Abstract

An array of optical Fredkin gates implemented by optically controlled waveguide couplers is shown to constitute a very efficient and versatile optical interconnection network with parallel addressing capabilities. The characteristics of the array are analyzed using linear algebra to indicate interconnect programming procedures. In terms of SNR this network is estimated to be comparable with previously proposed architectures. However, from many other aspects (light transmission efficiency, number of switching elements, speed, and fault tolerance) it has significant advantages.

© 1987 Optical Society of America

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References

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  1. J. W. Goodman et al. “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850 (1984).
    [CrossRef]
  2. R. K. Kostuk, J. W. Goodman, L. Hesselink, “Optical Imaging Applied to Microelectronic Chip-to-Chip Interconnections,” Appl. Opt. 24, 2851 (1985).
    [CrossRef] [PubMed]
  3. A. A. Sawchuk, B. K. Jenkins, “Dynamic Optical Interconnections for Parallel Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143 (1986).
  4. A. W. Lohmann, “What Classical Optics can do for the Digital Optical Computer,” Appl. Opt. 25, 1543 (1986).
    [CrossRef] [PubMed]
  5. E. Marom, N. Konforti, “Programmable Optical Interconnects,” Soc. Photo-Opt. Instrum. Eng. 700, 296 (1986).
  6. J. Shamir, H. J. Caulfield, W. Miceli, R. J. Seymour, “Optical Computing and the Fredkin Gate,” Appl. Opt. 25, 1604 (1986).
    [CrossRef] [PubMed]
  7. T. M. Gaylord, “Digital Data Storage,” in Handbook of Optical Holography, H. J. Caulfield, Ed. (Academic, New York, 1979), pp. 379–413.
  8. M. M. Mirsalehi, T. K. Gaylord, “Truth-Table Look-up Parallel Data Processing using an Optical Content-Addressable Memory,” Appl. Opt. 25, 2277 (1986).
    [CrossRef] [PubMed]
  9. U. J. Schmidt, “Present State of the Digital Laser Beam Deflection Technique for Alphanumeric and Graphic Displays,” in Progress in Electro-Optics, E. Camatini, Ed. (Plenum, New York, 1975), pp. 161–180.
    [CrossRef]
  10. E. H. Young, S.-K. Yao, “Design Considerations of Acoustooptic Devices,” Proc. IEEE 69, 54 (1981).
    [CrossRef]
  11. L. McCaughan, G. A. Bogert, “4 × 4 Ti:LiNbO3 Integrated Optical Crossbar Switch Array,” Appl. Phys. Lett. 47, 348 (1985).
    [CrossRef]
  12. R. Chen, C. S. Tsai, “Thermally Annealed Single-Mode Proton-Exchanged Channel-Waveguide Cutoff Modulator,” Opt. Lett. 11, 546 (1986).
    [CrossRef] [PubMed]
  13. S. K. Korotky et al., “Fully Connectorized High-Speed Ti:LiNbO3 Switch/Modulator for Time-Division Multiplexing and Data Encoding,” IEEE/OSA J. Lightwave Technol. 3, 1 (1985).
    [CrossRef]
  14. R. A. Becker, W. S. C. Chang, “Electrooptical Switching in Thin Film Waveguides for a Computer Communication Bus,” Appl. Opt. 18, 3296 (1979).
    [CrossRef] [PubMed]
  15. D. F. Clark, I. Andonovic, B. Culshaw, “Perturbation Analysis for the Design of an Optically Controlled Fiber-Optic Directional Coupler,” Opt. Lett. 11, 540 (1986).
    [CrossRef] [PubMed]
  16. L. A. Molter-Orr, H. A. Haus, “Multiple Coupled Waveguide Switches Using Alternating Δβ Phase Mismatch,” Appl. Opt. 24, 1260 (1985).
    [CrossRef] [PubMed]
  17. B. Clymer, J. W. Goodman, “Optical Clock Distribution to an IC Chip,” Opt. Eng. 25, 1103 (1986).
  18. See, for example, C. Clos, “A study of Non-blocking Switching Networks,” Bell Syst. Tech. J. 32, 406 (1953).
  19. J. W. Goodman, “Fan-in and Fan-out with Optical Interconnections,” Opt. Acta 32, 1489 (1985).
    [CrossRef]

1986 (8)

1985 (5)

L. A. Molter-Orr, H. A. Haus, “Multiple Coupled Waveguide Switches Using Alternating Δβ Phase Mismatch,” Appl. Opt. 24, 1260 (1985).
[CrossRef] [PubMed]

R. K. Kostuk, J. W. Goodman, L. Hesselink, “Optical Imaging Applied to Microelectronic Chip-to-Chip Interconnections,” Appl. Opt. 24, 2851 (1985).
[CrossRef] [PubMed]

J. W. Goodman, “Fan-in and Fan-out with Optical Interconnections,” Opt. Acta 32, 1489 (1985).
[CrossRef]

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

S. K. Korotky et al., “Fully Connectorized High-Speed Ti:LiNbO3 Switch/Modulator for Time-Division Multiplexing and Data Encoding,” IEEE/OSA J. Lightwave Technol. 3, 1 (1985).
[CrossRef]

1984 (1)

J. W. Goodman et al. “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850 (1984).
[CrossRef]

1981 (1)

E. H. Young, S.-K. Yao, “Design Considerations of Acoustooptic Devices,” Proc. IEEE 69, 54 (1981).
[CrossRef]

1979 (1)

1953 (1)

See, for example, C. Clos, “A study of Non-blocking Switching Networks,” Bell Syst. Tech. J. 32, 406 (1953).

Andonovic, I.

Becker, R. A.

Bogert, G. A.

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

Caulfield, H. J.

Chang, W. S. C.

Chen, R.

Clark, D. F.

Clos, C.

See, for example, C. Clos, “A study of Non-blocking Switching Networks,” Bell Syst. Tech. J. 32, 406 (1953).

Clymer, B.

B. Clymer, J. W. Goodman, “Optical Clock Distribution to an IC Chip,” Opt. Eng. 25, 1103 (1986).

Culshaw, B.

Gaylord, T. K.

Gaylord, T. M.

T. M. Gaylord, “Digital Data Storage,” in Handbook of Optical Holography, H. J. Caulfield, Ed. (Academic, New York, 1979), pp. 379–413.

Goodman, J. W.

B. Clymer, J. W. Goodman, “Optical Clock Distribution to an IC Chip,” Opt. Eng. 25, 1103 (1986).

R. K. Kostuk, J. W. Goodman, L. Hesselink, “Optical Imaging Applied to Microelectronic Chip-to-Chip Interconnections,” Appl. Opt. 24, 2851 (1985).
[CrossRef] [PubMed]

J. W. Goodman, “Fan-in and Fan-out with Optical Interconnections,” Opt. Acta 32, 1489 (1985).
[CrossRef]

J. W. Goodman et al. “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850 (1984).
[CrossRef]

Haus, H. A.

Hesselink, L.

Jenkins, B. K.

A. A. Sawchuk, B. K. Jenkins, “Dynamic Optical Interconnections for Parallel Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143 (1986).

Konforti, N.

E. Marom, N. Konforti, “Programmable Optical Interconnects,” Soc. Photo-Opt. Instrum. Eng. 700, 296 (1986).

Korotky, S. K.

S. K. Korotky et al., “Fully Connectorized High-Speed Ti:LiNbO3 Switch/Modulator for Time-Division Multiplexing and Data Encoding,” IEEE/OSA J. Lightwave Technol. 3, 1 (1985).
[CrossRef]

Kostuk, R. K.

Lohmann, A. W.

Marom, E.

E. Marom, N. Konforti, “Programmable Optical Interconnects,” Soc. Photo-Opt. Instrum. Eng. 700, 296 (1986).

McCaughan, L.

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

Miceli, W.

Mirsalehi, M. M.

Molter-Orr, L. A.

Sawchuk, A. A.

A. A. Sawchuk, B. K. Jenkins, “Dynamic Optical Interconnections for Parallel Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143 (1986).

Schmidt, U. J.

U. J. Schmidt, “Present State of the Digital Laser Beam Deflection Technique for Alphanumeric and Graphic Displays,” in Progress in Electro-Optics, E. Camatini, Ed. (Plenum, New York, 1975), pp. 161–180.
[CrossRef]

Seymour, R. J.

Shamir, J.

Tsai, C. S.

Yao, S.-K.

E. H. Young, S.-K. Yao, “Design Considerations of Acoustooptic Devices,” Proc. IEEE 69, 54 (1981).
[CrossRef]

Young, E. H.

E. H. Young, S.-K. Yao, “Design Considerations of Acoustooptic Devices,” Proc. IEEE 69, 54 (1981).
[CrossRef]

Appl. Opt. (6)

Appl. Phys. Lett. (1)

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

Bell Syst. Tech. J. (1)

See, for example, C. Clos, “A study of Non-blocking Switching Networks,” Bell Syst. Tech. J. 32, 406 (1953).

IEEE/OSA J. Lightwave Technol. (1)

S. K. Korotky et al., “Fully Connectorized High-Speed Ti:LiNbO3 Switch/Modulator for Time-Division Multiplexing and Data Encoding,” IEEE/OSA J. Lightwave Technol. 3, 1 (1985).
[CrossRef]

Opt. Acta (1)

J. W. Goodman, “Fan-in and Fan-out with Optical Interconnections,” Opt. Acta 32, 1489 (1985).
[CrossRef]

Opt. Eng. (1)

B. Clymer, J. W. Goodman, “Optical Clock Distribution to an IC Chip,” Opt. Eng. 25, 1103 (1986).

Opt. Lett. (2)

Proc. IEEE (2)

J. W. Goodman et al. “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850 (1984).
[CrossRef]

E. H. Young, S.-K. Yao, “Design Considerations of Acoustooptic Devices,” Proc. IEEE 69, 54 (1981).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

A. A. Sawchuk, B. K. Jenkins, “Dynamic Optical Interconnections for Parallel Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143 (1986).

Soc. Photo-Opt. Instrum. Eng. (1)

E. Marom, N. Konforti, “Programmable Optical Interconnects,” Soc. Photo-Opt. Instrum. Eng. 700, 296 (1986).

Other (2)

T. M. Gaylord, “Digital Data Storage,” in Handbook of Optical Holography, H. J. Caulfield, Ed. (Academic, New York, 1979), pp. 379–413.

U. J. Schmidt, “Present State of the Digital Laser Beam Deflection Technique for Alphanumeric and Graphic Displays,” in Progress in Electro-Optics, E. Camatini, Ed. (Plenum, New York, 1975), pp. 161–180.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Fredkin gate.

Fig. 2
Fig. 2

Waveguide coupler implementation of the Fredkin gate. I is the interaction region where coupling is switched on or off.

Fig. 3
Fig. 3

Four-channel array with four switching layers.

Fig. 4
Fig. 4

n-channel array with the addition of two more.

Fig. 5
Fig. 5

Six-channel array with selected interconnections.

Fig. 6
Fig. 6

Nonblocking optical crossbar containing two parallel networks.

Equations (15)

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C = C , if C = 0 : A = A ; B = B ; if C = 1 : A = B ; B = A .
F ( 0 ) = [ 1 0 0 1 ]             F ( 1 ) = [ 0 1 1 0 ] .
b = F ( C ) a .
b = T a ,
T = Q n P n - 1 Q n - 2 Q 2 P 1 ,
P 1 Q 2 P n - 1 Q n T = I ,
T = [ 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 ] .
P 5 = [ 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ] ,
Q 4 = [ 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 ] ;             P 3 = [ 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 ] .
F ( 0 ) = [ 1 - α β β 1 - α ]             F ( 1 ) = [ γ 1 - δ 1 - δ γ ] ,
a + = ( 1 , 1 , 1 , 0 ) .
b = [ γ [ γ + ( 1 - δ ) 2 ] + γ ( 1 - δ ) [ 2 γ + ( 1 - δ ) 2 + ( 1 - δ ) ( 1 + 2 γ ) ] γ 4 + γ ( 1 - δ ) ( 1 + γ ) ( 2 - δ ) + 2 γ 3 ( 1 - δ ) + ( 1 - δ ) 3 γ 4 + γ ( 1 - δ ) 2 ( 2 + γ ) + ( 1 - δ ) [ 2 γ 3 + ( 1 - δ ) 2 ] ( 1 - δ ) 3 + γ ( 1 - δ ) 2 ( 2 γ + 1 ) + γ ( 1 - δ ) [ ( 1 - δ ) 2 + γ 2 + γ ] ] .
SNR = ( 1 - δ ) 3 + γ ( 1 - δ ) 2 ( 2 γ + 1 ) + γ ( 1 - δ ) [ ( 1 - δ ) 2 + γ 2 + γ ] γ [ γ + ( 1 - δ ) 2 ] + γ ( 1 - δ ) [ 2 γ + ( 1 - δ ) 2 + ( 1 - δ ) ( 1 + 2 γ ) ] .
SNR = 1 - δ 3 γ .
SNR = 1 - δ ( n - 1 ) γ .

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