Fig. 6(b)]. Note the improvement in the worst-case interconnect of the SFP (fourth column, second row) versus the worst-case interconnect distance of the matching algorithm placement (first column, second row).

Fig. 9
Fig. 9

Computation time required with the simulated annealing algorithm for the transmissive MCM, reflective MCM, and reflective WSI (on a Sun Sparcstation 2 with a performance of 26 MIPS). See Appendix A for the reflective WSI case.

Fig. 10
Fig. 10

Comparison of simulated annealing placement and SFP for all eight physical cases.

Fig. 11
Fig. 11

Comparison of placement results for the constrained I/O and unconstrained I/O cases with the simulated annealing algorithm.

Fig. 12
Fig. 12

Illustration of the GS algorithm modified for reconstruction in the near field.

Fig. 13
Fig. 13

2 × 2 array of 16 phase-level kinoforms designed with the modified GS algorithm.

Fig. 14
Fig. 14

Scanning electron microscopy micrograph of the modified GS hologram fabricated with direct-write electron-beam lithography.

Fig. 15
Fig. 15

Modified GS hologram reconstruction: (a) simulated reconstruction, (b) experimental reconstruction.

Fig. 16
Fig. 16

Physical model used for WSI placement.

Fig. 17
Fig. 17

Logical model used to formulate the placement problem for the WSI case. Note that the cost function, in this case, is defined as the MID over the entire wafer.

Fig. 18
Fig. 18

Comparison of simulated annealing WSI placement (constrained and unconstrained cases) with SFP.

Tables (2)

Tables Icon

Table 1 Statistical Comparison between the MID Value Produced by Matching, Simulated Annealing and SFP Algorithms

Tables Icon

Table 2 Theoretical Diffraction Efficiency (DE) and SNR Values Three Different DOE Design Methods

Equations (12)

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

ϕ ( x , y ) = 2 π λ { f - [ f 2 + ( x - δ x ) 2 + ( y - δ y ) 2 ] 1 / 2 } ,
Δ r = r ( i max ) - r ( i max - 1 ) ,
r ( i ) = [ i f λ 2 n - 1 + ( i λ 2 n ) 2 ] 1 / 2 , i max = 2 n λ { [ ( D / 2 + δ ) 2 + f 2 ] 1 / 2 - f } ,
tan ( θ ) = δ f = d t
d ( p k i , p m j ) = [ ( x k i - x m j ) 2 + ( y k i - y m j ) 2 ] 1 / 2 ,
C k = max i j { d [ p k i , p ( k - 1 ) j ] , d [ p k i , p ( k + 1 ) j ] } .
d ( p k i , p m j ) = [ ( x k i - x m j - w ) 2 + ( y k i - y m j ) 2 ] ,
w g i = max v W v ( g , i ) ,             k = 1 , w g i = max u , v W u ( g , i ) W v ( g , i ) ,             1 < k < N , w g i = max u W u ( g , i ) ,             k = N
W u = { d { σ ( k - 1 ) [ e ( k - 1 ) u ] , p k j } e ( k - 1 ) u and e k g are interconnected } , W v = { d { p k j , σ ( k + 1 ) [ e ( k + 1 ) v ] } e ( k + 1 ) v and e k g are interconnected } ,
n = 1 N exp [ - i ϕ n ( x , y ) ] rect ( x - x n X ) rect ( y - y n Y ) ,
ϕ n ( x , y ) = π λ z [ ( x - x n ) 2 + ( y - y n ) 2 ]
n = 1 N exp [ - i ϕ n ( x , y ) ] rect ( x X ) rect ( y Y ) ,

Metrics