Abstract

We present a general-purpose three-dimensional interconnection network that models various parallel operations between two data planes. This volume interconnection system exhibits reconfigurable capabilities because of parallel and externally weighted interconnection modules, called nodes. We propose a generic optical implementation based on the cascading of two planar hologram arrays, coupled with a bistable optically addressed spatial light modulator. The role of this component is discussed in terms of energy regeneration and spatial cross-talk limitation. As an example, a binary matrix–matrix multiplier is implemented that uses a ferroelectric liquid-crystal light valve.

© 1994 Optical Society of America

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References

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  1. L. M. Deen, J. F. Walkup, M. O. Hagler, “Representations of space-variant optical systems using volume holograms,” Appl. Opt. 14, 2438–2446 (1975).
    [CrossRef] [PubMed]
  2. B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuk, T. C. Strand, “Architectural implications of a digital optical processor,” Appl. Opt. 23, 3465–3474 (1984).
    [CrossRef] [PubMed]
  3. H. J. Caulfield, “Parallel N4 weighted optical interconnections,” Appl. Opt. 26, 4039–4040 (1987).
    [CrossRef] [PubMed]
  4. J. Shamir, H. J. Caulfield, R. B. Johnson, “Massive holographic interconnection networks and their limitations,” Appl. Opt. 28, 311–324 (1989).
    [CrossRef] [PubMed]
  5. P. Ambs, Y. Fainman, S.-H. Lee, J. Gresser, “Computerized design and generation of space-variant holographic filters. 1. System design considerations and applications of space-variant filters to image processing,” Appl. Opt. 27, 4753–4760 (1988).
    [CrossRef] [PubMed]
  6. P. Ambs, Y. Fainman, S.-H. Lee, J. Gresser, “Computerized design and generation of space-variant holographic filters. 2. Applications of space-variant filters to optical computing,” Appl. Opt. 27, 4761–4765 (1988).
    [CrossRef] [PubMed]
  7. H. J. Caulfield, H. H. Szu, “Parallel discrete and continuous wavelet transforms,” Opt. Eng. 31, 1835–1839 (1992).
    [CrossRef]
  8. F. Lin, “Practical realizations of N4 optical interconnects,” Appl. Opt. 29, 5226–5227 (1990).
    [CrossRef] [PubMed]
  9. Y. C. Lee, G. Doolen, H. H. Chen, G. Z. Sun, T. Maxwell, Y. H. Lee, C. L. Giles, “Machine learning using a higher order correlation network,” Physica D. 22, 276–280 (1986).
  10. C. L. Giles, T. Maxwell, “Learning, invariance, and generalization in high-order neural networks,” Appl. Opt. 26, 4972–4978 (1987).
    [CrossRef] [PubMed]
  11. J. W. Goodman, A. R. Dias, L. M. Woody, “Fully parallel high-speed incoherent method for performing discrete Fourier transforms,” Opt. Lett. 2, 1–3 (1978).
    [CrossRef] [PubMed]
  12. R. A. Athale, W. C. Collins, “Optical matrix–matrix multiplier based on outer product decomposition,” Appl. Opt. 21, 2089–2090 (1982).
    [CrossRef] [PubMed]
  13. P. S. Guilfoyle, “Systolic acousto-optic binary convolvers,” Opt. Eng. 23, 20–25 (1984).
  14. D. Casasent, “Acousto-optic transducers in iterative optical vector–matrix processors,” Appl. Opt. 21, 1859–1865 (1982).
    [CrossRef] [PubMed]
  15. J.-S. Yang, S.-Y. Chin, Y. S. Lee, “Programmable quadratic associative memory using holographic lenslet arrays,” Opt. Lett. 14, 838–840 (1989).
    [CrossRef]
  16. J.-S. Yang, S.-G. Chin, S.-W. Yuk, S.-Y. Chin, Y.-S. Lee, “Dynamic optical interconnections using holographic lenslet arrays for adaptive neural networks,” Opt. Eng. 32, 80–87 (1993).
    [CrossRef]
  17. B. Fracasso, C. Maissiat, P. Ambs, J.-L. de Bougrenet de la Tocnaye, “Optical implementation of inference machine using a binary multilayer interconnection network,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Phot-Opt. Instrum. Eng. 1319, 273–1274 (1990).
  18. J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, L. T. Florez, “Vertical-cavity surface emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
    [CrossRef]
  19. M. Orenstein, A. C. von Lehmen, C. Chang-Hasnain, N. G. Stoffel, J. P. Harbison, L. T. Florez, “Matrix addressable vertical-cavity surface emitting lasers array,” Electron. Lett. 27, 437–438 (1991).
    [CrossRef]
  20. A. W. Lohmann, S. Sinzinger, “Improved array illuminators,” Appl. Opt. 31, 5447–5452 (1992).
    [CrossRef] [PubMed]
  21. J. Weigelt, “Space-bandwidth product and crosstalk of spatial filtering methods for performing binary logic optically,” Opt. Eng. 27, 883–892 (1988).
  22. D. Slepian, H. O. Pollack, H. J. Landau, “Prolate spheroidal wave functions, Fourier analysis and uncertainty,” Bell Syst. Tech. J. 40, 43–84 (1961).
  23. H. Hamam, B. Fracasso, J.-L. de Bougrenet de la Tocnaye, “Node-based reconfiguration volume interconnections. 2. Hologram encoding considerations,” Appl. Opt. (1994).
    [CrossRef] [PubMed]
  24. J.-L. de Bougrenet de la Tocnaye, J. R. Brocklehurst, “Parallel access read/write memory using an optically addressed spatial light modulator,” Appl. Opt. 30, 179–180 (1991).
    [CrossRef] [PubMed]
  25. J.-L. de Bougrenet de la Tocnaye, “Ferroelectric liquid crystal light valves: application to parallel information processing,” Int. J. Opt. Comput. 2, 319–339 (1991).
  26. B. Fracasso, P. Ambs, J.-L. de Bougrenet de la Tocnaye, “Recording reconfigurable binary computer generated holograms on bistable optically addressed ferroelectric liquid-crystal spatial light modulator,” Opt. Lett. 15, 1473–1475 (1990).
    [CrossRef] [PubMed]
  27. M. Killinger, J.-L. de Bougrenet de la Tocnaye, P. Cambon, R. C. Chittick, W. A. Crossland, “Bistability and nonlinearity in optically addressed ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 31, 3930–3936 (1992).
    [CrossRef] [PubMed]
  28. K. M. Johnson, M. R. Surette, J. Shamir, “Optical interconnection network using polarization-based ferroelectric liquid crystal gates,” Appl. Opt. 27, 1727–1733 (1988).
    [CrossRef] [PubMed]
  29. K. M. Johnson, G. Moddel, “Motivations for using ferroelectric liquid crystal spatial light modulators in neurocomputing,” Appl. Opt. 28, 4888–4899 (1989).
    [CrossRef] [PubMed]
  30. A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
    [CrossRef] [PubMed]
  31. N. Davidson, A. A. Friesem, E. Hasman, “On the limits of optical interconnects,” Appl. Opt. 31, 5426–5430 (1992).
    [CrossRef] [PubMed]

1994 (1)

H. Hamam, B. Fracasso, J.-L. de Bougrenet de la Tocnaye, “Node-based reconfiguration volume interconnections. 2. Hologram encoding considerations,” Appl. Opt. (1994).
[CrossRef] [PubMed]

1993 (1)

J.-S. Yang, S.-G. Chin, S.-W. Yuk, S.-Y. Chin, Y.-S. Lee, “Dynamic optical interconnections using holographic lenslet arrays for adaptive neural networks,” Opt. Eng. 32, 80–87 (1993).
[CrossRef]

1992 (4)

1991 (4)

J.-L. de Bougrenet de la Tocnaye, J. R. Brocklehurst, “Parallel access read/write memory using an optically addressed spatial light modulator,” Appl. Opt. 30, 179–180 (1991).
[CrossRef] [PubMed]

J.-L. de Bougrenet de la Tocnaye, “Ferroelectric liquid crystal light valves: application to parallel information processing,” Int. J. Opt. Comput. 2, 319–339 (1991).

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, L. T. Florez, “Vertical-cavity surface emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[CrossRef]

M. Orenstein, A. C. von Lehmen, C. Chang-Hasnain, N. G. Stoffel, J. P. Harbison, L. T. Florez, “Matrix addressable vertical-cavity surface emitting lasers array,” Electron. Lett. 27, 437–438 (1991).
[CrossRef]

1990 (2)

1989 (3)

1988 (4)

1987 (2)

1986 (1)

Y. C. Lee, G. Doolen, H. H. Chen, G. Z. Sun, T. Maxwell, Y. H. Lee, C. L. Giles, “Machine learning using a higher order correlation network,” Physica D. 22, 276–280 (1986).

1984 (2)

1982 (2)

1978 (1)

1975 (1)

1967 (1)

1961 (1)

D. Slepian, H. O. Pollack, H. J. Landau, “Prolate spheroidal wave functions, Fourier analysis and uncertainty,” Bell Syst. Tech. J. 40, 43–84 (1961).

Ambs, P.

Athale, R. A.

Brocklehurst, J. R.

Cambon, P.

Casasent, D.

Caulfield, H. J.

Chang-Hasnain, C.

M. Orenstein, A. C. von Lehmen, C. Chang-Hasnain, N. G. Stoffel, J. P. Harbison, L. T. Florez, “Matrix addressable vertical-cavity surface emitting lasers array,” Electron. Lett. 27, 437–438 (1991).
[CrossRef]

Chavel, P.

Chen, H. H.

Y. C. Lee, G. Doolen, H. H. Chen, G. Z. Sun, T. Maxwell, Y. H. Lee, C. L. Giles, “Machine learning using a higher order correlation network,” Physica D. 22, 276–280 (1986).

Chin, S.-G.

J.-S. Yang, S.-G. Chin, S.-W. Yuk, S.-Y. Chin, Y.-S. Lee, “Dynamic optical interconnections using holographic lenslet arrays for adaptive neural networks,” Opt. Eng. 32, 80–87 (1993).
[CrossRef]

Chin, S.-Y.

J.-S. Yang, S.-G. Chin, S.-W. Yuk, S.-Y. Chin, Y.-S. Lee, “Dynamic optical interconnections using holographic lenslet arrays for adaptive neural networks,” Opt. Eng. 32, 80–87 (1993).
[CrossRef]

J.-S. Yang, S.-Y. Chin, Y. S. Lee, “Programmable quadratic associative memory using holographic lenslet arrays,” Opt. Lett. 14, 838–840 (1989).
[CrossRef]

Chittick, R. C.

Collins, W. C.

Crossland, W. A.

Davidson, N.

de Bougrenet de la Tocnaye, J.-L.

H. Hamam, B. Fracasso, J.-L. de Bougrenet de la Tocnaye, “Node-based reconfiguration volume interconnections. 2. Hologram encoding considerations,” Appl. Opt. (1994).
[CrossRef] [PubMed]

M. Killinger, J.-L. de Bougrenet de la Tocnaye, P. Cambon, R. C. Chittick, W. A. Crossland, “Bistability and nonlinearity in optically addressed ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 31, 3930–3936 (1992).
[CrossRef] [PubMed]

J.-L. de Bougrenet de la Tocnaye, J. R. Brocklehurst, “Parallel access read/write memory using an optically addressed spatial light modulator,” Appl. Opt. 30, 179–180 (1991).
[CrossRef] [PubMed]

J.-L. de Bougrenet de la Tocnaye, “Ferroelectric liquid crystal light valves: application to parallel information processing,” Int. J. Opt. Comput. 2, 319–339 (1991).

B. Fracasso, P. Ambs, J.-L. de Bougrenet de la Tocnaye, “Recording reconfigurable binary computer generated holograms on bistable optically addressed ferroelectric liquid-crystal spatial light modulator,” Opt. Lett. 15, 1473–1475 (1990).
[CrossRef] [PubMed]

B. Fracasso, C. Maissiat, P. Ambs, J.-L. de Bougrenet de la Tocnaye, “Optical implementation of inference machine using a binary multilayer interconnection network,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Phot-Opt. Instrum. Eng. 1319, 273–1274 (1990).

Deen, L. M.

Dias, A. R.

Doolen, G.

Y. C. Lee, G. Doolen, H. H. Chen, G. Z. Sun, T. Maxwell, Y. H. Lee, C. L. Giles, “Machine learning using a higher order correlation network,” Physica D. 22, 276–280 (1986).

Fainman, Y.

Florez, L. T.

M. Orenstein, A. C. von Lehmen, C. Chang-Hasnain, N. G. Stoffel, J. P. Harbison, L. T. Florez, “Matrix addressable vertical-cavity surface emitting lasers array,” Electron. Lett. 27, 437–438 (1991).
[CrossRef]

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, L. T. Florez, “Vertical-cavity surface emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[CrossRef]

Forchheimer, R.

Fracasso, B.

H. Hamam, B. Fracasso, J.-L. de Bougrenet de la Tocnaye, “Node-based reconfiguration volume interconnections. 2. Hologram encoding considerations,” Appl. Opt. (1994).
[CrossRef] [PubMed]

B. Fracasso, P. Ambs, J.-L. de Bougrenet de la Tocnaye, “Recording reconfigurable binary computer generated holograms on bistable optically addressed ferroelectric liquid-crystal spatial light modulator,” Opt. Lett. 15, 1473–1475 (1990).
[CrossRef] [PubMed]

B. Fracasso, C. Maissiat, P. Ambs, J.-L. de Bougrenet de la Tocnaye, “Optical implementation of inference machine using a binary multilayer interconnection network,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Phot-Opt. Instrum. Eng. 1319, 273–1274 (1990).

Friesem, A. A.

Giles, C. L.

C. L. Giles, T. Maxwell, “Learning, invariance, and generalization in high-order neural networks,” Appl. Opt. 26, 4972–4978 (1987).
[CrossRef] [PubMed]

Y. C. Lee, G. Doolen, H. H. Chen, G. Z. Sun, T. Maxwell, Y. H. Lee, C. L. Giles, “Machine learning using a higher order correlation network,” Physica D. 22, 276–280 (1986).

Goodman, J. W.

Gresser, J.

Guilfoyle, P. S.

P. S. Guilfoyle, “Systolic acousto-optic binary convolvers,” Opt. Eng. 23, 20–25 (1984).

Hagler, M. O.

Hamam, H.

H. Hamam, B. Fracasso, J.-L. de Bougrenet de la Tocnaye, “Node-based reconfiguration volume interconnections. 2. Hologram encoding considerations,” Appl. Opt. (1994).
[CrossRef] [PubMed]

Harbison, J. P.

M. Orenstein, A. C. von Lehmen, C. Chang-Hasnain, N. G. Stoffel, J. P. Harbison, L. T. Florez, “Matrix addressable vertical-cavity surface emitting lasers array,” Electron. Lett. 27, 437–438 (1991).
[CrossRef]

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, L. T. Florez, “Vertical-cavity surface emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[CrossRef]

Hasman, E.

Jenkins, B. K.

Jewell, J. L.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, L. T. Florez, “Vertical-cavity surface emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[CrossRef]

Johnson, K. M.

Johnson, R. B.

Killinger, M.

Landau, H. J.

D. Slepian, H. O. Pollack, H. J. Landau, “Prolate spheroidal wave functions, Fourier analysis and uncertainty,” Bell Syst. Tech. J. 40, 43–84 (1961).

Lee, S.-H.

Lee, Y. C.

Y. C. Lee, G. Doolen, H. H. Chen, G. Z. Sun, T. Maxwell, Y. H. Lee, C. L. Giles, “Machine learning using a higher order correlation network,” Physica D. 22, 276–280 (1986).

Lee, Y. H.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, L. T. Florez, “Vertical-cavity surface emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[CrossRef]

Y. C. Lee, G. Doolen, H. H. Chen, G. Z. Sun, T. Maxwell, Y. H. Lee, C. L. Giles, “Machine learning using a higher order correlation network,” Physica D. 22, 276–280 (1986).

Lee, Y. S.

Lee, Y.-S.

J.-S. Yang, S.-G. Chin, S.-W. Yuk, S.-Y. Chin, Y.-S. Lee, “Dynamic optical interconnections using holographic lenslet arrays for adaptive neural networks,” Opt. Eng. 32, 80–87 (1993).
[CrossRef]

Lin, F.

Lohmann, A. W.

Maissiat, C.

B. Fracasso, C. Maissiat, P. Ambs, J.-L. de Bougrenet de la Tocnaye, “Optical implementation of inference machine using a binary multilayer interconnection network,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Phot-Opt. Instrum. Eng. 1319, 273–1274 (1990).

Maxwell, T.

C. L. Giles, T. Maxwell, “Learning, invariance, and generalization in high-order neural networks,” Appl. Opt. 26, 4972–4978 (1987).
[CrossRef] [PubMed]

Y. C. Lee, G. Doolen, H. H. Chen, G. Z. Sun, T. Maxwell, Y. H. Lee, C. L. Giles, “Machine learning using a higher order correlation network,” Physica D. 22, 276–280 (1986).

Moddel, G.

Orenstein, M.

M. Orenstein, A. C. von Lehmen, C. Chang-Hasnain, N. G. Stoffel, J. P. Harbison, L. T. Florez, “Matrix addressable vertical-cavity surface emitting lasers array,” Electron. Lett. 27, 437–438 (1991).
[CrossRef]

Paris, D. P.

Pollack, H. O.

D. Slepian, H. O. Pollack, H. J. Landau, “Prolate spheroidal wave functions, Fourier analysis and uncertainty,” Bell Syst. Tech. J. 40, 43–84 (1961).

Sawchuk, A. A.

Scherer, A.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, L. T. Florez, “Vertical-cavity surface emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[CrossRef]

Shamir, J.

Sinzinger, S.

Slepian, D.

D. Slepian, H. O. Pollack, H. J. Landau, “Prolate spheroidal wave functions, Fourier analysis and uncertainty,” Bell Syst. Tech. J. 40, 43–84 (1961).

Stoffel, N. G.

M. Orenstein, A. C. von Lehmen, C. Chang-Hasnain, N. G. Stoffel, J. P. Harbison, L. T. Florez, “Matrix addressable vertical-cavity surface emitting lasers array,” Electron. Lett. 27, 437–438 (1991).
[CrossRef]

Strand, T. C.

Sun, G. Z.

Y. C. Lee, G. Doolen, H. H. Chen, G. Z. Sun, T. Maxwell, Y. H. Lee, C. L. Giles, “Machine learning using a higher order correlation network,” Physica D. 22, 276–280 (1986).

Surette, M. R.

Szu, H. H.

H. J. Caulfield, H. H. Szu, “Parallel discrete and continuous wavelet transforms,” Opt. Eng. 31, 1835–1839 (1992).
[CrossRef]

von Lehmen, A. C.

M. Orenstein, A. C. von Lehmen, C. Chang-Hasnain, N. G. Stoffel, J. P. Harbison, L. T. Florez, “Matrix addressable vertical-cavity surface emitting lasers array,” Electron. Lett. 27, 437–438 (1991).
[CrossRef]

Walkup, J. F.

Weigelt, J.

J. Weigelt, “Space-bandwidth product and crosstalk of spatial filtering methods for performing binary logic optically,” Opt. Eng. 27, 883–892 (1988).

Woody, L. M.

Yang, J.-S.

J.-S. Yang, S.-G. Chin, S.-W. Yuk, S.-Y. Chin, Y.-S. Lee, “Dynamic optical interconnections using holographic lenslet arrays for adaptive neural networks,” Opt. Eng. 32, 80–87 (1993).
[CrossRef]

J.-S. Yang, S.-Y. Chin, Y. S. Lee, “Programmable quadratic associative memory using holographic lenslet arrays,” Opt. Lett. 14, 838–840 (1989).
[CrossRef]

Yuk, S.-W.

J.-S. Yang, S.-G. Chin, S.-W. Yuk, S.-Y. Chin, Y.-S. Lee, “Dynamic optical interconnections using holographic lenslet arrays for adaptive neural networks,” Opt. Eng. 32, 80–87 (1993).
[CrossRef]

Appl. Opt. (18)

A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
[CrossRef] [PubMed]

L. M. Deen, J. F. Walkup, M. O. Hagler, “Representations of space-variant optical systems using volume holograms,” Appl. Opt. 14, 2438–2446 (1975).
[CrossRef] [PubMed]

D. Casasent, “Acousto-optic transducers in iterative optical vector–matrix processors,” Appl. Opt. 21, 1859–1865 (1982).
[CrossRef] [PubMed]

R. A. Athale, W. C. Collins, “Optical matrix–matrix multiplier based on outer product decomposition,” Appl. Opt. 21, 2089–2090 (1982).
[CrossRef] [PubMed]

B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuk, T. C. Strand, “Architectural implications of a digital optical processor,” Appl. Opt. 23, 3465–3474 (1984).
[CrossRef] [PubMed]

C. L. Giles, T. Maxwell, “Learning, invariance, and generalization in high-order neural networks,” Appl. Opt. 26, 4972–4978 (1987).
[CrossRef] [PubMed]

K. M. Johnson, M. R. Surette, J. Shamir, “Optical interconnection network using polarization-based ferroelectric liquid crystal gates,” Appl. Opt. 27, 1727–1733 (1988).
[CrossRef] [PubMed]

P. Ambs, Y. Fainman, S.-H. Lee, J. Gresser, “Computerized design and generation of space-variant holographic filters. 1. System design considerations and applications of space-variant filters to image processing,” Appl. Opt. 27, 4753–4760 (1988).
[CrossRef] [PubMed]

P. Ambs, Y. Fainman, S.-H. Lee, J. Gresser, “Computerized design and generation of space-variant holographic filters. 2. Applications of space-variant filters to optical computing,” Appl. Opt. 27, 4761–4765 (1988).
[CrossRef] [PubMed]

J. Shamir, H. J. Caulfield, R. B. Johnson, “Massive holographic interconnection networks and their limitations,” Appl. Opt. 28, 311–324 (1989).
[CrossRef] [PubMed]

K. M. Johnson, G. Moddel, “Motivations for using ferroelectric liquid crystal spatial light modulators in neurocomputing,” Appl. Opt. 28, 4888–4899 (1989).
[CrossRef] [PubMed]

F. Lin, “Practical realizations of N4 optical interconnects,” Appl. Opt. 29, 5226–5227 (1990).
[CrossRef] [PubMed]

M. Killinger, J.-L. de Bougrenet de la Tocnaye, P. Cambon, R. C. Chittick, W. A. Crossland, “Bistability and nonlinearity in optically addressed ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 31, 3930–3936 (1992).
[CrossRef] [PubMed]

N. Davidson, A. A. Friesem, E. Hasman, “On the limits of optical interconnects,” Appl. Opt. 31, 5426–5430 (1992).
[CrossRef] [PubMed]

A. W. Lohmann, S. Sinzinger, “Improved array illuminators,” Appl. Opt. 31, 5447–5452 (1992).
[CrossRef] [PubMed]

H. J. Caulfield, “Parallel N4 weighted optical interconnections,” Appl. Opt. 26, 4039–4040 (1987).
[CrossRef] [PubMed]

J.-L. de Bougrenet de la Tocnaye, J. R. Brocklehurst, “Parallel access read/write memory using an optically addressed spatial light modulator,” Appl. Opt. 30, 179–180 (1991).
[CrossRef] [PubMed]

H. Hamam, B. Fracasso, J.-L. de Bougrenet de la Tocnaye, “Node-based reconfiguration volume interconnections. 2. Hologram encoding considerations,” Appl. Opt. (1994).
[CrossRef] [PubMed]

Bell Syst. Tech. J. (1)

D. Slepian, H. O. Pollack, H. J. Landau, “Prolate spheroidal wave functions, Fourier analysis and uncertainty,” Bell Syst. Tech. J. 40, 43–84 (1961).

Electron. Lett. (1)

M. Orenstein, A. C. von Lehmen, C. Chang-Hasnain, N. G. Stoffel, J. P. Harbison, L. T. Florez, “Matrix addressable vertical-cavity surface emitting lasers array,” Electron. Lett. 27, 437–438 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, L. T. Florez, “Vertical-cavity surface emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[CrossRef]

Int. J. Opt. Comput. (1)

J.-L. de Bougrenet de la Tocnaye, “Ferroelectric liquid crystal light valves: application to parallel information processing,” Int. J. Opt. Comput. 2, 319–339 (1991).

Opt. Eng. (4)

J. Weigelt, “Space-bandwidth product and crosstalk of spatial filtering methods for performing binary logic optically,” Opt. Eng. 27, 883–892 (1988).

H. J. Caulfield, H. H. Szu, “Parallel discrete and continuous wavelet transforms,” Opt. Eng. 31, 1835–1839 (1992).
[CrossRef]

P. S. Guilfoyle, “Systolic acousto-optic binary convolvers,” Opt. Eng. 23, 20–25 (1984).

J.-S. Yang, S.-G. Chin, S.-W. Yuk, S.-Y. Chin, Y.-S. Lee, “Dynamic optical interconnections using holographic lenslet arrays for adaptive neural networks,” Opt. Eng. 32, 80–87 (1993).
[CrossRef]

Opt. Lett. (3)

Physica D. (1)

Y. C. Lee, G. Doolen, H. H. Chen, G. Z. Sun, T. Maxwell, Y. H. Lee, C. L. Giles, “Machine learning using a higher order correlation network,” Physica D. 22, 276–280 (1986).

Other (1)

B. Fracasso, C. Maissiat, P. Ambs, J.-L. de Bougrenet de la Tocnaye, “Optical implementation of inference machine using a binary multilayer interconnection network,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Phot-Opt. Instrum. Eng. 1319, 273–1274 (1990).

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Figures (22)

Fig. 1
Fig. 1

Parallel N 4 optical interconnects: SA, source array; HA, hologram array; DA, detector array.

Fig. 2
Fig. 2

Interconnection node, with spatial tensor [T] and weight w.

Fig. 3
Fig. 3

Node of interconnection in the matrix–matrix multiplication case. Arrows indicate how the information coming from the input plane, A, is redirected to appropriate locations in the output plane, C.

Fig. 4
Fig. 4

NBIN in a second-order neural network scheme. The input-states matrix (i.e., the image to recognize) corresponds both to the input plane and to the weight matrix of the plane of nodes. The second-order weights are here fixed.

Fig. 5
Fig. 5

Node-based interconnection architecture. A one-dimensional representation is used here for the sake of clarity. Even if additional components such as focusing lenses may be required, they are not represented here.

Fig. 6
Fig. 6

Two input channels and the sets of nodes to which they are linked, in the case of matrix–matrix multiplication. We have N 11 = {B 11, B 12, B 13} and N 13 = {B 31, B 32, B 33}.

Fig. 7
Fig. 7

Three layers of the plane of nodes, represented in the transmissive configuration. The incoming interconnection patterns are memorized in the light valve, which then acts as an optically programmed shutter. The latter is read with a second (uniform) beam, and the node responses are generated at the output plane by the second multifaceted hologram. The matrix W of (positive) weights is input by the pixels transmittance of an electrically addressed spatial light modulator (EASLM).

Fig. 8
Fig. 8

Spatial multiplexing at the OASLM.

Fig. 9
Fig. 9

Possible spatial tessellation of the plane of nodes for the 3 × 3 matrix–matrix product. As the klth node is addressed only by the elements of the klth column of the input matrix, three subdomains are required per node.

Fig. 10
Fig. 10

Node-plane addressing. Each input subhologram is designed as a Fourier-transform hologram, which encodes the interconnection pattern between an input channel and a set of node inputs.

Fig. 11
Fig. 11

Reconstructed intensity distributions for different window sizes. The computer simulations were performed on 256 × 256 pixel images, and the extent of the interconnect is B = 30 pixels. Only the central parts of the images are displayed.

Fig. 12
Fig. 12

Energy concentration geometry. The input plane and the node plane are supposed to be Fourier conjugate spaces.

Fig. 13
Fig. 13

Energy concentration into several subdomains.

Fig. 14
Fig. 14

Structure of the surface-stabilized FLC light valve.

Fig. 15
Fig. 15

Nonlinear characteristic of the FLC BOASLM. On writing, the incoming light intensity, I e , is measured over the disk surface for a given voltage pulse of amplitude V c and duration T c . The SLM is then read with a uniform beam to measure the device extinction ratio.

Fig. 16
Fig. 16

Correction for the spatial cross talk. The driving voltage parameters of the BOASLM are set to V c = 17 V and T c = 1.5 ms. The incident intensity distribution corresponds to the simulation in Fig. 11(d).

Fig. 17
Fig. 17

Influence of the limited device extinction ratio on the output state accuracy (binary input and weight states).

Fig. 18
Fig. 18

Experimental setup: SF, spatial filter; M’s, mirrors.

Fig. 19
Fig. 19

Spatial interconnection function generated by three input holographic facets at the nodes inputs, i.e., at the plane of nodes and before the OASLM. The Gibbs phenomenon can be noticed at each individual subdomain.

Fig. 20
Fig. 20

Enlarged view of two square subdomains of the interconnection distribution shown in Fig. 19. Two engravements onto the OASLM are performed for different values of the voltage amplitude and duration. The device is then read with a uniform beam.

Fig. 21
Fig. 21

Faceted subhologram mask corresponding to one node (B 12) in the BMMM case. Each facet is a 64 × 64 cell amplitude CGH that addresses a single output channel.

Fig. 22
Fig. 22

When the first OASLM (OASLM1) is read out with a uniform beam, the output binary matrix C is given by the diffracted intensity distribution in the output plane (first diffraction order).

Equations (45)

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C m n = i = 1 N j = 1 N T i j m n A i j ,
C m n ( t ) = i = 1 N j = 1 N T i j m n ( t ) A i j ( t ) .
T i j m n ( t ) = w ( t ) Φ i j m n ,
C m n k l = W k l i = 1 N j = 1 N Φ i j m n k l A i j ,
C m n = k = 1 M l = 1 M C m n k l = k = 1 M l = 1 M i = 1 M j = 1 M Φ i j m n k l A i j W k l .
[ T ( W ) ] i j m n = k = 1 M l = 1 M W k l Φ i j m n k l .
Φ i j m n k l = δ ( j - k ) δ ( m - i ) δ ( n - l ) , W k l = B k l .
C m n = k , l = 1 M i , j = 1 N δ ( j - k ) δ ( m - i ) δ ( n - l ) A i j B k l = j = 1 N A m j B j n ;
y i = S [ q = 1 k T q ( i ) , ] ,
T 0 ( i ) = W 0 , T 1 ( i ) = j = 1 N W 1 ( i , j ) x j , T 2 ( i ) = j = 1 N k = 1 N W 2 ( i , j , k ) x j x k ,
T 2 ( m , n ) = k , l i , j W 2 ( i , j , k , l , m , n ) X i j X k l ,
Φ i j m n k l = W 2 ( i , j , k , l , m , n ) .
A ( x , y ) = i = 1 N j = 1 N A i j U i j ( x - a i , y - a j ) ,
U i j ( x , y ) rect ( x d , y d )             for i , j = { 1 , , N } ,
H 1 ( x , y ) = i = 1 N j = 1 N [ f i j ( x , y ) rect ( x d , y d ) ] * δ ( x - a i , y i - a j ) ,
F i j ( u , v ) = A i j φ i j ( u , v ) [ F f i j ( u , v ) * sinc ( d u , d v ) ] ,
F i j ( u , v ) = ( k , l ) N i j F i j k l ( u , v ) .
H k l ( u , v ) = ( i , j ) J k l F i j k l ( u , v ) ,
p i j = I 0 A i j 2 η i j N 2 σ i j ,
F ( u , v ) = rect ( u B , v B ) ,
F r ( u , v ) = F [ sinc ( B x ) sinc ( B y ) rect ( x d , y d ) ] = G ( u ) G ( v ) ,
π D G ( u ) = Si [ π d ( u + B 2 ) ] - Si [ π d ( u - B 2 ) ] ,
β = B F ( u ) 2 d u - + F ( u ) 2 d u
κ φ ( x ) = B φ ( ξ ) sin π d ( x - ξ ) π ( x - ξ ) d ξ
f 0 ( x ) = φ 0 ( x , d B ) rect ( x d ) .
f i j ( x , y ) = f 0 ( x , y ; d B ) ( k , l ) N i j exp [ i 2 π ( u i j k l x + v i j k l y ) ] .
F n t ( u ) = F n ( u ) k = 1 N rect ( u - u k B ) ,
f n + 1 ( x ) = f n ( x ) rect ( x D ) .
A = [ 1 0 0 0 0 0 0 0 0 ] , B = [ 1 0 0 1 0 0 1 0 0 ] .
C 11 = A 11 B 11 = 1 + k 1 A 1 k B k 1 = 0 = 1.
p 11 = p T 1 + ( N - 1 ) p T 0 ,
P s P c = p T 1 p ( N - 1 ) T 0 E r N .
f 11 in = 1 , N 11 = { node ( 1 , 1 ) } .
Φ 11 m n 11 = 1 N 2             for m , n = 1 , , N .
A 1 = [ 1 0 0 0 0 0 0 0 0 ] ,
P m n 1 = p T 1 N 2 .
W 2 = [ 0 1 1 1 1 1 1 1 1 ] ,
P m n 2 = p T 0 i j k 1 l 1 Φ i j m n k l .
P m n 2 = p T 0 M 2 - 1 N 2 .
A = [ 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ] ,             B = [ 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 ] , C = [ 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 ] .
Δ h Δ i = n λ f ,
Δ A Δ B = n N λ f .
s = p 2 N 2 δ mfs 2 ,
S PN = M 2 N 2 p 2 f in δ mfs 2 ,
N = [ ( S PN ) 1 / 2 p δ mfs ] 2 / 5 .

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