Abstract

An optical spatial interconnection network consisting of a 2-D source array, a lens array, and a detector array is suitable for use as the interconnection device in multiprocessor systems and neural networks. This paper describes the theoretical limits on the maximum channel numbers of these networks derived from optical restrictions. These results yield optimum design parameters for an interconnection network.

© 1990 Optical Society of America

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References

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  1. T. Fountain, Processor Arrays: Architectures and Applications (Academic, London, 1987).
  2. R. P. Lippmann, “An Introduction to Computing with Neural Nets,” IEEE ASSP Mag., 4–22 (Apr.1987).
    [CrossRef]
  3. R. W. Keyes, “Fundamental Limits in Digital Information Processing,” Proc. IEEE 69, 267–278 (1981).
    [CrossRef]
  4. J. W. Goodman, F. I. Leonberger, S. Y. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850–866 (1984).
    [CrossRef]
  5. J. L. Horner, Optical Signal Processing (Academic, San Diego, 1987).
  6. K. Noguchi, T. Sakano, “Optically Implemented Hopfield Associative Memory Using Two-Dimensional Incoherent Optical Array Devices,” to be reported at IJCNN-90, Washington, DC (Jan. 1990).
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).
  8. B. Rossi, Optics (Addison-Wesley, Reading, MA1967).
  9. D. H. Hartman, “Digital High Speed Interconnections: a Study of the Optical Alternative,” Opt. Eng. 25, 1086–1102 (1986).
    [CrossRef]
  10. T. V. Muoi, “Receiver Design for High-Speed Optical-Fiber Systems,” IEEE/OSA J. Lightwave Technol. LT-2, 243–267 (1984).
    [CrossRef]
  11. F. Koyama, K. Tomomatsu, K. Iga, “GaAs Surface Emitting Lasers with Circular Buried Heterostructure Grown by Metalorganic Chemical Vapor Deposition and Two-Dimensional Laser Array,” Appl. Phys. Lett. 52, 528–529 (1988).
    [CrossRef]
  12. J. N. Walpole, Z. L. Liau, “Monolithic Two-Dimensional Arrays of High-Power GaInAsP/InP Surface-Emitting Diode Lasers,” Appl. Phys. Lett. 48, 1636–1638 (1986).
    [CrossRef]
  13. G. D. Khoe, H. G. Kock, J. A. Luijendijk, C. H. J. van den Brekel, D. Kuppers, “Plasma CVD Prepared SiO2/Si3N4 Graded Index Lenses Integrated in Windows of Laser Diode Packages,” in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), paper 7.6.
  14. H. Sugiyama, M. Kato, S. Misawa, K. Iga, “Fabrication of Planar Microlens by Transverse Electromigration Methodx,” Jpn. J. Appl. Phys. 25, 1959–1960 (1986).
    [CrossRef]
  15. M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452–453 (1981).
    [CrossRef]
  16. K. Kojima, S. Noda, K. Mitsunaga, K. Kyuma, K. Hamanaka, “Continuous Wave Operation of a Surface-Emitting Al-GaAs/GaAs Multiquantum Well-Distributed Bragg Reflector Laser,” Appl. Phys. Lett. 50, 1705–1707 (1987).
    [CrossRef]

1988 (1)

F. Koyama, K. Tomomatsu, K. Iga, “GaAs Surface Emitting Lasers with Circular Buried Heterostructure Grown by Metalorganic Chemical Vapor Deposition and Two-Dimensional Laser Array,” Appl. Phys. Lett. 52, 528–529 (1988).
[CrossRef]

1987 (2)

R. P. Lippmann, “An Introduction to Computing with Neural Nets,” IEEE ASSP Mag., 4–22 (Apr.1987).
[CrossRef]

K. Kojima, S. Noda, K. Mitsunaga, K. Kyuma, K. Hamanaka, “Continuous Wave Operation of a Surface-Emitting Al-GaAs/GaAs Multiquantum Well-Distributed Bragg Reflector Laser,” Appl. Phys. Lett. 50, 1705–1707 (1987).
[CrossRef]

1986 (3)

D. H. Hartman, “Digital High Speed Interconnections: a Study of the Optical Alternative,” Opt. Eng. 25, 1086–1102 (1986).
[CrossRef]

J. N. Walpole, Z. L. Liau, “Monolithic Two-Dimensional Arrays of High-Power GaInAsP/InP Surface-Emitting Diode Lasers,” Appl. Phys. Lett. 48, 1636–1638 (1986).
[CrossRef]

H. Sugiyama, M. Kato, S. Misawa, K. Iga, “Fabrication of Planar Microlens by Transverse Electromigration Methodx,” Jpn. J. Appl. Phys. 25, 1959–1960 (1986).
[CrossRef]

1984 (2)

T. V. Muoi, “Receiver Design for High-Speed Optical-Fiber Systems,” IEEE/OSA J. Lightwave Technol. LT-2, 243–267 (1984).
[CrossRef]

J. W. Goodman, F. I. Leonberger, S. Y. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

1981 (2)

R. W. Keyes, “Fundamental Limits in Digital Information Processing,” Proc. IEEE 69, 267–278 (1981).
[CrossRef]

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452–453 (1981).
[CrossRef]

Athale, R. A.

J. W. Goodman, F. I. Leonberger, S. Y. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

Fountain, T.

T. Fountain, Processor Arrays: Architectures and Applications (Academic, London, 1987).

Goodman, J. W.

J. W. Goodman, F. I. Leonberger, S. Y. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Hamanaka, K.

K. Kojima, S. Noda, K. Mitsunaga, K. Kyuma, K. Hamanaka, “Continuous Wave Operation of a Surface-Emitting Al-GaAs/GaAs Multiquantum Well-Distributed Bragg Reflector Laser,” Appl. Phys. Lett. 50, 1705–1707 (1987).
[CrossRef]

Hartman, D. H.

D. H. Hartman, “Digital High Speed Interconnections: a Study of the Optical Alternative,” Opt. Eng. 25, 1086–1102 (1986).
[CrossRef]

Horner, J. L.

J. L. Horner, Optical Signal Processing (Academic, San Diego, 1987).

Iga, K.

F. Koyama, K. Tomomatsu, K. Iga, “GaAs Surface Emitting Lasers with Circular Buried Heterostructure Grown by Metalorganic Chemical Vapor Deposition and Two-Dimensional Laser Array,” Appl. Phys. Lett. 52, 528–529 (1988).
[CrossRef]

H. Sugiyama, M. Kato, S. Misawa, K. Iga, “Fabrication of Planar Microlens by Transverse Electromigration Methodx,” Jpn. J. Appl. Phys. 25, 1959–1960 (1986).
[CrossRef]

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452–453 (1981).
[CrossRef]

Kato, M.

H. Sugiyama, M. Kato, S. Misawa, K. Iga, “Fabrication of Planar Microlens by Transverse Electromigration Methodx,” Jpn. J. Appl. Phys. 25, 1959–1960 (1986).
[CrossRef]

Keyes, R. W.

R. W. Keyes, “Fundamental Limits in Digital Information Processing,” Proc. IEEE 69, 267–278 (1981).
[CrossRef]

Khoe, G. D.

G. D. Khoe, H. G. Kock, J. A. Luijendijk, C. H. J. van den Brekel, D. Kuppers, “Plasma CVD Prepared SiO2/Si3N4 Graded Index Lenses Integrated in Windows of Laser Diode Packages,” in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), paper 7.6.

Kock, H. G.

G. D. Khoe, H. G. Kock, J. A. Luijendijk, C. H. J. van den Brekel, D. Kuppers, “Plasma CVD Prepared SiO2/Si3N4 Graded Index Lenses Integrated in Windows of Laser Diode Packages,” in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), paper 7.6.

Kojima, K.

K. Kojima, S. Noda, K. Mitsunaga, K. Kyuma, K. Hamanaka, “Continuous Wave Operation of a Surface-Emitting Al-GaAs/GaAs Multiquantum Well-Distributed Bragg Reflector Laser,” Appl. Phys. Lett. 50, 1705–1707 (1987).
[CrossRef]

Koyama, F.

F. Koyama, K. Tomomatsu, K. Iga, “GaAs Surface Emitting Lasers with Circular Buried Heterostructure Grown by Metalorganic Chemical Vapor Deposition and Two-Dimensional Laser Array,” Appl. Phys. Lett. 52, 528–529 (1988).
[CrossRef]

Kung, S. Y.

J. W. Goodman, F. I. Leonberger, S. Y. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Kuppers, D.

G. D. Khoe, H. G. Kock, J. A. Luijendijk, C. H. J. van den Brekel, D. Kuppers, “Plasma CVD Prepared SiO2/Si3N4 Graded Index Lenses Integrated in Windows of Laser Diode Packages,” in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), paper 7.6.

Kyuma, K.

K. Kojima, S. Noda, K. Mitsunaga, K. Kyuma, K. Hamanaka, “Continuous Wave Operation of a Surface-Emitting Al-GaAs/GaAs Multiquantum Well-Distributed Bragg Reflector Laser,” Appl. Phys. Lett. 50, 1705–1707 (1987).
[CrossRef]

Leonberger, F. I.

J. W. Goodman, F. I. Leonberger, S. Y. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Liau, Z. L.

J. N. Walpole, Z. L. Liau, “Monolithic Two-Dimensional Arrays of High-Power GaInAsP/InP Surface-Emitting Diode Lasers,” Appl. Phys. Lett. 48, 1636–1638 (1986).
[CrossRef]

Lippmann, R. P.

R. P. Lippmann, “An Introduction to Computing with Neural Nets,” IEEE ASSP Mag., 4–22 (Apr.1987).
[CrossRef]

Luijendijk, J. A.

G. D. Khoe, H. G. Kock, J. A. Luijendijk, C. H. J. van den Brekel, D. Kuppers, “Plasma CVD Prepared SiO2/Si3N4 Graded Index Lenses Integrated in Windows of Laser Diode Packages,” in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), paper 7.6.

Misawa, S.

H. Sugiyama, M. Kato, S. Misawa, K. Iga, “Fabrication of Planar Microlens by Transverse Electromigration Methodx,” Jpn. J. Appl. Phys. 25, 1959–1960 (1986).
[CrossRef]

Mitsunaga, K.

K. Kojima, S. Noda, K. Mitsunaga, K. Kyuma, K. Hamanaka, “Continuous Wave Operation of a Surface-Emitting Al-GaAs/GaAs Multiquantum Well-Distributed Bragg Reflector Laser,” Appl. Phys. Lett. 50, 1705–1707 (1987).
[CrossRef]

Muoi, T. V.

T. V. Muoi, “Receiver Design for High-Speed Optical-Fiber Systems,” IEEE/OSA J. Lightwave Technol. LT-2, 243–267 (1984).
[CrossRef]

Noda, S.

K. Kojima, S. Noda, K. Mitsunaga, K. Kyuma, K. Hamanaka, “Continuous Wave Operation of a Surface-Emitting Al-GaAs/GaAs Multiquantum Well-Distributed Bragg Reflector Laser,” Appl. Phys. Lett. 50, 1705–1707 (1987).
[CrossRef]

Noguchi, K.

K. Noguchi, T. Sakano, “Optically Implemented Hopfield Associative Memory Using Two-Dimensional Incoherent Optical Array Devices,” to be reported at IJCNN-90, Washington, DC (Jan. 1990).

Oikawa, M.

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452–453 (1981).
[CrossRef]

Rossi, B.

B. Rossi, Optics (Addison-Wesley, Reading, MA1967).

Sakano, T.

K. Noguchi, T. Sakano, “Optically Implemented Hopfield Associative Memory Using Two-Dimensional Incoherent Optical Array Devices,” to be reported at IJCNN-90, Washington, DC (Jan. 1990).

Sanada, T.

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452–453 (1981).
[CrossRef]

Sugiyama, H.

H. Sugiyama, M. Kato, S. Misawa, K. Iga, “Fabrication of Planar Microlens by Transverse Electromigration Methodx,” Jpn. J. Appl. Phys. 25, 1959–1960 (1986).
[CrossRef]

Tomomatsu, K.

F. Koyama, K. Tomomatsu, K. Iga, “GaAs Surface Emitting Lasers with Circular Buried Heterostructure Grown by Metalorganic Chemical Vapor Deposition and Two-Dimensional Laser Array,” Appl. Phys. Lett. 52, 528–529 (1988).
[CrossRef]

van den Brekel, C. H. J.

G. D. Khoe, H. G. Kock, J. A. Luijendijk, C. H. J. van den Brekel, D. Kuppers, “Plasma CVD Prepared SiO2/Si3N4 Graded Index Lenses Integrated in Windows of Laser Diode Packages,” in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), paper 7.6.

Walpole, J. N.

J. N. Walpole, Z. L. Liau, “Monolithic Two-Dimensional Arrays of High-Power GaInAsP/InP Surface-Emitting Diode Lasers,” Appl. Phys. Lett. 48, 1636–1638 (1986).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

Appl. Phys. Lett. (3)

F. Koyama, K. Tomomatsu, K. Iga, “GaAs Surface Emitting Lasers with Circular Buried Heterostructure Grown by Metalorganic Chemical Vapor Deposition and Two-Dimensional Laser Array,” Appl. Phys. Lett. 52, 528–529 (1988).
[CrossRef]

J. N. Walpole, Z. L. Liau, “Monolithic Two-Dimensional Arrays of High-Power GaInAsP/InP Surface-Emitting Diode Lasers,” Appl. Phys. Lett. 48, 1636–1638 (1986).
[CrossRef]

K. Kojima, S. Noda, K. Mitsunaga, K. Kyuma, K. Hamanaka, “Continuous Wave Operation of a Surface-Emitting Al-GaAs/GaAs Multiquantum Well-Distributed Bragg Reflector Laser,” Appl. Phys. Lett. 50, 1705–1707 (1987).
[CrossRef]

Electron. Lett. (1)

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452–453 (1981).
[CrossRef]

IEEE ASSP Mag. (1)

R. P. Lippmann, “An Introduction to Computing with Neural Nets,” IEEE ASSP Mag., 4–22 (Apr.1987).
[CrossRef]

IEEE/OSA J. Lightwave Technol. (1)

T. V. Muoi, “Receiver Design for High-Speed Optical-Fiber Systems,” IEEE/OSA J. Lightwave Technol. LT-2, 243–267 (1984).
[CrossRef]

Jpn. J. Appl. Phys. (1)

H. Sugiyama, M. Kato, S. Misawa, K. Iga, “Fabrication of Planar Microlens by Transverse Electromigration Methodx,” Jpn. J. Appl. Phys. 25, 1959–1960 (1986).
[CrossRef]

Opt. Eng. (1)

D. H. Hartman, “Digital High Speed Interconnections: a Study of the Optical Alternative,” Opt. Eng. 25, 1086–1102 (1986).
[CrossRef]

Proc. IEEE (2)

R. W. Keyes, “Fundamental Limits in Digital Information Processing,” Proc. IEEE 69, 267–278 (1981).
[CrossRef]

J. W. Goodman, F. I. Leonberger, S. Y. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Other (6)

J. L. Horner, Optical Signal Processing (Academic, San Diego, 1987).

K. Noguchi, T. Sakano, “Optically Implemented Hopfield Associative Memory Using Two-Dimensional Incoherent Optical Array Devices,” to be reported at IJCNN-90, Washington, DC (Jan. 1990).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

B. Rossi, Optics (Addison-Wesley, Reading, MA1967).

T. Fountain, Processor Arrays: Architectures and Applications (Academic, London, 1987).

G. D. Khoe, H. G. Kock, J. A. Luijendijk, C. H. J. van den Brekel, D. Kuppers, “Plasma CVD Prepared SiO2/Si3N4 Graded Index Lenses Integrated in Windows of Laser Diode Packages,” in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), paper 7.6.

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Figures (12)

Fig. 1
Fig. 1

Type A configuration consisting of a source array, a lens array, and a detector array. Each lens on the lens array forms the image of the source array on the detector array.

Fig. 2
Fig. 2

Type B configuration. Lens array forms overlapping images of the source array on each detector in the detector array.

Fig. 3
Fig. 3

Model for aberration analysis. ΔY1 denotes the astigmatic aberration quantity when the off-axis value is Y0.

Fig. 4
Fig. 4

Maximum N value in type A configurations determined by aberration restriction. The shaded region indicates that the real N value does not exist.

Fig. 5
Fig. 5

Diffraction limit to the value of parameter ξ in type A configurations determined by aberration restriction. ξ is a parameter that is proportional to the number of sources N.

Fig. 6
Fig. 6

Relationship between the length of a network apparatus L and the parameter ξ in type A configurations on the assumption that λ = 0.8 μm. The shaded region at the top of the figure expresses the aberration restriction.

Fig. 7
Fig. 7

Relationship between the bit rate B and the number of sources N in type A configurations. θ0 represents the radiation angle of each source.

Fig. 8
Fig. 8

Diffraction limit to parameter ζ in type B configurations. The shaded region at the top of the figure represents the aberration restriction. The parameter ζ is proportional to the network density N

Fig. 9
Fig. 9

Relationship between L and ζ in type B configurations. The shaded region at the top of the figure represents the restriction of aberration when α = 1.0.

Fig. 10
Fig. 10

Relationship between B and N in type B configurations. θ0 = 36° is the angle at which the optical power from the sources on the source array can cover the necessary lenses on a lens array when θ is maximum.

Fig. 11
Fig. 11

Relationship between L and Nmax in A and B types.

Fig. 12
Fig. 12

Relationship between N and the figure of merit BN2 in A and B types.

Equations (31)

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Δ Y 1 = I ( 1 + α ) d l l f 2 Y 0 2 ,
I = 3 n + 1 4 n ,
α = l b l f ,
d d = α d s = α D s / N ;
l f = L 1 + α .
2 Δ Y 1 d d .
2 Y 0 2 I ( 1 + α ) 3 d l L 2 α D s N .
α D s = ( 1 + α ) d l = ( 1 + α ) D l N .
2 Y 0 2 I N ( 1 + α ) 2 L 2 1.
Y 0 max = 1 2 1 / 2 ( D s + D l ) = D l 2 1 / 2 ( 1 + α + N α N α ) .
N 2 + [ 2 ( 1 + α ) α - 1 I { ( 1 + α ) β } 2 ] N + ( 1 + α ) 2 α 2 0 ,
β = D l / L .
d S = ( 1 + α ) N α 2 β L ;
d d = α d s = ( 1 + α ) N 2 β L .
N max = 1 + { 1 - 4 I ( 1 + α ) 3 β 2 / α } 1 / 2 2 I ( 1 + α ) 2 β 2 - 1 + α α .
β 2 α 4 I ( 1 + α ) 3 ,
D = 2.44 l λ d ,
D = 2.44 l b λ d l d d .
β 2 2.44 α ξ 3 ( 1 + α ) 3 ,
ξ = N max ( λ L ) 1 / 3 .
ξ 1 ( 9.76 I ) 1 / 3 .
P r = P 0 8 d l 2 l f 2 1 1 - cos θ 0 ,
N 2 = P 0 3 P r γ 2 1 - cos θ 0 ;
γ = ( 1 + α ) β .
α D s N = α d s = ( 1 + α ) d l = d d ;
Y 0 max = 1 2 1 / 2 1 + α α N 2 N - 1 · D l .
β 2 α 2 ( 2 N - 1 ) 2 I ( 1 + α ) 4 N 2 4 α 2 I ( 1 + α ) 4 ,
β 2 9.76 α ζ 2 ( 1 + α ) 2 ,
ζ = N ( λ L ) 1 / 2 .
P r = P 0 N 2 2 ( 2 ) 1 / 2 α 3 β 2 ( 1 + α ) 2 { 8 α 2 + β 2 ( 1 + α ) 4 } 3 / 2 ( 1 - cos θ 0 ) .
N max = ( L 9.76 λ I ) m ,

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