Abstract

Because of the lack of fast, accurate, and large dynamic range analog-to-digital converters (ADCs), optical implementation of the digital multiplication through analog convolution (DMAC) algorithm yields a slow digital multiplier. By replacing both the optical adder and ADC arrays by an optical combinatorial logic counter array, a new optical fast digital multiplication method is proposed. Compared to the existing optical DMAC scheme, the new method promises both higher processing speed and accuracy. A comparison of this and some of the other optical and electronic fast digital multiplication schemes is also presented.

© 1991 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. C. Majithia, R. Kitai, “An Iterative Array For Multiplication of Signed Bin Numbers,” IEEE Trans. Comput. C-20, 214–216 (1971).
    [Crossref]
  2. I. D. Deegan, “Cellular Multiplier For Signed Binary Numbers,” Electron. Lett. 7, 436–437 (1971).
    [Crossref]
  3. C. S. Wallace, “A Suggestion For a Fast Multiplier,” IEEE Trans. Electron. Comput. EC-13, 14–17 (1964).
    [Crossref]
  4. L. Dadda, “Some Schemes For Parallel Multipliers,” Alta Freq. 19, 349–356 (1965).
  5. A. Habibi, P. A. Wintz, “Fast Multipliers,” IEEE Trans. Comput. C-19, 153–157 (1973).
    [Crossref]
  6. E. E. Swartzlander, “The Quasi-Serial Multiplier,” IEEE Trans. Comput. C-22, 317–321 (1973).
    [Crossref]
  7. W. J. Stenzel, W. J. Kubitz, G. H. Garcia, “A Compact High-Speed Parallel Multiplication Scheme,” IEEE Trans. Comput. C-26, 948–957 (1977).
    [Crossref]
  8. I. N. Chen, R. Willoner, “An O(n) Parallel Multiplier With Bit-Sequential Input and Output,” IEEE Trans. Comput. C-28, 721–727 (1979).
    [Crossref]
  9. R. Gnanasekaran, “A Fast Serial-Parallel Binary Multiplier,” IEEE Trans. Comput. C-34, 741–744 (1985).
    [Crossref]
  10. H. J. Whitehouse, J. Speiser, “Linear Signal Processing Architectures,” in Aspects of Signal Processing with Emphasis on Underwater Acoustics,” G. Tacconi, Ed. (Reidel, Hingham, MA, 1977).
    [Crossref]
  11. S. Vassiliadis, E. M. Schwarz, D. J. Hanrahan, “A General Proof For Overlapped Multiple-Bit Scanning Multiplications,” IEEE Trans. Comput. C-38, 172–183 (1989).
    [Crossref]
  12. L. Dadda, “On Serial-Input Multipliers For Two’s Complement Numbers,” IEEE Trans. Comput. C-38, 1341–1345 (1989).
    [Crossref]
  13. D. Psaltis et al.“Accurate Numerical Computation by Optical Convolution,” Proc. Soc. Photo-Opt. Instrum. Eng. 232, 151 (1980).
  14. P. S. Guilfoyle, “Systolic Acousto-Optic Binary Convolver,” Opt. Eng. 23, 20–25 (1984).
    [Crossref]
  15. W. C. Collins, R. A. Athale, P. D. Stilwell, “Improved Accuracy For Optical Iterative Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 352, 59 (1983).
  16. R. P. Bocker, “Optical Digital RUBIC Cube Processor,” Opt. Eng. 23, 26–33 (1984).
  17. A. P. Goutzoulis, “Systolic Time-Integrating Acoustooptic Binary Processor,” Appl. Opt. 23, 4095–4099 (1984).
    [Crossref] [PubMed]
  18. G. Eichmann, Y. Li, P. P. Ho, R. R. Alfano, “Optical Digital Isochronous Array Processing,” Appl. Opt. 26, 2726–2733 (1987).
    [Crossref] [PubMed]
  19. Y. Li, G. Eichmann, R. R. Alfano, “Fast Parallel Optical Digital Multiplication,” Opt. Commun. 64, 99–104 (1987).
    [Crossref]
  20. Y. Li, L. Wang, P. Neos, G. Zhang, X. L. Liang, R. R. Alfano, “Ultrafast Noncollinear Second-Harmonic-Generation- Based 4 × 4 Optical Switching Array,” Opt. Lett. 14, 347–349 (1989).
    [Crossref] [PubMed]
  21. D. Psaltis, R. A. Athale, “High Accuracy Computation With Linear Analog Optical Systems: a Critical Study,” Appl. Opt. 25, 3071–3077 (1986).
    [Crossref] [PubMed]
  22. Z. Kohavi, Switching and Finite Automata (McGraw-Hill, New York, 1978), Chap. 6.
  23. Y. Li, B. Ha, G. Eichmann, “Optical Implementation of Binary Symmetric Logic Functions,” Opt. Lett. 13, 1144–1146 (1988).
    [Crossref] [PubMed]
  24. Y. Li, B. Ha, G. Eichmann, “Optical Binary Symmetric Logic Functions and Their Applications,” Opt. Eng. 28, 380–389 (1989).
    [Crossref]
  25. Y. Li, G. Eichmann, “Parallel Optical Mapping of Binomial Probability Functions,” Opt. Commun. 71, 161–164 (1989).
    [Crossref]
  26. J. Shamir, H. J. Caulfield, W. J. Micelli, R. J. Seymour, “Optical Computing and the Fredkin Gates,” Appl. Opt. 25, 1604–1607 (1986).
    [Crossref] [PubMed]
  27. P. Le, D. Y. Zhang, C. S. Tsai, “Integrated Electrooptic Bragg Modulator Modules For Matrix–Vector and Matrix–Matrix Multiplications,” Appl. Opt. 27, 1780–1785 (1988).
    [Crossref] [PubMed]
  28. Y. Suematsu, S. Arai, “Integrated Optics Approach For Advanced Semiconductor Lasers,” Proc. IEEE 75, 1472 (1987).
    [Crossref]
  29. S. Y. Wang, S. H. Lin, Y. M. Houng, “GaAs Traveling-Wave Polarization Electro-Optic Waveguide Modulator With Bandwidth In Excess of 20 GHz at 1.3 μm,” Appl. Phys. Lett. 51, 83–85 (1987).
    [Crossref]
  30. L. McCaughan, G. A. Bogert, “4 × 4 Ti:LiNbO3 Integrated Optical Crossbar Switch Array,” Appl. Phys. Lett. 47, 348 (1985).
    [Crossref]
  31. P. Granestrand, B. Stoltz, L. Thylen, K. Bergvall, W. Doldissen, H. Heinrich, D. Hoffmann, “Strictly Nonblocking 8 × 8 Integrated Optical Switch Matrix,” Electron. Lett. 22, 816–817 (1987).
    [Crossref]
  32. S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, P. S. Smith, “Femtosecond Switching in a Dual-Core-Fiber Nonlinear Coupler,” Opt. Lett. 13, 904–906 (1988).
    [Crossref] [PubMed]
  33. N. A. Clark, S. T. Lagerwall, “Submicrosecond Bistable Electro-Optic Switching in Liquid Crystals,” Appl. Phys. Lett. 36, 899 (1980).
    [Crossref]
  34. K. M. Johnson, M. A. Handschy, L. A. Pagano-Stauffer, “Optical Computing and Image Processing With Ferroelectric Liquid Crystals,” Opt. Eng. 26, 385–391 (1987).
    [Crossref]
  35. 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]
  36. L. M. F. Chirovsky, L. A. D’Asaro, C. W. Tu, A. L. Lentine, G. D. Boyd, D. A. B. Miller, “Batch Fabricated Symmetric Self-Electrooptic Effect Devices,” in Technical Digest, Topical Meeting on Photonic Switching (Optical Society of America, Washington, DC, 1989), paper ThD4.
  37. M. E. Prise, N. C. Craft, R. E. LaMarche, M. M. Downs, S. J. Walker, L. A. D’Asaro, L. M. F. Chirovsky, “Module For Optical Logic Circuits Using Symmetric Self-Electrooptic Effect Devices,” Appl. Opt. 29, 2164–2170 (1990).
    [Crossref] [PubMed]
  38. P. W. Smith, W. J. Tomlinson, “Bistable Optical Devices Promise Subpicosecond Switching,” IEEE Spectrum 18, 25 (1981).

1990 (1)

1989 (5)

Y. Li, L. Wang, P. Neos, G. Zhang, X. L. Liang, R. R. Alfano, “Ultrafast Noncollinear Second-Harmonic-Generation- Based 4 × 4 Optical Switching Array,” Opt. Lett. 14, 347–349 (1989).
[Crossref] [PubMed]

Y. Li, B. Ha, G. Eichmann, “Optical Binary Symmetric Logic Functions and Their Applications,” Opt. Eng. 28, 380–389 (1989).
[Crossref]

Y. Li, G. Eichmann, “Parallel Optical Mapping of Binomial Probability Functions,” Opt. Commun. 71, 161–164 (1989).
[Crossref]

S. Vassiliadis, E. M. Schwarz, D. J. Hanrahan, “A General Proof For Overlapped Multiple-Bit Scanning Multiplications,” IEEE Trans. Comput. C-38, 172–183 (1989).
[Crossref]

L. Dadda, “On Serial-Input Multipliers For Two’s Complement Numbers,” IEEE Trans. Comput. C-38, 1341–1345 (1989).
[Crossref]

1988 (4)

1987 (6)

P. Granestrand, B. Stoltz, L. Thylen, K. Bergvall, W. Doldissen, H. Heinrich, D. Hoffmann, “Strictly Nonblocking 8 × 8 Integrated Optical Switch Matrix,” Electron. Lett. 22, 816–817 (1987).
[Crossref]

K. M. Johnson, M. A. Handschy, L. A. Pagano-Stauffer, “Optical Computing and Image Processing With Ferroelectric Liquid Crystals,” Opt. Eng. 26, 385–391 (1987).
[Crossref]

Y. Suematsu, S. Arai, “Integrated Optics Approach For Advanced Semiconductor Lasers,” Proc. IEEE 75, 1472 (1987).
[Crossref]

S. Y. Wang, S. H. Lin, Y. M. Houng, “GaAs Traveling-Wave Polarization Electro-Optic Waveguide Modulator With Bandwidth In Excess of 20 GHz at 1.3 μm,” Appl. Phys. Lett. 51, 83–85 (1987).
[Crossref]

G. Eichmann, Y. Li, P. P. Ho, R. R. Alfano, “Optical Digital Isochronous Array Processing,” Appl. Opt. 26, 2726–2733 (1987).
[Crossref] [PubMed]

Y. Li, G. Eichmann, R. R. Alfano, “Fast Parallel Optical Digital Multiplication,” Opt. Commun. 64, 99–104 (1987).
[Crossref]

1986 (2)

1985 (2)

L. McCaughan, G. A. Bogert, “4 × 4 Ti:LiNbO3 Integrated Optical Crossbar Switch Array,” Appl. Phys. Lett. 47, 348 (1985).
[Crossref]

R. Gnanasekaran, “A Fast Serial-Parallel Binary Multiplier,” IEEE Trans. Comput. C-34, 741–744 (1985).
[Crossref]

1984 (3)

R. P. Bocker, “Optical Digital RUBIC Cube Processor,” Opt. Eng. 23, 26–33 (1984).

A. P. Goutzoulis, “Systolic Time-Integrating Acoustooptic Binary Processor,” Appl. Opt. 23, 4095–4099 (1984).
[Crossref] [PubMed]

P. S. Guilfoyle, “Systolic Acousto-Optic Binary Convolver,” Opt. Eng. 23, 20–25 (1984).
[Crossref]

1983 (1)

W. C. Collins, R. A. Athale, P. D. Stilwell, “Improved Accuracy For Optical Iterative Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 352, 59 (1983).

1981 (1)

P. W. Smith, W. J. Tomlinson, “Bistable Optical Devices Promise Subpicosecond Switching,” IEEE Spectrum 18, 25 (1981).

1980 (2)

N. A. Clark, S. T. Lagerwall, “Submicrosecond Bistable Electro-Optic Switching in Liquid Crystals,” Appl. Phys. Lett. 36, 899 (1980).
[Crossref]

D. Psaltis et al.“Accurate Numerical Computation by Optical Convolution,” Proc. Soc. Photo-Opt. Instrum. Eng. 232, 151 (1980).

1979 (1)

I. N. Chen, R. Willoner, “An O(n) Parallel Multiplier With Bit-Sequential Input and Output,” IEEE Trans. Comput. C-28, 721–727 (1979).
[Crossref]

1977 (1)

W. J. Stenzel, W. J. Kubitz, G. H. Garcia, “A Compact High-Speed Parallel Multiplication Scheme,” IEEE Trans. Comput. C-26, 948–957 (1977).
[Crossref]

1973 (2)

A. Habibi, P. A. Wintz, “Fast Multipliers,” IEEE Trans. Comput. C-19, 153–157 (1973).
[Crossref]

E. E. Swartzlander, “The Quasi-Serial Multiplier,” IEEE Trans. Comput. C-22, 317–321 (1973).
[Crossref]

1971 (2)

J. C. Majithia, R. Kitai, “An Iterative Array For Multiplication of Signed Bin Numbers,” IEEE Trans. Comput. C-20, 214–216 (1971).
[Crossref]

I. D. Deegan, “Cellular Multiplier For Signed Binary Numbers,” Electron. Lett. 7, 436–437 (1971).
[Crossref]

1965 (1)

L. Dadda, “Some Schemes For Parallel Multipliers,” Alta Freq. 19, 349–356 (1965).

1964 (1)

C. S. Wallace, “A Suggestion For a Fast Multiplier,” IEEE Trans. Electron. Comput. EC-13, 14–17 (1964).
[Crossref]

Alfano, R. R.

Arai, S.

Y. Suematsu, S. Arai, “Integrated Optics Approach For Advanced Semiconductor Lasers,” Proc. IEEE 75, 1472 (1987).
[Crossref]

Athale, R. A.

D. Psaltis, R. A. Athale, “High Accuracy Computation With Linear Analog Optical Systems: a Critical Study,” Appl. Opt. 25, 3071–3077 (1986).
[Crossref] [PubMed]

W. C. Collins, R. A. Athale, P. D. Stilwell, “Improved Accuracy For Optical Iterative Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 352, 59 (1983).

Bergvall, K.

P. Granestrand, B. Stoltz, L. Thylen, K. Bergvall, W. Doldissen, H. Heinrich, D. Hoffmann, “Strictly Nonblocking 8 × 8 Integrated Optical Switch Matrix,” Electron. Lett. 22, 816–817 (1987).
[Crossref]

Bocker, R. P.

R. P. Bocker, “Optical Digital RUBIC Cube Processor,” Opt. Eng. 23, 26–33 (1984).

Bogert, G. A.

L. McCaughan, G. A. Bogert, “4 × 4 Ti:LiNbO3 Integrated Optical Crossbar Switch Array,” Appl. Phys. Lett. 47, 348 (1985).
[Crossref]

Boyd, G. D.

L. M. F. Chirovsky, L. A. D’Asaro, C. W. Tu, A. L. Lentine, G. D. Boyd, D. A. B. Miller, “Batch Fabricated Symmetric Self-Electrooptic Effect Devices,” in Technical Digest, Topical Meeting on Photonic Switching (Optical Society of America, Washington, DC, 1989), paper ThD4.

Caulfield, H. J.

Chen, I. N.

I. N. Chen, R. Willoner, “An O(n) Parallel Multiplier With Bit-Sequential Input and Output,” IEEE Trans. Comput. C-28, 721–727 (1979).
[Crossref]

Chirovsky, L. M. F.

M. E. Prise, N. C. Craft, R. E. LaMarche, M. M. Downs, S. J. Walker, L. A. D’Asaro, L. M. F. Chirovsky, “Module For Optical Logic Circuits Using Symmetric Self-Electrooptic Effect Devices,” Appl. Opt. 29, 2164–2170 (1990).
[Crossref] [PubMed]

L. M. F. Chirovsky, L. A. D’Asaro, C. W. Tu, A. L. Lentine, G. D. Boyd, D. A. B. Miller, “Batch Fabricated Symmetric Self-Electrooptic Effect Devices,” in Technical Digest, Topical Meeting on Photonic Switching (Optical Society of America, Washington, DC, 1989), paper ThD4.

Clark, N. A.

N. A. Clark, S. T. Lagerwall, “Submicrosecond Bistable Electro-Optic Switching in Liquid Crystals,” Appl. Phys. Lett. 36, 899 (1980).
[Crossref]

Collins, W. C.

W. C. Collins, R. A. Athale, P. D. Stilwell, “Improved Accuracy For Optical Iterative Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 352, 59 (1983).

Craft, N. C.

D’Asaro, L. A.

M. E. Prise, N. C. Craft, R. E. LaMarche, M. M. Downs, S. J. Walker, L. A. D’Asaro, L. M. F. Chirovsky, “Module For Optical Logic Circuits Using Symmetric Self-Electrooptic Effect Devices,” Appl. Opt. 29, 2164–2170 (1990).
[Crossref] [PubMed]

L. M. F. Chirovsky, L. A. D’Asaro, C. W. Tu, A. L. Lentine, G. D. Boyd, D. A. B. Miller, “Batch Fabricated Symmetric Self-Electrooptic Effect Devices,” in Technical Digest, Topical Meeting on Photonic Switching (Optical Society of America, Washington, DC, 1989), paper ThD4.

Dadda, L.

L. Dadda, “On Serial-Input Multipliers For Two’s Complement Numbers,” IEEE Trans. Comput. C-38, 1341–1345 (1989).
[Crossref]

L. Dadda, “Some Schemes For Parallel Multipliers,” Alta Freq. 19, 349–356 (1965).

Deegan, I. D.

I. D. Deegan, “Cellular Multiplier For Signed Binary Numbers,” Electron. Lett. 7, 436–437 (1971).
[Crossref]

Doldissen, W.

P. Granestrand, B. Stoltz, L. Thylen, K. Bergvall, W. Doldissen, H. Heinrich, D. Hoffmann, “Strictly Nonblocking 8 × 8 Integrated Optical Switch Matrix,” Electron. Lett. 22, 816–817 (1987).
[Crossref]

Downs, M. M.

Eichmann, G.

Y. Li, G. Eichmann, “Parallel Optical Mapping of Binomial Probability Functions,” Opt. Commun. 71, 161–164 (1989).
[Crossref]

Y. Li, B. Ha, G. Eichmann, “Optical Binary Symmetric Logic Functions and Their Applications,” Opt. Eng. 28, 380–389 (1989).
[Crossref]

Y. Li, B. Ha, G. Eichmann, “Optical Implementation of Binary Symmetric Logic Functions,” Opt. Lett. 13, 1144–1146 (1988).
[Crossref] [PubMed]

G. Eichmann, Y. Li, P. P. Ho, R. R. Alfano, “Optical Digital Isochronous Array Processing,” Appl. Opt. 26, 2726–2733 (1987).
[Crossref] [PubMed]

Y. Li, G. Eichmann, R. R. Alfano, “Fast Parallel Optical Digital Multiplication,” Opt. Commun. 64, 99–104 (1987).
[Crossref]

Friberg, S. R.

Garcia, G. H.

W. J. Stenzel, W. J. Kubitz, G. H. Garcia, “A Compact High-Speed Parallel Multiplication Scheme,” IEEE Trans. Comput. C-26, 948–957 (1977).
[Crossref]

Gnanasekaran, R.

R. Gnanasekaran, “A Fast Serial-Parallel Binary Multiplier,” IEEE Trans. Comput. C-34, 741–744 (1985).
[Crossref]

Goutzoulis, A. P.

Granestrand, P.

P. Granestrand, B. Stoltz, L. Thylen, K. Bergvall, W. Doldissen, H. Heinrich, D. Hoffmann, “Strictly Nonblocking 8 × 8 Integrated Optical Switch Matrix,” Electron. Lett. 22, 816–817 (1987).
[Crossref]

Guilfoyle, P. S.

P. S. Guilfoyle, “Systolic Acousto-Optic Binary Convolver,” Opt. Eng. 23, 20–25 (1984).
[Crossref]

Ha, B.

Y. Li, B. Ha, G. Eichmann, “Optical Binary Symmetric Logic Functions and Their Applications,” Opt. Eng. 28, 380–389 (1989).
[Crossref]

Y. Li, B. Ha, G. Eichmann, “Optical Implementation of Binary Symmetric Logic Functions,” Opt. Lett. 13, 1144–1146 (1988).
[Crossref] [PubMed]

Habibi, A.

A. Habibi, P. A. Wintz, “Fast Multipliers,” IEEE Trans. Comput. C-19, 153–157 (1973).
[Crossref]

Handschy, M. A.

K. M. Johnson, M. A. Handschy, L. A. Pagano-Stauffer, “Optical Computing and Image Processing With Ferroelectric Liquid Crystals,” Opt. Eng. 26, 385–391 (1987).
[Crossref]

Hanrahan, D. J.

S. Vassiliadis, E. M. Schwarz, D. J. Hanrahan, “A General Proof For Overlapped Multiple-Bit Scanning Multiplications,” IEEE Trans. Comput. C-38, 172–183 (1989).
[Crossref]

Heinrich, H.

P. Granestrand, B. Stoltz, L. Thylen, K. Bergvall, W. Doldissen, H. Heinrich, D. Hoffmann, “Strictly Nonblocking 8 × 8 Integrated Optical Switch Matrix,” Electron. Lett. 22, 816–817 (1987).
[Crossref]

Ho, P. P.

Hoffmann, D.

P. Granestrand, B. Stoltz, L. Thylen, K. Bergvall, W. Doldissen, H. Heinrich, D. Hoffmann, “Strictly Nonblocking 8 × 8 Integrated Optical Switch Matrix,” Electron. Lett. 22, 816–817 (1987).
[Crossref]

Houng, Y. M.

S. Y. Wang, S. H. Lin, Y. M. Houng, “GaAs Traveling-Wave Polarization Electro-Optic Waveguide Modulator With Bandwidth In Excess of 20 GHz at 1.3 μm,” Appl. Phys. Lett. 51, 83–85 (1987).
[Crossref]

Johnson, K. M.

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]

K. M. Johnson, M. A. Handschy, L. A. Pagano-Stauffer, “Optical Computing and Image Processing With Ferroelectric Liquid Crystals,” Opt. Eng. 26, 385–391 (1987).
[Crossref]

Kitai, R.

J. C. Majithia, R. Kitai, “An Iterative Array For Multiplication of Signed Bin Numbers,” IEEE Trans. Comput. C-20, 214–216 (1971).
[Crossref]

Kohavi, Z.

Z. Kohavi, Switching and Finite Automata (McGraw-Hill, New York, 1978), Chap. 6.

Kubitz, W. J.

W. J. Stenzel, W. J. Kubitz, G. H. Garcia, “A Compact High-Speed Parallel Multiplication Scheme,” IEEE Trans. Comput. C-26, 948–957 (1977).
[Crossref]

Lagerwall, S. T.

N. A. Clark, S. T. Lagerwall, “Submicrosecond Bistable Electro-Optic Switching in Liquid Crystals,” Appl. Phys. Lett. 36, 899 (1980).
[Crossref]

LaMarche, R. E.

Le, P.

Lentine, A. L.

L. M. F. Chirovsky, L. A. D’Asaro, C. W. Tu, A. L. Lentine, G. D. Boyd, D. A. B. Miller, “Batch Fabricated Symmetric Self-Electrooptic Effect Devices,” in Technical Digest, Topical Meeting on Photonic Switching (Optical Society of America, Washington, DC, 1989), paper ThD4.

Li, Y.

Y. Li, G. Eichmann, “Parallel Optical Mapping of Binomial Probability Functions,” Opt. Commun. 71, 161–164 (1989).
[Crossref]

Y. Li, B. Ha, G. Eichmann, “Optical Binary Symmetric Logic Functions and Their Applications,” Opt. Eng. 28, 380–389 (1989).
[Crossref]

Y. Li, L. Wang, P. Neos, G. Zhang, X. L. Liang, R. R. Alfano, “Ultrafast Noncollinear Second-Harmonic-Generation- Based 4 × 4 Optical Switching Array,” Opt. Lett. 14, 347–349 (1989).
[Crossref] [PubMed]

Y. Li, B. Ha, G. Eichmann, “Optical Implementation of Binary Symmetric Logic Functions,” Opt. Lett. 13, 1144–1146 (1988).
[Crossref] [PubMed]

G. Eichmann, Y. Li, P. P. Ho, R. R. Alfano, “Optical Digital Isochronous Array Processing,” Appl. Opt. 26, 2726–2733 (1987).
[Crossref] [PubMed]

Y. Li, G. Eichmann, R. R. Alfano, “Fast Parallel Optical Digital Multiplication,” Opt. Commun. 64, 99–104 (1987).
[Crossref]

Liang, X. L.

Lin, S. H.

S. Y. Wang, S. H. Lin, Y. M. Houng, “GaAs Traveling-Wave Polarization Electro-Optic Waveguide Modulator With Bandwidth In Excess of 20 GHz at 1.3 μm,” Appl. Phys. Lett. 51, 83–85 (1987).
[Crossref]

Majithia, J. C.

J. C. Majithia, R. Kitai, “An Iterative Array For Multiplication of Signed Bin Numbers,” IEEE Trans. Comput. C-20, 214–216 (1971).
[Crossref]

McCaughan, L.

L. McCaughan, G. A. Bogert, “4 × 4 Ti:LiNbO3 Integrated Optical Crossbar Switch Array,” Appl. Phys. Lett. 47, 348 (1985).
[Crossref]

Micelli, W. J.

Miller, D. A. B.

L. M. F. Chirovsky, L. A. D’Asaro, C. W. Tu, A. L. Lentine, G. D. Boyd, D. A. B. Miller, “Batch Fabricated Symmetric Self-Electrooptic Effect Devices,” in Technical Digest, Topical Meeting on Photonic Switching (Optical Society of America, Washington, DC, 1989), paper ThD4.

Neos, P.

Pagano-Stauffer, L. A.

K. M. Johnson, M. A. Handschy, L. A. Pagano-Stauffer, “Optical Computing and Image Processing With Ferroelectric Liquid Crystals,” Opt. Eng. 26, 385–391 (1987).
[Crossref]

Prise, M. E.

Psaltis, D.

D. Psaltis, R. A. Athale, “High Accuracy Computation With Linear Analog Optical Systems: a Critical Study,” Appl. Opt. 25, 3071–3077 (1986).
[Crossref] [PubMed]

D. Psaltis et al.“Accurate Numerical Computation by Optical Convolution,” Proc. Soc. Photo-Opt. Instrum. Eng. 232, 151 (1980).

Schwarz, E. M.

S. Vassiliadis, E. M. Schwarz, D. J. Hanrahan, “A General Proof For Overlapped Multiple-Bit Scanning Multiplications,” IEEE Trans. Comput. C-38, 172–183 (1989).
[Crossref]

Seymour, R. J.

Sfez, B. G.

Shamir, J.

Silberberg, Y.

Smith, P. S.

Smith, P. W.

P. W. Smith, W. J. Tomlinson, “Bistable Optical Devices Promise Subpicosecond Switching,” IEEE Spectrum 18, 25 (1981).

Speiser, J.

H. J. Whitehouse, J. Speiser, “Linear Signal Processing Architectures,” in Aspects of Signal Processing with Emphasis on Underwater Acoustics,” G. Tacconi, Ed. (Reidel, Hingham, MA, 1977).
[Crossref]

Stenzel, W. J.

W. J. Stenzel, W. J. Kubitz, G. H. Garcia, “A Compact High-Speed Parallel Multiplication Scheme,” IEEE Trans. Comput. C-26, 948–957 (1977).
[Crossref]

Stilwell, P. D.

W. C. Collins, R. A. Athale, P. D. Stilwell, “Improved Accuracy For Optical Iterative Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 352, 59 (1983).

Stoltz, B.

P. Granestrand, B. Stoltz, L. Thylen, K. Bergvall, W. Doldissen, H. Heinrich, D. Hoffmann, “Strictly Nonblocking 8 × 8 Integrated Optical Switch Matrix,” Electron. Lett. 22, 816–817 (1987).
[Crossref]

Suematsu, Y.

Y. Suematsu, S. Arai, “Integrated Optics Approach For Advanced Semiconductor Lasers,” Proc. IEEE 75, 1472 (1987).
[Crossref]

Surette, M. R.

Swartzlander, E. E.

E. E. Swartzlander, “The Quasi-Serial Multiplier,” IEEE Trans. Comput. C-22, 317–321 (1973).
[Crossref]

Thylen, L.

P. Granestrand, B. Stoltz, L. Thylen, K. Bergvall, W. Doldissen, H. Heinrich, D. Hoffmann, “Strictly Nonblocking 8 × 8 Integrated Optical Switch Matrix,” Electron. Lett. 22, 816–817 (1987).
[Crossref]

Tomlinson, W. J.

P. W. Smith, W. J. Tomlinson, “Bistable Optical Devices Promise Subpicosecond Switching,” IEEE Spectrum 18, 25 (1981).

Tsai, C. S.

Tu, C. W.

L. M. F. Chirovsky, L. A. D’Asaro, C. W. Tu, A. L. Lentine, G. D. Boyd, D. A. B. Miller, “Batch Fabricated Symmetric Self-Electrooptic Effect Devices,” in Technical Digest, Topical Meeting on Photonic Switching (Optical Society of America, Washington, DC, 1989), paper ThD4.

Vassiliadis, S.

S. Vassiliadis, E. M. Schwarz, D. J. Hanrahan, “A General Proof For Overlapped Multiple-Bit Scanning Multiplications,” IEEE Trans. Comput. C-38, 172–183 (1989).
[Crossref]

Walker, S. J.

Wallace, C. S.

C. S. Wallace, “A Suggestion For a Fast Multiplier,” IEEE Trans. Electron. Comput. EC-13, 14–17 (1964).
[Crossref]

Wang, L.

Wang, S. Y.

S. Y. Wang, S. H. Lin, Y. M. Houng, “GaAs Traveling-Wave Polarization Electro-Optic Waveguide Modulator With Bandwidth In Excess of 20 GHz at 1.3 μm,” Appl. Phys. Lett. 51, 83–85 (1987).
[Crossref]

Weiner, A. M.

Whitehouse, H. J.

H. J. Whitehouse, J. Speiser, “Linear Signal Processing Architectures,” in Aspects of Signal Processing with Emphasis on Underwater Acoustics,” G. Tacconi, Ed. (Reidel, Hingham, MA, 1977).
[Crossref]

Willoner, R.

I. N. Chen, R. Willoner, “An O(n) Parallel Multiplier With Bit-Sequential Input and Output,” IEEE Trans. Comput. C-28, 721–727 (1979).
[Crossref]

Wintz, P. A.

A. Habibi, P. A. Wintz, “Fast Multipliers,” IEEE Trans. Comput. C-19, 153–157 (1973).
[Crossref]

Zhang, D. Y.

Zhang, G.

Alta Freq. (1)

L. Dadda, “Some Schemes For Parallel Multipliers,” Alta Freq. 19, 349–356 (1965).

Appl. Opt. (7)

Appl. Phys. Lett. (3)

N. A. Clark, S. T. Lagerwall, “Submicrosecond Bistable Electro-Optic Switching in Liquid Crystals,” Appl. Phys. Lett. 36, 899 (1980).
[Crossref]

S. Y. Wang, S. H. Lin, Y. M. Houng, “GaAs Traveling-Wave Polarization Electro-Optic Waveguide Modulator With Bandwidth In Excess of 20 GHz at 1.3 μm,” Appl. Phys. Lett. 51, 83–85 (1987).
[Crossref]

L. McCaughan, G. A. Bogert, “4 × 4 Ti:LiNbO3 Integrated Optical Crossbar Switch Array,” Appl. Phys. Lett. 47, 348 (1985).
[Crossref]

Electron. Lett. (2)

P. Granestrand, B. Stoltz, L. Thylen, K. Bergvall, W. Doldissen, H. Heinrich, D. Hoffmann, “Strictly Nonblocking 8 × 8 Integrated Optical Switch Matrix,” Electron. Lett. 22, 816–817 (1987).
[Crossref]

I. D. Deegan, “Cellular Multiplier For Signed Binary Numbers,” Electron. Lett. 7, 436–437 (1971).
[Crossref]

IEEE Spectrum (1)

P. W. Smith, W. J. Tomlinson, “Bistable Optical Devices Promise Subpicosecond Switching,” IEEE Spectrum 18, 25 (1981).

IEEE Trans. Comput. (8)

S. Vassiliadis, E. M. Schwarz, D. J. Hanrahan, “A General Proof For Overlapped Multiple-Bit Scanning Multiplications,” IEEE Trans. Comput. C-38, 172–183 (1989).
[Crossref]

L. Dadda, “On Serial-Input Multipliers For Two’s Complement Numbers,” IEEE Trans. Comput. C-38, 1341–1345 (1989).
[Crossref]

A. Habibi, P. A. Wintz, “Fast Multipliers,” IEEE Trans. Comput. C-19, 153–157 (1973).
[Crossref]

E. E. Swartzlander, “The Quasi-Serial Multiplier,” IEEE Trans. Comput. C-22, 317–321 (1973).
[Crossref]

W. J. Stenzel, W. J. Kubitz, G. H. Garcia, “A Compact High-Speed Parallel Multiplication Scheme,” IEEE Trans. Comput. C-26, 948–957 (1977).
[Crossref]

I. N. Chen, R. Willoner, “An O(n) Parallel Multiplier With Bit-Sequential Input and Output,” IEEE Trans. Comput. C-28, 721–727 (1979).
[Crossref]

R. Gnanasekaran, “A Fast Serial-Parallel Binary Multiplier,” IEEE Trans. Comput. C-34, 741–744 (1985).
[Crossref]

J. C. Majithia, R. Kitai, “An Iterative Array For Multiplication of Signed Bin Numbers,” IEEE Trans. Comput. C-20, 214–216 (1971).
[Crossref]

IEEE Trans. Electron. Comput. (1)

C. S. Wallace, “A Suggestion For a Fast Multiplier,” IEEE Trans. Electron. Comput. EC-13, 14–17 (1964).
[Crossref]

Opt. Commun. (2)

Y. Li, G. Eichmann, R. R. Alfano, “Fast Parallel Optical Digital Multiplication,” Opt. Commun. 64, 99–104 (1987).
[Crossref]

Y. Li, G. Eichmann, “Parallel Optical Mapping of Binomial Probability Functions,” Opt. Commun. 71, 161–164 (1989).
[Crossref]

Opt. Eng. (4)

R. P. Bocker, “Optical Digital RUBIC Cube Processor,” Opt. Eng. 23, 26–33 (1984).

P. S. Guilfoyle, “Systolic Acousto-Optic Binary Convolver,” Opt. Eng. 23, 20–25 (1984).
[Crossref]

K. M. Johnson, M. A. Handschy, L. A. Pagano-Stauffer, “Optical Computing and Image Processing With Ferroelectric Liquid Crystals,” Opt. Eng. 26, 385–391 (1987).
[Crossref]

Y. Li, B. Ha, G. Eichmann, “Optical Binary Symmetric Logic Functions and Their Applications,” Opt. Eng. 28, 380–389 (1989).
[Crossref]

Opt. Lett. (3)

Proc. IEEE (1)

Y. Suematsu, S. Arai, “Integrated Optics Approach For Advanced Semiconductor Lasers,” Proc. IEEE 75, 1472 (1987).
[Crossref]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

W. C. Collins, R. A. Athale, P. D. Stilwell, “Improved Accuracy For Optical Iterative Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 352, 59 (1983).

D. Psaltis et al.“Accurate Numerical Computation by Optical Convolution,” Proc. Soc. Photo-Opt. Instrum. Eng. 232, 151 (1980).

Other (3)

H. J. Whitehouse, J. Speiser, “Linear Signal Processing Architectures,” in Aspects of Signal Processing with Emphasis on Underwater Acoustics,” G. Tacconi, Ed. (Reidel, Hingham, MA, 1977).
[Crossref]

L. M. F. Chirovsky, L. A. D’Asaro, C. W. Tu, A. L. Lentine, G. D. Boyd, D. A. B. Miller, “Batch Fabricated Symmetric Self-Electrooptic Effect Devices,” in Technical Digest, Topical Meeting on Photonic Switching (Optical Society of America, Washington, DC, 1989), paper ThD4.

Z. Kohavi, Switching and Finite Automata (McGraw-Hill, New York, 1978), Chap. 6.

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 (11)

Fig. 1
Fig. 1

(a) A 4-bit binary digital multiplication-through-counting process: here p and c are a partial product digit and a carry digit produced through a count in a previous summation column, respectively; U0 through U6 denote the seven summation columns. (b) The same process expressed in a compact form.

Fig. 2
Fig. 2

Numerical example of a 4-bit multiplication-through-counting. Digits within the dashed lines are the carry bits.

Fig. 3
Fig. 3

schematic of an N-variable OBSLM. In the upper right hand side corner, a switching node is drawn separately.

Fig. 4
Fig. 4

Implementation of the various smaller size BSLFs through an N-variable OBSLM. Optical inputs are used at different network levels.

Fig. 5
Fig. 5

Schematic of a guide wave OBSLM. Each switching node contains a wave combiner and a directional coupler.

Fig. 6
Fig. 6

Schematic of a free-space OBSLM. Each switching node contains a FELC switch, two halfwave plates, a regular beam splitter, and a polarizing beam splitter.

Fig. 7
Fig. 7

(a) An OBSLM-based (3,2) parallel digital counter. A three-variable OBSLM and a passive scription network are used. (b) Schematic of an OBSLM (7,3) parallel digital counter.

Fig. 8
Fig. 8

Interconnect topology for an OBSLM counter-based 4-bit optical multiplier: U0U6 are seven partial products and intermediate carry columns.

Fig. 9
Fig. 9

Schematic of an OBSLM counter-based 8-bit optical digital multiplier. Fourteen OBSLM counter arrays are used.

Fig. 10
Fig. 10

Timing diagram for an OBSLM counter-based 4-bit optical digital multiplication example (see also Fig. 2).

Fig. 11
Fig. 11

Several fast digital multiplication-through-partial-product reduction schemes.

Tables (2)

Tables Icon

Table I Speed Comparison of Different Schemes for Binary Multiplicationa

Tables Icon

Table II Complexity Comparison of Different Schemes for a 12-bit Binary Multiplication

Equations (15)

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

| A · B | = i = 0 N 1 a i 2 i j = 0 N 1 b j 2 j ,
| A · B | = j = 0 N 1 ( i = 0 N 1 a i 2 i b j ) 2 j .
| A · B | = i = 0 2 N 2 s i 2 i ,
s i = k = 0 i a k b i k ,
h i = { i + 1 if i = 0 , , N 1 , 2 N i 1 if i = N , , 2 N 2 .
d = [ log 2 c ] + 1 ,
A = i = 0 3 a i 2 i , B = j = 0 3 b j 2 j
h i = h i + Δ h i ,
Δ h i = { [ log 2 i ] 0 i N , [ log 2 h i k ] N + 1 i 2 N 3 , 2 i = 2 N 2 , 2 N 1 ,
k = [ log 2 h i ] + 1 .
f ( x , y , z ) = x ¯ y ¯ z + x y ¯ z ¯ + x ¯ y z ¯ ,
T H > N n L c ,
T PP + ( ln N / ln 1 . 5 ) T C C + ( 2 N 2 ln N / ln 1 . 5 ) T ADD ,
Q = j = 1 2 N 2 h j ( h j + 1 ) 2 .
T OPP + T A/D ( N ) + N [ log 2 N ] T ADD ,

Metrics