Abstract

Fundamental and practical limitations to be encountered in the implementation of massive free space optical interconnects are discussed in detail, and some improved architectures are proposed. The long term optimum design uses currently unavailable large arrays of laser diodes. An interim solution, using available spatial light modulators, is shown to be capable of storing ~1010 bits of information and performing ~1011 interconnections/s.

© 1989 Optical Society of America

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References

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  1. J. W. Goodman, F. I. Leonberger, S. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850 (1984).
    [CrossRef]
  2. R. K. Kostuk, J. W. Goodman, L. Hesselink, “Design Considerations for Holographic Optical Interconnects,” Appl. Opt. 26, 3947 (1987).
    [CrossRef] [PubMed]
  3. E. Marom, N. Konforti, “Dynamic Optical Interconnections,” Opt. Lett. 12, 539 (1987).
    [CrossRef] [PubMed]
  4. Ho-In Jeon, A. A. Sawchuk, “Optical Crossbar Interconnections Using Variable Grating Mode Devices,” Appl. Opt. 26, 261 (1987).
    [CrossRef] [PubMed]
  5. J. Shamir, H. J. Caulfield, “High-Efficiency Rapidly Programmable Optical Interconnections,” Appl. Opt. 26, 1032 (1987).
    [CrossRef] [PubMed]
  6. K. M. Johnson, M. R. Surette, J. Shamir, “Optical Interconnection Network Using Polarization Based Ferroelectric Liquid Crystal Gates,” Appl. Opt. 27, 1727 (1988).
    [CrossRef] [PubMed]
  7. H. J. Caulfield, “Parallel N4 Weighted Optical Interconnections,” Appl. Opt. 26, 4039 (1987).
    [CrossRef] [PubMed]
  8. K. Wagner, D. Psaltis, “Multilayer Optical Learning Networks,” Appl. Opt. 26, 5061 (1987).
    [CrossRef] [PubMed]
  9. J. Kinser, H. J. Caulfield, J. Shamir, “A Design for a Massive All-Optical Bidirectional Associative Memory: The Big BAM,” Proc. Soc. Photo-Opt. Instrum. Eng. 881, 269 (1988).
  10. H. J. White, W. A. Wright, “Holographic Implementation of a Hopfield Model with Discrete Weightings,” Appl. Opt. 27, 331 (1988).
    [CrossRef] [PubMed]
  11. P. A. Ambs, Y. Fainman, S. Esner, S. H. Lee, “Holographic Optical Elements for SLM Defect Removal and for Optical Interconnects,” Proc. Soc. Photo-Opt. Instrum. Eng. 883, paper 31 (1988).
  12. P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space Variant Holographic Filter,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 62 (1988).
  13. J.-S. Jang, S.-W. Jung, S.-Y. Lee, S.-Y. Shin, “Optical Implementation of the Hopfield Model for Two-Dimensional Associative Memory,” Opt. Lett. 13, 248 (1988).
    [CrossRef] [PubMed]
  14. N. H. Farhat, “Architectures for Optoelectronic Analogs of Self-Organizing Neural Network,” Opt. Lett. 12, 448 (1987).
    [CrossRef] [PubMed]
  15. N. H. Farhat, “Optoelectronic Analogs of Self-Programming Neural Nets: Architecture and Methodologies for Implementing Fast Stochastic Learning by Simulated Annealing,” Appl. Opt. 26, 5093 (1987).
    [CrossRef] [PubMed]
  16. K. Fukushima, “Neocognitron: A Hierarchical Neural Network Capable of Visual Pattern Recognition,” Neural Networks 1, 119 (1988).
    [CrossRef]
  17. T. Kohonen, “An Introduction to Neural Computing,” Neural Networks 1, 3 (1988).
    [CrossRef]
  18. J. Ghosh, K. Hwang, “Optically Connected Multiprocessors for Simulating Artificial Neural Networks,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 2 (1988).
  19. S. C. Gustafson, G. R. Little, “Optical Neural Classification for Binary Patterns,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 83 (1988).
  20. D. Brady, X.-G. Gu, D. Psaltis, “Photorefractive Crystal in Optical Neural Computers,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 132 (1988).
  21. H. Wagner, R. E. Feinleib, “Competitive Optoelectronic Learning Networks,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 162 (1988).
  22. H. J. White, N. B. Aldridge, I. Lindsay, “Digital and Analog Holographic Associative Memories,” Opt. Eng. 27, 30 (1988).
    [CrossRef]
  23. N. Duklias, J. Shamir, “Relation between Object Position and Autocorrelation Spots in the VanderLugt Filtering Process. 2: Influence of the Volume Nature of the Photographic Emulsion,” Appl. Opt. 5, 78 (1973).
  24. Y. Tsunoda, Y. Takeda, “High Density Image-Storage Holograms by a Random Phase Sampling Method,” Appl. Opt. 13, 2046 (1974).
    [CrossRef] [PubMed]
  25. M. Nazarathy, J. Shamir, “Fourier Optics Described by Operator Algebra,” J. Opt. Soc. Am. 70, 150 (1980).
    [CrossRef]
  26. M. Nazarathy, J. Shamir, “Holography Described by Operator Algebra,” J. Opt. Soc. Am. 71, 529 (1981).
    [CrossRef]
  27. M. Nazarathy, J. Shamir, “Wavelength Variation in Fourier Optics and Holography Described by Operator Algebra,” Isr. J. Technol. 18, 224 (1980).
  28. Y. Fainman, J. Shamir, “Polarization of Nonplanar Wave Fronts,” Appl. Opt. 23, 3188 (1984).
    [CrossRef] [PubMed]
  29. M. N. Deeter, D. Sarid, “Effects of Incidence Angle on Readout in Magnetooptic Storage Media,” Appl. Opt. 27, 713 (1988).
    [CrossRef] [PubMed]
  30. R. Clark, C. Hester, P. Lindberg, “Mapping Sequential Processing Algorithms onto Parallel Distributed Processing Architectures,” Proc. Soc. Photo-Opt. Instrum. Eng. 880, paper 5 (1988).
  31. J.-S. Jang, S.-W. Jung, S.-Y. Lee, S.-Y. Shin, “Optical Implementation of the Hopfield Model for Two-Dimensional Associative Memory,” Opt. Lett. 13, 248 (1988).
    [CrossRef] [PubMed]

1988 (16)

J. Kinser, H. J. Caulfield, J. Shamir, “A Design for a Massive All-Optical Bidirectional Associative Memory: The Big BAM,” Proc. Soc. Photo-Opt. Instrum. Eng. 881, 269 (1988).

H. J. White, W. A. Wright, “Holographic Implementation of a Hopfield Model with Discrete Weightings,” Appl. Opt. 27, 331 (1988).
[CrossRef] [PubMed]

P. A. Ambs, Y. Fainman, S. Esner, S. H. Lee, “Holographic Optical Elements for SLM Defect Removal and for Optical Interconnects,” Proc. Soc. Photo-Opt. Instrum. Eng. 883, paper 31 (1988).

P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space Variant Holographic Filter,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 62 (1988).

J.-S. Jang, S.-W. Jung, S.-Y. Lee, S.-Y. Shin, “Optical Implementation of the Hopfield Model for Two-Dimensional Associative Memory,” Opt. Lett. 13, 248 (1988).
[CrossRef] [PubMed]

K. Fukushima, “Neocognitron: A Hierarchical Neural Network Capable of Visual Pattern Recognition,” Neural Networks 1, 119 (1988).
[CrossRef]

T. Kohonen, “An Introduction to Neural Computing,” Neural Networks 1, 3 (1988).
[CrossRef]

J. Ghosh, K. Hwang, “Optically Connected Multiprocessors for Simulating Artificial Neural Networks,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 2 (1988).

S. C. Gustafson, G. R. Little, “Optical Neural Classification for Binary Patterns,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 83 (1988).

D. Brady, X.-G. Gu, D. Psaltis, “Photorefractive Crystal in Optical Neural Computers,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 132 (1988).

H. Wagner, R. E. Feinleib, “Competitive Optoelectronic Learning Networks,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 162 (1988).

H. J. White, N. B. Aldridge, I. Lindsay, “Digital and Analog Holographic Associative Memories,” Opt. Eng. 27, 30 (1988).
[CrossRef]

K. M. Johnson, M. R. Surette, J. Shamir, “Optical Interconnection Network Using Polarization Based Ferroelectric Liquid Crystal Gates,” Appl. Opt. 27, 1727 (1988).
[CrossRef] [PubMed]

M. N. Deeter, D. Sarid, “Effects of Incidence Angle on Readout in Magnetooptic Storage Media,” Appl. Opt. 27, 713 (1988).
[CrossRef] [PubMed]

R. Clark, C. Hester, P. Lindberg, “Mapping Sequential Processing Algorithms onto Parallel Distributed Processing Architectures,” Proc. Soc. Photo-Opt. Instrum. Eng. 880, paper 5 (1988).

J.-S. Jang, S.-W. Jung, S.-Y. Lee, S.-Y. Shin, “Optical Implementation of the Hopfield Model for Two-Dimensional Associative Memory,” Opt. Lett. 13, 248 (1988).
[CrossRef] [PubMed]

1987 (8)

1984 (2)

J. W. Goodman, F. I. Leonberger, S. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850 (1984).
[CrossRef]

Y. Fainman, J. Shamir, “Polarization of Nonplanar Wave Fronts,” Appl. Opt. 23, 3188 (1984).
[CrossRef] [PubMed]

1981 (1)

1980 (2)

M. Nazarathy, J. Shamir, “Wavelength Variation in Fourier Optics and Holography Described by Operator Algebra,” Isr. J. Technol. 18, 224 (1980).

M. Nazarathy, J. Shamir, “Fourier Optics Described by Operator Algebra,” J. Opt. Soc. Am. 70, 150 (1980).
[CrossRef]

1974 (1)

1973 (1)

N. Duklias, J. Shamir, “Relation between Object Position and Autocorrelation Spots in the VanderLugt Filtering Process. 2: Influence of the Volume Nature of the Photographic Emulsion,” Appl. Opt. 5, 78 (1973).

Aldridge, N. B.

H. J. White, N. B. Aldridge, I. Lindsay, “Digital and Analog Holographic Associative Memories,” Opt. Eng. 27, 30 (1988).
[CrossRef]

Ambs, P.

P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space Variant Holographic Filter,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 62 (1988).

Ambs, P. A.

P. A. Ambs, Y. Fainman, S. Esner, S. H. Lee, “Holographic Optical Elements for SLM Defect Removal and for Optical Interconnects,” Proc. Soc. Photo-Opt. Instrum. Eng. 883, paper 31 (1988).

Athale, R. A.

J. W. Goodman, F. I. Leonberger, S. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850 (1984).
[CrossRef]

Brady, D.

D. Brady, X.-G. Gu, D. Psaltis, “Photorefractive Crystal in Optical Neural Computers,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 132 (1988).

Caulfield, H. J.

J. Kinser, H. J. Caulfield, J. Shamir, “A Design for a Massive All-Optical Bidirectional Associative Memory: The Big BAM,” Proc. Soc. Photo-Opt. Instrum. Eng. 881, 269 (1988).

J. Shamir, H. J. Caulfield, “High-Efficiency Rapidly Programmable Optical Interconnections,” Appl. Opt. 26, 1032 (1987).
[CrossRef] [PubMed]

H. J. Caulfield, “Parallel N4 Weighted Optical Interconnections,” Appl. Opt. 26, 4039 (1987).
[CrossRef] [PubMed]

Clark, R.

R. Clark, C. Hester, P. Lindberg, “Mapping Sequential Processing Algorithms onto Parallel Distributed Processing Architectures,” Proc. Soc. Photo-Opt. Instrum. Eng. 880, paper 5 (1988).

Deeter, M. N.

Duklias, N.

N. Duklias, J. Shamir, “Relation between Object Position and Autocorrelation Spots in the VanderLugt Filtering Process. 2: Influence of the Volume Nature of the Photographic Emulsion,” Appl. Opt. 5, 78 (1973).

Esner, S.

P. A. Ambs, Y. Fainman, S. Esner, S. H. Lee, “Holographic Optical Elements for SLM Defect Removal and for Optical Interconnects,” Proc. Soc. Photo-Opt. Instrum. Eng. 883, paper 31 (1988).

Fainman, Y.

P. A. Ambs, Y. Fainman, S. Esner, S. H. Lee, “Holographic Optical Elements for SLM Defect Removal and for Optical Interconnects,” Proc. Soc. Photo-Opt. Instrum. Eng. 883, paper 31 (1988).

P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space Variant Holographic Filter,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 62 (1988).

Y. Fainman, J. Shamir, “Polarization of Nonplanar Wave Fronts,” Appl. Opt. 23, 3188 (1984).
[CrossRef] [PubMed]

Farhat, N. H.

Feinleib, R. E.

H. Wagner, R. E. Feinleib, “Competitive Optoelectronic Learning Networks,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 162 (1988).

Fukushima, K.

K. Fukushima, “Neocognitron: A Hierarchical Neural Network Capable of Visual Pattern Recognition,” Neural Networks 1, 119 (1988).
[CrossRef]

Ghosh, J.

J. Ghosh, K. Hwang, “Optically Connected Multiprocessors for Simulating Artificial Neural Networks,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 2 (1988).

Goodman, J. W.

R. K. Kostuk, J. W. Goodman, L. Hesselink, “Design Considerations for Holographic Optical Interconnects,” Appl. Opt. 26, 3947 (1987).
[CrossRef] [PubMed]

J. W. Goodman, F. I. Leonberger, S. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850 (1984).
[CrossRef]

Gresser, J.

P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space Variant Holographic Filter,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 62 (1988).

Gu, X.-G.

D. Brady, X.-G. Gu, D. Psaltis, “Photorefractive Crystal in Optical Neural Computers,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 132 (1988).

Gustafson, S. C.

S. C. Gustafson, G. R. Little, “Optical Neural Classification for Binary Patterns,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 83 (1988).

Hesselink, L.

Hester, C.

R. Clark, C. Hester, P. Lindberg, “Mapping Sequential Processing Algorithms onto Parallel Distributed Processing Architectures,” Proc. Soc. Photo-Opt. Instrum. Eng. 880, paper 5 (1988).

Hwang, K.

J. Ghosh, K. Hwang, “Optically Connected Multiprocessors for Simulating Artificial Neural Networks,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 2 (1988).

Jang, J.-S.

Jeon, Ho-In

Johnson, K. M.

Jung, S.-W.

Kinser, J.

J. Kinser, H. J. Caulfield, J. Shamir, “A Design for a Massive All-Optical Bidirectional Associative Memory: The Big BAM,” Proc. Soc. Photo-Opt. Instrum. Eng. 881, 269 (1988).

Kohonen, T.

T. Kohonen, “An Introduction to Neural Computing,” Neural Networks 1, 3 (1988).
[CrossRef]

Konforti, N.

Kostuk, R. K.

Kung, S.

J. W. Goodman, F. I. Leonberger, S. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850 (1984).
[CrossRef]

Lee, S. H.

P. A. Ambs, Y. Fainman, S. Esner, S. H. Lee, “Holographic Optical Elements for SLM Defect Removal and for Optical Interconnects,” Proc. Soc. Photo-Opt. Instrum. Eng. 883, paper 31 (1988).

P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space Variant Holographic Filter,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 62 (1988).

Lee, S.-Y.

Leonberger, F. I.

J. W. Goodman, F. I. Leonberger, S. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850 (1984).
[CrossRef]

Lindberg, P.

R. Clark, C. Hester, P. Lindberg, “Mapping Sequential Processing Algorithms onto Parallel Distributed Processing Architectures,” Proc. Soc. Photo-Opt. Instrum. Eng. 880, paper 5 (1988).

Lindsay, I.

H. J. White, N. B. Aldridge, I. Lindsay, “Digital and Analog Holographic Associative Memories,” Opt. Eng. 27, 30 (1988).
[CrossRef]

Little, G. R.

S. C. Gustafson, G. R. Little, “Optical Neural Classification for Binary Patterns,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 83 (1988).

Marom, E.

Nazarathy, M.

Psaltis, D.

D. Brady, X.-G. Gu, D. Psaltis, “Photorefractive Crystal in Optical Neural Computers,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 132 (1988).

K. Wagner, D. Psaltis, “Multilayer Optical Learning Networks,” Appl. Opt. 26, 5061 (1987).
[CrossRef] [PubMed]

Sarid, D.

Sawchuk, A. A.

Shamir, J.

K. M. Johnson, M. R. Surette, J. Shamir, “Optical Interconnection Network Using Polarization Based Ferroelectric Liquid Crystal Gates,” Appl. Opt. 27, 1727 (1988).
[CrossRef] [PubMed]

J. Kinser, H. J. Caulfield, J. Shamir, “A Design for a Massive All-Optical Bidirectional Associative Memory: The Big BAM,” Proc. Soc. Photo-Opt. Instrum. Eng. 881, 269 (1988).

J. Shamir, H. J. Caulfield, “High-Efficiency Rapidly Programmable Optical Interconnections,” Appl. Opt. 26, 1032 (1987).
[CrossRef] [PubMed]

Y. Fainman, J. Shamir, “Polarization of Nonplanar Wave Fronts,” Appl. Opt. 23, 3188 (1984).
[CrossRef] [PubMed]

M. Nazarathy, J. Shamir, “Holography Described by Operator Algebra,” J. Opt. Soc. Am. 71, 529 (1981).
[CrossRef]

M. Nazarathy, J. Shamir, “Wavelength Variation in Fourier Optics and Holography Described by Operator Algebra,” Isr. J. Technol. 18, 224 (1980).

M. Nazarathy, J. Shamir, “Fourier Optics Described by Operator Algebra,” J. Opt. Soc. Am. 70, 150 (1980).
[CrossRef]

N. Duklias, J. Shamir, “Relation between Object Position and Autocorrelation Spots in the VanderLugt Filtering Process. 2: Influence of the Volume Nature of the Photographic Emulsion,” Appl. Opt. 5, 78 (1973).

Shin, S.-Y.

Surette, M. R.

Takeda, Y.

Tsunoda, Y.

Wagner, H.

H. Wagner, R. E. Feinleib, “Competitive Optoelectronic Learning Networks,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 162 (1988).

Wagner, K.

White, H. J.

H. J. White, W. A. Wright, “Holographic Implementation of a Hopfield Model with Discrete Weightings,” Appl. Opt. 27, 331 (1988).
[CrossRef] [PubMed]

H. J. White, N. B. Aldridge, I. Lindsay, “Digital and Analog Holographic Associative Memories,” Opt. Eng. 27, 30 (1988).
[CrossRef]

Wright, W. A.

Appl. Opt. (12)

N. Duklias, J. Shamir, “Relation between Object Position and Autocorrelation Spots in the VanderLugt Filtering Process. 2: Influence of the Volume Nature of the Photographic Emulsion,” Appl. Opt. 5, 78 (1973).

Y. Tsunoda, Y. Takeda, “High Density Image-Storage Holograms by a Random Phase Sampling Method,” Appl. Opt. 13, 2046 (1974).
[CrossRef] [PubMed]

Y. Fainman, J. Shamir, “Polarization of Nonplanar Wave Fronts,” Appl. Opt. 23, 3188 (1984).
[CrossRef] [PubMed]

Ho-In Jeon, A. A. Sawchuk, “Optical Crossbar Interconnections Using Variable Grating Mode Devices,” Appl. Opt. 26, 261 (1987).
[CrossRef] [PubMed]

J. Shamir, H. J. Caulfield, “High-Efficiency Rapidly Programmable Optical Interconnections,” Appl. Opt. 26, 1032 (1987).
[CrossRef] [PubMed]

R. K. Kostuk, J. W. Goodman, L. Hesselink, “Design Considerations for Holographic Optical Interconnects,” Appl. Opt. 26, 3947 (1987).
[CrossRef] [PubMed]

K. Wagner, D. Psaltis, “Multilayer Optical Learning Networks,” Appl. Opt. 26, 5061 (1987).
[CrossRef] [PubMed]

N. H. Farhat, “Optoelectronic Analogs of Self-Programming Neural Nets: Architecture and Methodologies for Implementing Fast Stochastic Learning by Simulated Annealing,” Appl. Opt. 26, 5093 (1987).
[CrossRef] [PubMed]

H. J. White, W. A. Wright, “Holographic Implementation of a Hopfield Model with Discrete Weightings,” Appl. Opt. 27, 331 (1988).
[CrossRef] [PubMed]

M. N. Deeter, D. Sarid, “Effects of Incidence Angle on Readout in Magnetooptic Storage Media,” Appl. Opt. 27, 713 (1988).
[CrossRef] [PubMed]

K. M. Johnson, M. R. Surette, J. Shamir, “Optical Interconnection Network Using Polarization Based Ferroelectric Liquid Crystal Gates,” Appl. Opt. 27, 1727 (1988).
[CrossRef] [PubMed]

H. J. Caulfield, “Parallel N4 Weighted Optical Interconnections,” Appl. Opt. 26, 4039 (1987).
[CrossRef] [PubMed]

Isr. J. Technol. (1)

M. Nazarathy, J. Shamir, “Wavelength Variation in Fourier Optics and Holography Described by Operator Algebra,” Isr. J. Technol. 18, 224 (1980).

J. Opt. Soc. Am. (2)

Neural Networks (2)

K. Fukushima, “Neocognitron: A Hierarchical Neural Network Capable of Visual Pattern Recognition,” Neural Networks 1, 119 (1988).
[CrossRef]

T. Kohonen, “An Introduction to Neural Computing,” Neural Networks 1, 3 (1988).
[CrossRef]

Opt. Eng. (1)

H. J. White, N. B. Aldridge, I. Lindsay, “Digital and Analog Holographic Associative Memories,” Opt. Eng. 27, 30 (1988).
[CrossRef]

Opt. Lett. (4)

Proc. IEEE (1)

J. W. Goodman, F. I. Leonberger, S. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850 (1984).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (8)

J. Kinser, H. J. Caulfield, J. Shamir, “A Design for a Massive All-Optical Bidirectional Associative Memory: The Big BAM,” Proc. Soc. Photo-Opt. Instrum. Eng. 881, 269 (1988).

P. A. Ambs, Y. Fainman, S. Esner, S. H. Lee, “Holographic Optical Elements for SLM Defect Removal and for Optical Interconnects,” Proc. Soc. Photo-Opt. Instrum. Eng. 883, paper 31 (1988).

P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space Variant Holographic Filter,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 62 (1988).

J. Ghosh, K. Hwang, “Optically Connected Multiprocessors for Simulating Artificial Neural Networks,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 2 (1988).

S. C. Gustafson, G. R. Little, “Optical Neural Classification for Binary Patterns,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 83 (1988).

D. Brady, X.-G. Gu, D. Psaltis, “Photorefractive Crystal in Optical Neural Computers,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 132 (1988).

H. Wagner, R. E. Feinleib, “Competitive Optoelectronic Learning Networks,” Proc. Soc. Photo-Opt. Instrum. Eng. 882, 162 (1988).

R. Clark, C. Hester, P. Lindberg, “Mapping Sequential Processing Algorithms onto Parallel Distributed Processing Architectures,” Proc. Soc. Photo-Opt. Instrum. Eng. 880, paper 5 (1988).

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Figures (5)

Fig. 1
Fig. 1

Basic configuration for an N4 interconnection network: H, hologram array illuminated by a reconstruction beam R; SLM, spatial light modulator between two lenses L1 and L2 with their respective focal lengths f1 and f2; D, detector array or an array of nonlinear optical devices.

Fig. 2
Fig. 2

Definition of geometrical parameters: H hologram plane; S, SLM plane or the detector plane in the modified architecture; r, distance between the ijth hologram and klth SLM pixel. Polarization vectors P ^ and P ^ as well as the angle αmax and propagation vector k ^ are discussed later.

Fig. 3
Fig. 3

Layout of detector array.

Fig. 4
Fig. 4

Crosstalk percentage as a function of relative center-to-center distance of detectors. Parameter is detector size relative to central lobe o sinc function.

Fig. 5
Fig. 5

Modified architecture with SLM S adjacent to the hologram array H. P is an optional high efficiency grating that may be employed for tilting the reference beam.

Equations (108)

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

b i j = k l t i j k l a k l ,
T A = B .
N s = S / d s ;             N h = H / d h ;             N d = D / d d .
a = 2.44 λ r p h ,
tan θ max = H 2 f 1 .
d s 2.44 λ f 1 p h cos 2 θ max .
d s 2.44 λ H 2 p h sin 2 θ max
d s λ 3.45 sin 2 θ max H p h .
IC h = ( p h l ) 2 g h .
IC s = N s 2 g s ,
p h l N s g s g h .
t i j k l t i j k l + s 2 ( 1 ± 1 ) .
b i j = k l [ t i j k l + ( s ) k l 2 ( 1 ± 1 ) ] a k l / 2 + ( d ) i j 2 ( 1 ± 1 ) ,
d d = f 2 f 1 d h ,
D = f 2 f 1 H .
p h = f 2 f 1 p h ,
d ( λ D d d p s sin 2 θ max ) 2 ,
tan θ max = f 1 f 2 tan θ max .
d ( p h d s f 2 sin 2 θ max d d p s f 1 sin 2 θ max ) 2 ,
s ( λ H d s p h sin 2 θ max ) 2 .
s d ( f 2 d d p s f 1 sin 2 θ max λ H ) 2 .
s d ( f 2 2 f 1 2 d d p s sin 2 θ λ H ) 2 .
x 0 = λ f 2 p s ,
p d = 2 x 0 = λ f p s
( I d ) max M N s 2 I f ,
U = m n g m n h i j m n G ( - d m n s / f ) sinc ( x p s / λ f , y p s / λ f ) .
G [ - d m n s / f ] = exp [ j k f ( m d s x + n d s y ) ] .
U 2 = m n m n g m n h i j m n g m n h i j m n × G ( - d m n s / f ) G ( d m n s / f ) sinc 2 ( x p s / λ f , y p s / λ f ) .
U 2 = sinc 2 ( x p s λ f , y p s λ f ) × { m n g m n 2 h i j m n 2 + m < m , n < n g m n h i j m n g m n h i j m n × cos [ k ( d m n s - d m n s ) · ρ f ] } .
g k l 2 a k l ;             h i j k l 2 t i j k l ,
sinc 2 ( x p s / λ f , y p s / λ f ) [ α + β cos ( d d s f x ) ] ,
x i = λ f 4 d s ,
l ( 0 ) = ( n e - n o ) d = ( 2 N + 1 ) λ / 2 ,
l ( θ ) = ( n e - n o ) d 1 - sin 2 θ n 2 = ( 2 N + 1 ) λ 2 1 - sin 2 θ n 2 ,
l ( θ ) = ( 2 N + 1 ) λ 2 ( 1 + sin 2 θ 2 n 2 ) ,
ϕ ( 2 N + 1 ) π sin 2 θ 2 n 2 .
sin 2 [ ( 2 N + 1 ) π sin 2 θ 2 n 2 ] .
e ^ = P ^ - k ^ ( k ^ · P ^ ) 1 - ( k ^ · P ^ ) 2 .
e t = e ^ · e ^ = P ^ - k ^ ( k ^ · P ^ ) 1 - ( k ^ · P ^ ) 2 · P ^ - k ^ ( k ^ · P ^ ) 1 - ( k ^ · P ^ ) 2 .
e t = ( P ^ · k ^ ) ( P ^ · k ^ ) 1 - ( P ^ · k ^ ) 2 1 - ( P ^ · k ^ ) 2 .
P ^ · k ^ = P ^ · k ^ = sin α = sin θ max 2 .
e t max 2 = tan 4 α sin 4 θ max 4 ,
π 2 sin 4 θ max 4 n 4 .
b i j = k l t k l i j a k l .
d ( λ f p d p h ) 2
W d = N h 2 N s 2 n w o .
W l = N h 2 N s 2 n w o η .
w o = ( I d ) max = M N s 2 I f ,
N s 2 I ( I d ) max = 1 M f .
W l = N d 2 w o M f η .
d s λ 2 2 sin 60 ° H p h = 3.27 H p h .
U i j s = Q [ - 1 / f ] R [ f ] S [ i d d x ^ + j d d y ^ ] u ( x , y ) ,
h i j ( x , y ) = k l h i j k l S [ k d s x ^ + l d s y ^ ] rect ( x / p s , y / p s ) ,
U i j = R [ f ] Q [ - 1 / f ] h i j ( x , y ) U i j s .
U i j s = ν [ 1 / λ f ] F Q [ 1 / f ] S [ d i j d ] u ( x , y ) ,
d i j d = i d d x ^ + j d d y ^ .
U i j s = ν [ 1 / λ f ] F S [ d i j d ] G [ d i j d / f ] Q [ 1 / f ] u ( x , y ) .
U i j s = ν [ 1 / λ f ] G [ - λ d i j d ] S [ d i j d / λ f ] F Q [ 1 / f ] u ( x , y ) .
U i j s = G [ - d i j d / f ] S [ d i j d ] ν [ 1 / λ f ] F Q [ 1 / f ] u ( x , y ) .
U i j s = G [ - d i j d / f ] S [ d i j d ] .
U i j = Q [ 1 / f ] ν [ 1 / λ f ] F h i j ( x , y ) G [ - d i j d / f ] .
U i j = Q [ 1 / f ] ν [ 1 / λ f ] S [ - d i j d / λ f ] H i j = Q [ 1 / f ] S [ - d i j d ] ν [ 1 / λ f ] H i j ,
ν [ 1 / λ f ] H i j ( ν [ 1 / f ] H i j ) * [ G [ - d / f ] ν [ - 1 ] Q [ 1 / f ] u ( x , y ) ] ,
w ( x , y ) = rect ( x p h , y p h ) .
g ( x , y ) = m n g m n S [ m d s x ^ + n d s y ^ ] rect ( x / p s , y / p s ) .
U i j d = R [ f ] Q [ - 1 / f ] g ( x , y ) Q [ - 1 / f ] R [ f ] × { S [ d i j h ] w ( x , y ) } S [ - d i j d ] ν [ 1 / λ f ] H i j * ,
U d = i j U i j d .
U i j d = Q [ 1 / f ] ν [ 1 / λ f ] F g ( x , y ) ν [ 1 / λ f ] F S [ - d i j d ] w ( x , y ) ν [ 1 / λ f ] H i j * ,
S [ d i j h ] = S [ - d i j d ]
U i j d = Q [ 1 / f ] ν [ 1 / λ f ] F g ( x , y ) ν [ 1 / λ f ] G [ λ d i j d ] F w ( x , y ) ν [ 1 / f ] H i j * .
U i j d = Q [ 1 / f ] S [ d i j d ] ν [ 1 / λ f ] F g ( x , y ) ν [ 1 / λ f ] F w ( x , y ) ν [ 1 / λ f ] H i j * .
U i j d = Q [ 1 / f ] S [ d i j d ] ν [ 1 / λ f ] F g ( x , y ) F w ( λ f x , λ f y ) H i j * .
U i j d = Q [ 1 / f ] S [ d i j d ] U .
U = ν [ 1 / λ f ] F g ( x , y ) h * ( - x , - y ) ,
U = ν [ 1 / λ f ] F k l g k l h i j k l S [ d k l s ] rect ( x / p s , y / p s ) ,
U = k l g k l h i j k l G [ - d k l s / f ] sinc ( x p s / λ f , y p s / λ f ) .
U = ν [ 1 / λ f ] F g ( x , y ) F w ( λ f x , λ f y ) H i j * .
U = ν [ 1 / λ f ] { F g ( x , y ) } * { w ( x , y ) ν [ 1 / λ ] H i j * } ,
U i j d = Q [ - 1 / f ] R [ f ] g i j × { S [ - d i j d ] w ( x , y ) } Q [ - 1 / f ] S [ - d i j d ] ν [ 1 / λ f ] H i j * ,
U i j d = g i j ν [ - 1 / λ f ] F S [ - d i j d ] w ( x , y ) ν [ 1 / λ f ] H i j * .
U i j d = g i j G [ - d i j d / f ] { [ ν [ 1 / λ f ] F w ( x , y ) * h i j * ( - x , - y ) } .
U d = i j U i j d .
U d 2 = i j U i j d 2 ,
Q [ a ] = exp ( j k 2 a ρ 2 ) ,
ρ = x x ^ + y y ^ ;             ρ = ρ .
G [ s ] = exp ( j k s · ρ ) .
ν [ a ] f ( x , y ) = f ( a x , a y ) ν [ a ] ,
F f ( x , y ) = f ( x , y ) exp [ 2 π j ( x x + y y ) d x d y ] .
S [ m ] f ( x , y ) = f ( x - m x , y - m y ) S [ m ] .
[ f ] = Q [ - 1 / f ] .
Q [ a ] Q [ b ] = Q [ a + b ] ,
ν [ a ] ν [ b ] = ν [ a b ] ,
ν [ a ] Q [ b ] = Q [ a 2 b ] ν [ a ] ,
ν [ b ] S [ m ] = S [ m / b ] ν [ b ] ,
ν [ b ] G [ m ] = G [ m b ] ν [ b ] ,
Q [ a ] S [ m ] = S [ m ] G [ a m ] Q [ a ] .
ν [ b ] F = F ν [ 1 / b ] ,
F G [ s ] = S [ s / λ ] F ,
F S [ m ] = G [ - λ m ] F .
R [ d ] = F - 1 Q [ - λ 2 d ] F = F Q [ - λ 2 d ] F - 1 ,
R [ d ] = Q [ 1 / d ] ν [ 1 / λ d ] F Q [ 1 / d ] ,
lim d R [ d ] = lim d ν [ 1 / λ d ] F .
R [ a ] R [ b ] = R [ a + b ] .
R [ f ] Q [ - 1 / f ] R [ d ] = Q [ 1 f ( 1 - d f ) ] ν [ 1 λ f ] F
1 / a + 1 / b = 1 / f ,
R [ a ] Q [ - 1 / f ] R [ b ] = Q [ 1 b ( 1 + a b ) ] ν [ - a / b ] .
R [ d ] Q [ 1 / q ] = Q [ 1 / ( d + q ) ] ν [ 1 / ( 1 + d / q ) ] R [ ( 1 / d + 1 / q ) - 1 ] ,
ν [ b ] R [ d ] = R [ d / b 2 ] ν [ b ] .

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