Abstract

Here we propose two encoding schemes that utilize both light intensity and polarization to code input data in digital–optical computing. This approach results in a more efficient information carrying and processing technique when compared with the traditional intensity-only or polarization-only encoding schemes. Optical logic units that are based on the proposed encoding schemes are designed. A recursive parallel adder and a carry look-ahead adder that use these logic units as building blocks are also described.

© 1992 Optical Society of America

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  1. A. A. Sawchuk, T. C. Strand, “Digital optical computing,” Proc. IEEE 72, 758–779 (1984).
    [CrossRef]
  2. W. T. Cathey, K. Wagner, W. J. Miceli, “Digital computing with optics,” Proc. IEEE 77, 1558–1572 (1989).
    [CrossRef]
  3. K. H. Brenner, A. Huang, N. Streibl, “Digital optical computing with symbolic substitution,” Appl. Opt. 25, 3054–3060 (1986).
    [CrossRef] [PubMed]
  4. A. W. Lohmann, “Polarization and optical logic,” Appl. Opt. 25, 1594–1597 (1986).
    [CrossRef] [PubMed]
  5. K. H. Brenner, “New implementation of symbolic substitution logic,” Appl. Opt. 25, 3061–3064 (1986).
    [CrossRef] [PubMed]
  6. A. H. Khan, U. R. Nejib, “Optical logic gates employing liquid crystal optical switches,” Appl. Opt. 26, 270–273 (1987).
    [CrossRef] [PubMed]
  7. M. T. Fatehi, K. C. Wasmundt, S. A. Collins, “Optical logic-gates using liquid crystal light valve: implementation and application example,” Appl. Opt. 20, 2250–2256 (1981).
    [CrossRef] [PubMed]
  8. R. A. Athale, H. S. Barr, S. H. Lee, B. J. Bartholomew, “Digital optical processing,” in Real-Time Signal Processing III, T.F. Tao, ed., Proc. Soc. Photo-Opt. Instrum. Eng.241, 149 (1980).
  9. J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82 MHz optical logic gates in a room temperature. GaAs–AlGaAs as multiple-quantum-well étalon,” Appl. Phys. Lett. 46, 918–920 (1985).
    [CrossRef]
  10. M. Mano, Computer Logic Design (Prentice-Hall, Englewood Cliffs, N.J., 1972).
  11. S. Fukushima, T. Kurokawa, H. Suzuki, “Optical implementation of parallel digital adder and subtractor,” Appl. Opt. 29, 2099–2106 (1990).
    [CrossRef] [PubMed]
  12. P. P. Banerjee, A. Ghafoor, “Design of a pipeline optical binary processor,” Appl. Opt. 27, 4766–4770 (1988).
    [CrossRef] [PubMed]
  13. V. Chandran, T. F. Krile, J. F. Walkup, “Optical techniques for real time binary multiplication,” Appl. Opt. 25, 2272–2276 (1986).
    [CrossRef] [PubMed]
  14. E. Marom, B. H. Soffer, U. Efron, “Pixel-by-pixel array division by optical computing,” Opt. Lett. 10, 43–45 (1985).
    [CrossRef] [PubMed]
  15. J. N. Mait, K. H. Brenner, “Optical symbolic substitution: system design using phase-only holograms,” Appl. Opt. 27, 1692–1700 (1988).
    [CrossRef] [PubMed]
  16. H. I. Jeon, M. A. G. Alexander, A. A. Sawchuk, B. K. Jenkins, “Digital optical processor based on symbolic substitution using holographic matched filtering,” Appl. Opt. 29, 2113–2125 (1990).
    [CrossRef] [PubMed]
  17. J. L. Jewell, A. Scherer, S. L. McCall, A. C. Gossard, J. H. English, “GaAl-AlAs monolithic microresonator arrays,” in Optics and the Information Age: 14th Congress of the lnternational Commission for Optics, H. H. Arsenault, ed., Proc. Soc. Photo Opt. Instrum. Eng.813, 3–4 (1987).
  18. A. Huang, Y. Tsunoda, J. W. Goodman, S. Ishihara, “Optical computation using residue arithmetic,” Appl. Opt. 18, 149–162 (1979).
    [CrossRef] [PubMed]
  19. B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic computing using the modified-signed-digit number representation,” Opt. Eng. 25, 38–44 (1986).
  20. B. Arazi, “An electrooptical adder,” Proc. IEEE 73, 162–163, (1985).
    [CrossRef]
  21. J. B. McManus, S. Putnam, “Construction of an optical carry adder,” Appl. Opt. 26, 1557–1562 (1987).
    [CrossRef] [PubMed]
  22. A. Korpel, A. W. Lohmann, “Polarization and optical bistability,” Appl. Opt. 25, 1528–1529 (1986).
    [CrossRef] [PubMed]
  23. A. Korpel, A. W. Lohmann, “Criteria for optical bistability in ring cavities with two orthogonal modes of polarization,” Appl. Opt. 25, 2253–2257 (1986).
    [CrossRef] [PubMed]

1990 (2)

1989 (1)

W. T. Cathey, K. Wagner, W. J. Miceli, “Digital computing with optics,” Proc. IEEE 77, 1558–1572 (1989).
[CrossRef]

1988 (2)

1987 (2)

1986 (7)

1985 (3)

B. Arazi, “An electrooptical adder,” Proc. IEEE 73, 162–163, (1985).
[CrossRef]

E. Marom, B. H. Soffer, U. Efron, “Pixel-by-pixel array division by optical computing,” Opt. Lett. 10, 43–45 (1985).
[CrossRef] [PubMed]

J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82 MHz optical logic gates in a room temperature. GaAs–AlGaAs as multiple-quantum-well étalon,” Appl. Phys. Lett. 46, 918–920 (1985).
[CrossRef]

1984 (1)

A. A. Sawchuk, T. C. Strand, “Digital optical computing,” Proc. IEEE 72, 758–779 (1984).
[CrossRef]

1981 (1)

1979 (1)

Alexander, M. A. G.

Arazi, B.

B. Arazi, “An electrooptical adder,” Proc. IEEE 73, 162–163, (1985).
[CrossRef]

Athale, R. A.

R. A. Athale, H. S. Barr, S. H. Lee, B. J. Bartholomew, “Digital optical processing,” in Real-Time Signal Processing III, T.F. Tao, ed., Proc. Soc. Photo-Opt. Instrum. Eng.241, 149 (1980).

Banerjee, P. P.

Barr, H. S.

R. A. Athale, H. S. Barr, S. H. Lee, B. J. Bartholomew, “Digital optical processing,” in Real-Time Signal Processing III, T.F. Tao, ed., Proc. Soc. Photo-Opt. Instrum. Eng.241, 149 (1980).

Bartholomew, B. J.

R. A. Athale, H. S. Barr, S. H. Lee, B. J. Bartholomew, “Digital optical processing,” in Real-Time Signal Processing III, T.F. Tao, ed., Proc. Soc. Photo-Opt. Instrum. Eng.241, 149 (1980).

Bocker, R. P.

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic computing using the modified-signed-digit number representation,” Opt. Eng. 25, 38–44 (1986).

Brenner, K. H.

Cathey, W. T.

W. T. Cathey, K. Wagner, W. J. Miceli, “Digital computing with optics,” Proc. IEEE 77, 1558–1572 (1989).
[CrossRef]

Chandran, V.

Collins, S. A.

Drake, B. L.

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic computing using the modified-signed-digit number representation,” Opt. Eng. 25, 38–44 (1986).

Efron, U.

English, J. H.

J. L. Jewell, A. Scherer, S. L. McCall, A. C. Gossard, J. H. English, “GaAl-AlAs monolithic microresonator arrays,” in Optics and the Information Age: 14th Congress of the lnternational Commission for Optics, H. H. Arsenault, ed., Proc. Soc. Photo Opt. Instrum. Eng.813, 3–4 (1987).

Fatehi, M. T.

Fukushima, S.

Ghafoor, A.

Gibbs, H. M.

J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82 MHz optical logic gates in a room temperature. GaAs–AlGaAs as multiple-quantum-well étalon,” Appl. Phys. Lett. 46, 918–920 (1985).
[CrossRef]

Goodman, J. W.

Gossard, A. C.

J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82 MHz optical logic gates in a room temperature. GaAs–AlGaAs as multiple-quantum-well étalon,” Appl. Phys. Lett. 46, 918–920 (1985).
[CrossRef]

J. L. Jewell, A. Scherer, S. L. McCall, A. C. Gossard, J. H. English, “GaAl-AlAs monolithic microresonator arrays,” in Optics and the Information Age: 14th Congress of the lnternational Commission for Optics, H. H. Arsenault, ed., Proc. Soc. Photo Opt. Instrum. Eng.813, 3–4 (1987).

Huang, A.

Ishihara, S.

Jenkins, B. K.

Jeon, H. I.

Jewell, J. L.

J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82 MHz optical logic gates in a room temperature. GaAs–AlGaAs as multiple-quantum-well étalon,” Appl. Phys. Lett. 46, 918–920 (1985).
[CrossRef]

J. L. Jewell, A. Scherer, S. L. McCall, A. C. Gossard, J. H. English, “GaAl-AlAs monolithic microresonator arrays,” in Optics and the Information Age: 14th Congress of the lnternational Commission for Optics, H. H. Arsenault, ed., Proc. Soc. Photo Opt. Instrum. Eng.813, 3–4 (1987).

Khan, A. H.

Korpel, A.

Krile, T. F.

Kurokawa, T.

Lasher, M. E.

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic computing using the modified-signed-digit number representation,” Opt. Eng. 25, 38–44 (1986).

Lee, S. H.

R. A. Athale, H. S. Barr, S. H. Lee, B. J. Bartholomew, “Digital optical processing,” in Real-Time Signal Processing III, T.F. Tao, ed., Proc. Soc. Photo-Opt. Instrum. Eng.241, 149 (1980).

Lee, Y. H.

J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82 MHz optical logic gates in a room temperature. GaAs–AlGaAs as multiple-quantum-well étalon,” Appl. Phys. Lett. 46, 918–920 (1985).
[CrossRef]

Lohmann, A. W.

Mait, J. N.

Mano, M.

M. Mano, Computer Logic Design (Prentice-Hall, Englewood Cliffs, N.J., 1972).

Marom, E.

McCall, S. L.

J. L. Jewell, A. Scherer, S. L. McCall, A. C. Gossard, J. H. English, “GaAl-AlAs monolithic microresonator arrays,” in Optics and the Information Age: 14th Congress of the lnternational Commission for Optics, H. H. Arsenault, ed., Proc. Soc. Photo Opt. Instrum. Eng.813, 3–4 (1987).

McManus, J. B.

Miceli, W. J.

W. T. Cathey, K. Wagner, W. J. Miceli, “Digital computing with optics,” Proc. IEEE 77, 1558–1572 (1989).
[CrossRef]

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic computing using the modified-signed-digit number representation,” Opt. Eng. 25, 38–44 (1986).

Nejib, U. R.

Patterson, R. H.

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic computing using the modified-signed-digit number representation,” Opt. Eng. 25, 38–44 (1986).

Peyghambarian, N.

J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82 MHz optical logic gates in a room temperature. GaAs–AlGaAs as multiple-quantum-well étalon,” Appl. Phys. Lett. 46, 918–920 (1985).
[CrossRef]

Putnam, S.

Sawchuk, A. A.

Scherer, A.

J. L. Jewell, A. Scherer, S. L. McCall, A. C. Gossard, J. H. English, “GaAl-AlAs monolithic microresonator arrays,” in Optics and the Information Age: 14th Congress of the lnternational Commission for Optics, H. H. Arsenault, ed., Proc. Soc. Photo Opt. Instrum. Eng.813, 3–4 (1987).

Soffer, B. H.

Strand, T. C.

A. A. Sawchuk, T. C. Strand, “Digital optical computing,” Proc. IEEE 72, 758–779 (1984).
[CrossRef]

Streibl, N.

Suzuki, H.

Tsunoda, Y.

Wagner, K.

W. T. Cathey, K. Wagner, W. J. Miceli, “Digital computing with optics,” Proc. IEEE 77, 1558–1572 (1989).
[CrossRef]

Walkup, J. F.

Warren, M.

J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82 MHz optical logic gates in a room temperature. GaAs–AlGaAs as multiple-quantum-well étalon,” Appl. Phys. Lett. 46, 918–920 (1985).
[CrossRef]

Wasmundt, K. C.

Wiegmann, W.

J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82 MHz optical logic gates in a room temperature. GaAs–AlGaAs as multiple-quantum-well étalon,” Appl. Phys. Lett. 46, 918–920 (1985).
[CrossRef]

Appl. Opt. (14)

A. Huang, Y. Tsunoda, J. W. Goodman, S. Ishihara, “Optical computation using residue arithmetic,” Appl. Opt. 18, 149–162 (1979).
[CrossRef] [PubMed]

M. T. Fatehi, K. C. Wasmundt, S. A. Collins, “Optical logic-gates using liquid crystal light valve: implementation and application example,” Appl. Opt. 20, 2250–2256 (1981).
[CrossRef] [PubMed]

A. Korpel, A. W. Lohmann, “Polarization and optical bistability,” Appl. Opt. 25, 1528–1529 (1986).
[CrossRef] [PubMed]

A. W. Lohmann, “Polarization and optical logic,” Appl. Opt. 25, 1594–1597 (1986).
[CrossRef] [PubMed]

A. Korpel, A. W. Lohmann, “Criteria for optical bistability in ring cavities with two orthogonal modes of polarization,” Appl. Opt. 25, 2253–2257 (1986).
[CrossRef] [PubMed]

V. Chandran, T. F. Krile, J. F. Walkup, “Optical techniques for real time binary multiplication,” Appl. Opt. 25, 2272–2276 (1986).
[CrossRef] [PubMed]

K. H. Brenner, A. Huang, N. Streibl, “Digital optical computing with symbolic substitution,” Appl. Opt. 25, 3054–3060 (1986).
[CrossRef] [PubMed]

K. H. Brenner, “New implementation of symbolic substitution logic,” Appl. Opt. 25, 3061–3064 (1986).
[CrossRef] [PubMed]

A. H. Khan, U. R. Nejib, “Optical logic gates employing liquid crystal optical switches,” Appl. Opt. 26, 270–273 (1987).
[CrossRef] [PubMed]

J. B. McManus, S. Putnam, “Construction of an optical carry adder,” Appl. Opt. 26, 1557–1562 (1987).
[CrossRef] [PubMed]

J. N. Mait, K. H. Brenner, “Optical symbolic substitution: system design using phase-only holograms,” Appl. Opt. 27, 1692–1700 (1988).
[CrossRef] [PubMed]

P. P. Banerjee, A. Ghafoor, “Design of a pipeline optical binary processor,” Appl. Opt. 27, 4766–4770 (1988).
[CrossRef] [PubMed]

S. Fukushima, T. Kurokawa, H. Suzuki, “Optical implementation of parallel digital adder and subtractor,” Appl. Opt. 29, 2099–2106 (1990).
[CrossRef] [PubMed]

H. I. Jeon, M. A. G. Alexander, A. A. Sawchuk, B. K. Jenkins, “Digital optical processor based on symbolic substitution using holographic matched filtering,” Appl. Opt. 29, 2113–2125 (1990).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82 MHz optical logic gates in a room temperature. GaAs–AlGaAs as multiple-quantum-well étalon,” Appl. Phys. Lett. 46, 918–920 (1985).
[CrossRef]

Opt. Eng. (1)

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic computing using the modified-signed-digit number representation,” Opt. Eng. 25, 38–44 (1986).

Opt. Lett. (1)

Proc. IEEE (3)

B. Arazi, “An electrooptical adder,” Proc. IEEE 73, 162–163, (1985).
[CrossRef]

A. A. Sawchuk, T. C. Strand, “Digital optical computing,” Proc. IEEE 72, 758–779 (1984).
[CrossRef]

W. T. Cathey, K. Wagner, W. J. Miceli, “Digital computing with optics,” Proc. IEEE 77, 1558–1572 (1989).
[CrossRef]

Other (3)

R. A. Athale, H. S. Barr, S. H. Lee, B. J. Bartholomew, “Digital optical processing,” in Real-Time Signal Processing III, T.F. Tao, ed., Proc. Soc. Photo-Opt. Instrum. Eng.241, 149 (1980).

M. Mano, Computer Logic Design (Prentice-Hall, Englewood Cliffs, N.J., 1972).

J. L. Jewell, A. Scherer, S. L. McCall, A. C. Gossard, J. H. English, “GaAl-AlAs monolithic microresonator arrays,” in Optics and the Information Age: 14th Congress of the lnternational Commission for Optics, H. H. Arsenault, ed., Proc. Soc. Photo Opt. Instrum. Eng.813, 3–4 (1987).

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Figures (10)

Fig. 1
Fig. 1

Input operands that are coded by orthogonally polarized light.

Fig. 2
Fig. 2

Logic unit based on a LCC that uses orthogonal polarization states for the two operands.

Fig. 3
Fig. 3

Logic unit based on a LCLV that uses orthogonal polarization states for the two operands.

Fig. 4
Fig. 4

Logic unit based on a LCLV that uses the same polarization state for both operands.

Fig. 5
Fig. 5

Illustration of a recursive parallel addition.

Fig. 6
Fig. 6

Schematic diagram of an optical recursive parallel adder.

Fig. 7
Fig. 7

Optical storage design for a recursive parallel adder.

Fig. 8
Fig. 8

Illustration of a carry look-ahead addition.

Fig. 9
Fig. 9

Intermediate carry generator.

Fig. 10
Fig. 10

Schematic diagram of a carry look-ahead adder.

Equations (12)

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

AND ,             A B = AB ,
OR ,             A + B = A ¯ B + A B ¯ + AB ,
XOR ,             A B = A ¯ B + A B ¯ .
S = A B
C = A B
S i 1 = A i B i ,
C i + 1 1 = A i B i .
S i j = S i j - 1 C i j - 1 ,
C i + 1 j = S i j - 1 C i j - 1 .
T S = T MW + T SW + T MR .
T MW = T SW = T MR = 150 ps , T S = 450 ps .
( n + 1 ) T LCLV + n T S ,

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