Abstract

The density capabilities of free-space optical interconnects are analyzed by applying Gabor’s theory of information. It is shown that it is possible to increase the space–bandwidth product capabilities of space-variant interconnect schemes if they have symmetry properties. Several examples of such symmetries (locality, separability and smoothness) are discussed in detail, together with some experimental results.

© 1992 Optical Society of America

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References

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  1. R. Barakat, J. Reif, “Lower bounds on the computational efficiency of optical computing systems,” Appl. Opt. 26, 1015–1018 (1987).
    [Crossref] [PubMed]
  2. M. R. Feldman, C. G. Guest, “Interconnect density capabilities of computer generated holograms for optical interconnection of very large scale integrated circuits,” Appl. Opt. 28, 3134–3137 (1989).
    [Crossref] [PubMed]
  3. M. R. Feldman, C. G. Guest, T. J. Drabik, S. C. Esener, “Comparison between electrical and free space optical interconnects for fine grain processor arrays based on interconnect density capabilities,” Appl. Opt. 28, 3820–3829 (1989).
    [Crossref] [PubMed]
  4. B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuck, T. C. Strand, “Architectural implications of a digital optical processor,” Appl. Opt. 23, 3465–3474 (1984).
    [Crossref] [PubMed]
  5. J. W. Goodman, “Linear space-variant optical data processing,” in Optical Information Processing, S. H. Lee, ed. (Springer-Verlag, Berlin, Heidelberg, New York, 1981), p. 248.
  6. D. Gabor, “Light and information,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1961), Vol. 1, pp. 109–153.
    [Crossref]
  7. O. Bryngdahl, “Geometrical transformation in optics,” J. Opt. Soc. Am. 64, 1092–1099 (1974).
    [Crossref]
  8. G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
    [Crossref]
  9. A. Harootunian, E. Betzig, A. Muray, A. Lewis, M. Isaacson, “Near-field investigation of submicrometer apertures at optical wavelengths,” J. Opt. Soc. Am. A 1, 1293–1293 (1984).
  10. K. W. Urquhart, P. Marchand, Y. Fainman, S. H. Lee, “Design of free-space optical interconnection systems utilizing diffractive optics,” in Annual Meeting 1991, Vol. 17 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 70.
  11. S. Wolfram, Theory and Applications of Cellular Automata, (World Scientific, Singapore, 1986).
  12. A. W. Lohmann, W. Stork, G. Stucke, “Optical perfect shuffle,” Appl. Opt. 25, 1530–1531 (1986).
    [Crossref] [PubMed]
  13. N. Davidson, A. A. Friesem, E. Hasman, “Realization of perfect shuffle and inverse perfect shuffle transforms with holographic elements,” Appl. Opt. (to be published).
  14. J. Schwider, W. Stork, N. Streibl, R. Volkel, “Possibilities and limitations of space-variant holographic optical elements for switching networks and general interconnects,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 130–131 (1990).
  15. N. Davidson, A. A. Friesem, E. Hasman, “Optical coordinate transformations,” Appl. Opt. 31, 1067–1073 (1992).
    [Crossref] [PubMed]
  16. G. E. Lohman, A. W. Lohmann, “Optical interconnection networks utilizing diffraction gratings,” Opt. Eng. 27, 893–900 (1988).
  17. W. H. Lee, “Binary synthetic holograms,” Appl. Opt. 13, 1677–1682 (1974).
    [Crossref] [PubMed]

1992 (1)

1989 (2)

1988 (1)

G. E. Lohman, A. W. Lohmann, “Optical interconnection networks utilizing diffraction gratings,” Opt. Eng. 27, 893–900 (1988).

1987 (1)

1986 (1)

1984 (2)

B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuck, T. C. Strand, “Architectural implications of a digital optical processor,” Appl. Opt. 23, 3465–3474 (1984).
[Crossref] [PubMed]

A. Harootunian, E. Betzig, A. Muray, A. Lewis, M. Isaacson, “Near-field investigation of submicrometer apertures at optical wavelengths,” J. Opt. Soc. Am. A 1, 1293–1293 (1984).

1974 (2)

1952 (1)

G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
[Crossref]

Barakat, R.

Betzig, E.

A. Harootunian, E. Betzig, A. Muray, A. Lewis, M. Isaacson, “Near-field investigation of submicrometer apertures at optical wavelengths,” J. Opt. Soc. Am. A 1, 1293–1293 (1984).

Bryngdahl, O.

Chavel, P.

Davidson, N.

N. Davidson, A. A. Friesem, E. Hasman, “Optical coordinate transformations,” Appl. Opt. 31, 1067–1073 (1992).
[Crossref] [PubMed]

N. Davidson, A. A. Friesem, E. Hasman, “Realization of perfect shuffle and inverse perfect shuffle transforms with holographic elements,” Appl. Opt. (to be published).

Drabik, T. J.

Esener, S. C.

Fainman, Y.

K. W. Urquhart, P. Marchand, Y. Fainman, S. H. Lee, “Design of free-space optical interconnection systems utilizing diffractive optics,” in Annual Meeting 1991, Vol. 17 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 70.

Feldman, M. R.

Forchheimer, R.

Friesem, A. A.

N. Davidson, A. A. Friesem, E. Hasman, “Optical coordinate transformations,” Appl. Opt. 31, 1067–1073 (1992).
[Crossref] [PubMed]

N. Davidson, A. A. Friesem, E. Hasman, “Realization of perfect shuffle and inverse perfect shuffle transforms with holographic elements,” Appl. Opt. (to be published).

Gabor, D.

D. Gabor, “Light and information,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1961), Vol. 1, pp. 109–153.
[Crossref]

Goodman, J. W.

J. W. Goodman, “Linear space-variant optical data processing,” in Optical Information Processing, S. H. Lee, ed. (Springer-Verlag, Berlin, Heidelberg, New York, 1981), p. 248.

Guest, C. G.

Harootunian, A.

A. Harootunian, E. Betzig, A. Muray, A. Lewis, M. Isaacson, “Near-field investigation of submicrometer apertures at optical wavelengths,” J. Opt. Soc. Am. A 1, 1293–1293 (1984).

Hasman, E.

N. Davidson, A. A. Friesem, E. Hasman, “Optical coordinate transformations,” Appl. Opt. 31, 1067–1073 (1992).
[Crossref] [PubMed]

N. Davidson, A. A. Friesem, E. Hasman, “Realization of perfect shuffle and inverse perfect shuffle transforms with holographic elements,” Appl. Opt. (to be published).

Isaacson, M.

A. Harootunian, E. Betzig, A. Muray, A. Lewis, M. Isaacson, “Near-field investigation of submicrometer apertures at optical wavelengths,” J. Opt. Soc. Am. A 1, 1293–1293 (1984).

Jenkins, B. K.

Lee, S. H.

K. W. Urquhart, P. Marchand, Y. Fainman, S. H. Lee, “Design of free-space optical interconnection systems utilizing diffractive optics,” in Annual Meeting 1991, Vol. 17 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 70.

Lee, W. H.

Lewis, A.

A. Harootunian, E. Betzig, A. Muray, A. Lewis, M. Isaacson, “Near-field investigation of submicrometer apertures at optical wavelengths,” J. Opt. Soc. Am. A 1, 1293–1293 (1984).

Lohman, G. E.

G. E. Lohman, A. W. Lohmann, “Optical interconnection networks utilizing diffraction gratings,” Opt. Eng. 27, 893–900 (1988).

Lohmann, A. W.

G. E. Lohman, A. W. Lohmann, “Optical interconnection networks utilizing diffraction gratings,” Opt. Eng. 27, 893–900 (1988).

A. W. Lohmann, W. Stork, G. Stucke, “Optical perfect shuffle,” Appl. Opt. 25, 1530–1531 (1986).
[Crossref] [PubMed]

Marchand, P.

K. W. Urquhart, P. Marchand, Y. Fainman, S. H. Lee, “Design of free-space optical interconnection systems utilizing diffractive optics,” in Annual Meeting 1991, Vol. 17 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 70.

Muray, A.

A. Harootunian, E. Betzig, A. Muray, A. Lewis, M. Isaacson, “Near-field investigation of submicrometer apertures at optical wavelengths,” J. Opt. Soc. Am. A 1, 1293–1293 (1984).

Reif, J.

Sawchuck, A. A.

Schwider, J.

J. Schwider, W. Stork, N. Streibl, R. Volkel, “Possibilities and limitations of space-variant holographic optical elements for switching networks and general interconnects,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 130–131 (1990).

Stork, W.

A. W. Lohmann, W. Stork, G. Stucke, “Optical perfect shuffle,” Appl. Opt. 25, 1530–1531 (1986).
[Crossref] [PubMed]

J. Schwider, W. Stork, N. Streibl, R. Volkel, “Possibilities and limitations of space-variant holographic optical elements for switching networks and general interconnects,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 130–131 (1990).

Strand, T. C.

Streibl, N.

J. Schwider, W. Stork, N. Streibl, R. Volkel, “Possibilities and limitations of space-variant holographic optical elements for switching networks and general interconnects,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 130–131 (1990).

Stucke, G.

Toraldo di Francia, G.

G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
[Crossref]

Urquhart, K. W.

K. W. Urquhart, P. Marchand, Y. Fainman, S. H. Lee, “Design of free-space optical interconnection systems utilizing diffractive optics,” in Annual Meeting 1991, Vol. 17 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 70.

Volkel, R.

J. Schwider, W. Stork, N. Streibl, R. Volkel, “Possibilities and limitations of space-variant holographic optical elements for switching networks and general interconnects,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 130–131 (1990).

Wolfram, S.

S. Wolfram, Theory and Applications of Cellular Automata, (World Scientific, Singapore, 1986).

Appl. Opt. (7)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

A. Harootunian, E. Betzig, A. Muray, A. Lewis, M. Isaacson, “Near-field investigation of submicrometer apertures at optical wavelengths,” J. Opt. Soc. Am. A 1, 1293–1293 (1984).

Nuovo Cimento Suppl. (1)

G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
[Crossref]

Opt. Eng. (1)

G. E. Lohman, A. W. Lohmann, “Optical interconnection networks utilizing diffraction gratings,” Opt. Eng. 27, 893–900 (1988).

Other (6)

N. Davidson, A. A. Friesem, E. Hasman, “Realization of perfect shuffle and inverse perfect shuffle transforms with holographic elements,” Appl. Opt. (to be published).

J. Schwider, W. Stork, N. Streibl, R. Volkel, “Possibilities and limitations of space-variant holographic optical elements for switching networks and general interconnects,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 130–131 (1990).

K. W. Urquhart, P. Marchand, Y. Fainman, S. H. Lee, “Design of free-space optical interconnection systems utilizing diffractive optics,” in Annual Meeting 1991, Vol. 17 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 70.

S. Wolfram, Theory and Applications of Cellular Automata, (World Scientific, Singapore, 1986).

J. W. Goodman, “Linear space-variant optical data processing,” in Optical Information Processing, S. H. Lee, ed. (Springer-Verlag, Berlin, Heidelberg, New York, 1981), p. 248.

D. Gabor, “Light and information,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1961), Vol. 1, pp. 109–153.
[Crossref]

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Figures (3)

Fig. 1
Fig. 1

Optical arrangement for implementing the first stage of a two-dimensional separable CT.

Fig. 2
Fig. 2

Experimental results of a one-dimensional logarithmic CT on a two-dimensional input. The telescopic image of the input is shown ‘on the left and the corresponding transformed output is shown on the right. The actual size for all is 20 mm × 20 mm.

Fig. 3
Fig. 3

Optical arrangement for implementing a one-dimensional smooth CT. Some of the rays that emerge from section (x0, x0 + Δ) are shown.

Equations (17)

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

F = A Ω / λ 2 ,
F = M N ,
t ( x , y ) t [ u ( x , y ) , v ( x , y ) ] ,
N = A λ f # ,
η = Δ max / D ,
M = η 2 N .
N = F / η .
t ( x , y ) t [ u ( x ) , v ( y ) ] .
N = F 2 / 3 .
ϕ x ( x f , y f ) = 2 π λ u ( x 0 ) - x 0 f x f ,
t ( x , y ) t [ x , ( y + ln x ) ] .
u ( x ) = D u 0 ( x / D ) ,
δ u u 0 Δ 2 2 D ,
p 1 λ f # = λ f / Δ λ D / Δ ,
p 2 [ λ ( δ u ) ] 1 / 2 = Δ [ λ u 0 2 D ] ½ .
Δ opt = λ 1 / 4 D 3 / 4 ( 1 / 2 u 0 ) - 1 / 4 .
N D / ( p 1 + p 2 ) λ - 3 / 4 D 3 / 4 ( 1 / 2 u 0 ) - 1 / 4 = F 3 / 4 ( 1 / 2 u 0 ) - 1 / 4

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