Abstract

The use of optics to implement the Boolean logic functions traditionally used in conventional electronic computing is an active area of optical computing research. Many proposed optical implementations duplicate the configuration of electronic logic gates and hence may not optimally utilize the full benefits of optical techniques. We present here a new optical gate, the Fredkin gate, which may, in principle, be minimally dissipative (i.e., exhibit reversible logic) and whose response time may be limited in some implementations only by the duration of optical pulses (i.e., in the picosecond range). Such gates, which consist of three input and three output lines, can be programmed to produce a standard set of Boolean functions and appear well matched to the parallelism of optics. We present here a number of optical implementations of Fredkin gates and suggest ways of composing their interconnections to achieve combinatorial logic, circulating memories and generalized interconnects.

© 1986 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Landauer, “Irreversibility and Heat Generation in the Computing Process,” IBM J. Res. Dev. 5, 183 (1961).
    [CrossRef]
  2. E. Fredkin, T. Toffoli, “Conservative Logic,” Int. J. Theoret. Phys. 21, 219 (1982).
    [CrossRef]
  3. See, for example, R. A. Fisher, Ed., Optical Phase Conjugation (Academic, New York, 1983).
  4. C. S. Tsai, B. Kim, F. R. El-Akkari, “Optical Channel Waveguide Switch and Coupler Using Total Internal Reflection,” IEEE J. Quantum Electron. QE-14, 513 (1978).
    [CrossRef]
  5. C. L. Chang, C. S. Tsai, “GHz Bandwidth Optical Channel Waveguide TIR Switches and 4 × 4 Switching Networks,” in Technical Digest, Topical Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, DC, 1982), paper ThD2.
  6. R. A. Forber, E. Marom, “Optimization of Symmetric Zero-Gap Dielectric Couplers for Large Switch-Array Applications,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1985), paper FL2.
  7. A. Lattes, H. A. Haus, F. T. Leonberger, E. P. Ippen, “Title,” IEEE J. Quantum Electron. QE-19, 1718 (1983).
    [CrossRef]
  8. J. W. Goodman, F. I. Leonberger, S. Y. Kung, R. A. Athale “Optical Interconnections for VLSI,” Proc. IEEE 72, 850 (1984).
    [CrossRef]
  9. J. Haavisto, G. A. Pajer, “Resonance Effects in Low-Loss Ring Waveguides,” Opt. Lett. 5, 510 (1980).
    [CrossRef] [PubMed]
  10. A. Mahapatra, W. C. Robinson, “Integrated-Optic Ring Resonators Made by Proton Exchange in Lithium Niobate,” Appl. Opt. 24, 2285 (1985).
    [CrossRef] [PubMed]

1985 (1)

1984 (1)

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

1983 (1)

A. Lattes, H. A. Haus, F. T. Leonberger, E. P. Ippen, “Title,” IEEE J. Quantum Electron. QE-19, 1718 (1983).
[CrossRef]

1982 (1)

E. Fredkin, T. Toffoli, “Conservative Logic,” Int. J. Theoret. Phys. 21, 219 (1982).
[CrossRef]

1980 (1)

1978 (1)

C. S. Tsai, B. Kim, F. R. El-Akkari, “Optical Channel Waveguide Switch and Coupler Using Total Internal Reflection,” IEEE J. Quantum Electron. QE-14, 513 (1978).
[CrossRef]

1961 (1)

R. Landauer, “Irreversibility and Heat Generation in the Computing Process,” IBM J. Res. Dev. 5, 183 (1961).
[CrossRef]

Athale, R. A.

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

Chang, C. L.

C. L. Chang, C. S. Tsai, “GHz Bandwidth Optical Channel Waveguide TIR Switches and 4 × 4 Switching Networks,” in Technical Digest, Topical Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, DC, 1982), paper ThD2.

El-Akkari, F. R.

C. S. Tsai, B. Kim, F. R. El-Akkari, “Optical Channel Waveguide Switch and Coupler Using Total Internal Reflection,” IEEE J. Quantum Electron. QE-14, 513 (1978).
[CrossRef]

Forber, R. A.

R. A. Forber, E. Marom, “Optimization of Symmetric Zero-Gap Dielectric Couplers for Large Switch-Array Applications,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1985), paper FL2.

Fredkin, E.

E. Fredkin, T. Toffoli, “Conservative Logic,” Int. J. Theoret. Phys. 21, 219 (1982).
[CrossRef]

Goodman, J. W.

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

Haavisto, J.

Haus, H. A.

A. Lattes, H. A. Haus, F. T. Leonberger, E. P. Ippen, “Title,” IEEE J. Quantum Electron. QE-19, 1718 (1983).
[CrossRef]

Ippen, E. P.

A. Lattes, H. A. Haus, F. T. Leonberger, E. P. Ippen, “Title,” IEEE J. Quantum Electron. QE-19, 1718 (1983).
[CrossRef]

Kim, B.

C. S. Tsai, B. Kim, F. R. El-Akkari, “Optical Channel Waveguide Switch and Coupler Using Total Internal Reflection,” IEEE J. Quantum Electron. QE-14, 513 (1978).
[CrossRef]

Kung, S. Y.

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

Landauer, R.

R. Landauer, “Irreversibility and Heat Generation in the Computing Process,” IBM J. Res. Dev. 5, 183 (1961).
[CrossRef]

Lattes, A.

A. Lattes, H. A. Haus, F. T. Leonberger, E. P. Ippen, “Title,” IEEE J. Quantum Electron. QE-19, 1718 (1983).
[CrossRef]

Leonberger, F. I.

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

Leonberger, F. T.

A. Lattes, H. A. Haus, F. T. Leonberger, E. P. Ippen, “Title,” IEEE J. Quantum Electron. QE-19, 1718 (1983).
[CrossRef]

Mahapatra, A.

Marom, E.

R. A. Forber, E. Marom, “Optimization of Symmetric Zero-Gap Dielectric Couplers for Large Switch-Array Applications,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1985), paper FL2.

Pajer, G. A.

Robinson, W. C.

Toffoli, T.

E. Fredkin, T. Toffoli, “Conservative Logic,” Int. J. Theoret. Phys. 21, 219 (1982).
[CrossRef]

Tsai, C. S.

C. S. Tsai, B. Kim, F. R. El-Akkari, “Optical Channel Waveguide Switch and Coupler Using Total Internal Reflection,” IEEE J. Quantum Electron. QE-14, 513 (1978).
[CrossRef]

C. L. Chang, C. S. Tsai, “GHz Bandwidth Optical Channel Waveguide TIR Switches and 4 × 4 Switching Networks,” in Technical Digest, Topical Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, DC, 1982), paper ThD2.

Appl. Opt. (1)

IBM J. Res. Dev. (1)

R. Landauer, “Irreversibility and Heat Generation in the Computing Process,” IBM J. Res. Dev. 5, 183 (1961).
[CrossRef]

IEEE J. Quantum Electron. (2)

C. S. Tsai, B. Kim, F. R. El-Akkari, “Optical Channel Waveguide Switch and Coupler Using Total Internal Reflection,” IEEE J. Quantum Electron. QE-14, 513 (1978).
[CrossRef]

A. Lattes, H. A. Haus, F. T. Leonberger, E. P. Ippen, “Title,” IEEE J. Quantum Electron. QE-19, 1718 (1983).
[CrossRef]

Int. J. Theoret. Phys. (1)

E. Fredkin, T. Toffoli, “Conservative Logic,” Int. J. Theoret. Phys. 21, 219 (1982).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

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

Other (3)

See, for example, R. A. Fisher, Ed., Optical Phase Conjugation (Academic, New York, 1983).

C. L. Chang, C. S. Tsai, “GHz Bandwidth Optical Channel Waveguide TIR Switches and 4 × 4 Switching Networks,” in Technical Digest, Topical Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, DC, 1982), paper ThD2.

R. A. Forber, E. Marom, “Optimization of Symmetric Zero-Gap Dielectric Couplers for Large Switch-Array Applications,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1985), paper FL2.

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 (8)

Fig. 1
Fig. 1

Fredkin gate (see also text).

Fig. 2
Fig. 2

Logic gates implemented by the use of Fredkin gates: (a) an and gate; (b) or gate.

Fig. 3
Fig. 3

Polarization switching gate.

Fig. 4
Fig. 4

Acoustooptic gate.

Fig. 5
Fig. 5

Photorefractive gate using four-wave mixing in photorefractive material (P.R). Beam splitters (B.S) are needed for output coupling.

Fig. 6
Fig. 6

Waveguide coupler gate. The coupling region activated by line C is a photorefractive or other nonlinear material or electrooptic material: (a) out-of-plane control; (b) in-plane control.

Fig. 7
Fig. 7

Integrated optical crossbar. The elliptic regions are the nonlinear coupling switches.

Fig. 8
Fig. 8

Tapped delay line: (a) basic configuration; (b) reversing modification; (c) memory array.

Equations (1)

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

C = C if C = 0 : A = A ; B = B ; if C = 1 : A = B ; B = A .

Metrics