Abstract

The geometrical design characteristics of multiple-image holograms are evaluated. A figure of merit expressing these characteristics as a function of the hologram diameter and the distance between the hologram and the image plane is developed. This value is then used to compare two designs which are capable of forming several hundred interconnections. The results indicate that these connections can be formed between points on the substrate separated by 2–3 cm provided that the holograms are separated from the substrate plane by 0.5–1 cm. Each hologram design is experimentally demonstrated in bleached photographic emulsions.

© 1987 Optical Society of America

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References

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  1. R. W. Keyes, “Fundamental Limits in Digital Information Processing,” Proc. IEEE 69, 267 (1981).
    [CrossRef]
  2. P. M. Solomon, “Comparison of Semiconductor Devices for High-Speed Logic,” Proc. IEEE 70, 489 (1982).
    [CrossRef]
  3. A. J. Blodgett, “Microelectronic Packaging,” Sci. Am. 249, 86 (1983).
    [CrossRef]
  4. R. W. Keyes, “The Evolution of Digital Electronics Towards VLSI,” IEEE J. Solid State Circuits SC-14, 193 (1979).
    [CrossRef]
  5. A. J. Rainal, “Computing Inductive Noise of Chip Packages,” AT&T Tech. J. 63, 177 (1984).
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), Chap. 9.
  7. H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909 (1969).
  8. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 65.
  9. S. K. Case, P. R. Haugen, O. J. Lokberg, “Multifacet Holographic Optical Elements for Wave Front Transformations,” Appl. Opt. 20, 2670 (1981).
    [CrossRef] [PubMed]
  10. E. B. Champagne, “Nonparaxial Imaging, Magnification, and Aberration Properties in Holography,” J. Opt. Soc. Am. 57, 51 (1967).
    [CrossRef]
  11. J. N. Cederquist, J. R. Fienup, “Analytic Design of Optimum Holographic Optical Elements,” J. Opt. Soc. Am. 4, 699 (1987).
    [CrossRef]
  12. D. J. Cooke, A. A. Warde, “Reflection-Hologram Processing for High Efficiency in Silver-Halide Emulsions,” Appl. Opt. 23, 934 (1984).
    [CrossRef] [PubMed]
  13. R. K. Kostuk, J. W. Goodman, L. Hesselink, “Volume Reflection Holograms with Multiple Gratings: An Experimental and Theoretical Evaluation,” Appl. Opt. 25, 4362 (1986).
    [CrossRef] [PubMed]
  14. Y. Takeda, “Hologram Memory with High Quality and High Information Storage Density-Hologram Memory,” J. Jpn. J. Appl. Phys. 11, 656 (1972).
    [CrossRef]

1987 (1)

J. N. Cederquist, J. R. Fienup, “Analytic Design of Optimum Holographic Optical Elements,” J. Opt. Soc. Am. 4, 699 (1987).
[CrossRef]

1986 (1)

1984 (2)

1983 (1)

A. J. Blodgett, “Microelectronic Packaging,” Sci. Am. 249, 86 (1983).
[CrossRef]

1982 (1)

P. M. Solomon, “Comparison of Semiconductor Devices for High-Speed Logic,” Proc. IEEE 70, 489 (1982).
[CrossRef]

1981 (2)

1979 (1)

R. W. Keyes, “The Evolution of Digital Electronics Towards VLSI,” IEEE J. Solid State Circuits SC-14, 193 (1979).
[CrossRef]

1972 (1)

Y. Takeda, “Hologram Memory with High Quality and High Information Storage Density-Hologram Memory,” J. Jpn. J. Appl. Phys. 11, 656 (1972).
[CrossRef]

1969 (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909 (1969).

1967 (1)

Blodgett, A. J.

A. J. Blodgett, “Microelectronic Packaging,” Sci. Am. 249, 86 (1983).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), Chap. 9.

Case, S. K.

Cederquist, J. N.

J. N. Cederquist, J. R. Fienup, “Analytic Design of Optimum Holographic Optical Elements,” J. Opt. Soc. Am. 4, 699 (1987).
[CrossRef]

Champagne, E. B.

Cooke, D. J.

Fienup, J. R.

J. N. Cederquist, J. R. Fienup, “Analytic Design of Optimum Holographic Optical Elements,” J. Opt. Soc. Am. 4, 699 (1987).
[CrossRef]

Goodman, J. W.

Haugen, P. R.

Hesselink, L.

Keyes, R. W.

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

R. W. Keyes, “The Evolution of Digital Electronics Towards VLSI,” IEEE J. Solid State Circuits SC-14, 193 (1979).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909 (1969).

Kostuk, R. K.

Lokberg, O. J.

Rainal, A. J.

A. J. Rainal, “Computing Inductive Noise of Chip Packages,” AT&T Tech. J. 63, 177 (1984).

Solomon, P. M.

P. M. Solomon, “Comparison of Semiconductor Devices for High-Speed Logic,” Proc. IEEE 70, 489 (1982).
[CrossRef]

Takeda, Y.

Y. Takeda, “Hologram Memory with High Quality and High Information Storage Density-Hologram Memory,” J. Jpn. J. Appl. Phys. 11, 656 (1972).
[CrossRef]

Warde, A. A.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), Chap. 9.

Appl. Opt. (3)

AT&T Tech. J. (1)

A. J. Rainal, “Computing Inductive Noise of Chip Packages,” AT&T Tech. J. 63, 177 (1984).

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909 (1969).

IEEE J. Solid State Circuits (1)

R. W. Keyes, “The Evolution of Digital Electronics Towards VLSI,” IEEE J. Solid State Circuits SC-14, 193 (1979).
[CrossRef]

J. Jpn. J. Appl. Phys. (1)

Y. Takeda, “Hologram Memory with High Quality and High Information Storage Density-Hologram Memory,” J. Jpn. J. Appl. Phys. 11, 656 (1972).
[CrossRef]

J. Opt. Soc. Am. (2)

E. B. Champagne, “Nonparaxial Imaging, Magnification, and Aberration Properties in Holography,” J. Opt. Soc. Am. 57, 51 (1967).
[CrossRef]

J. N. Cederquist, J. R. Fienup, “Analytic Design of Optimum Holographic Optical Elements,” J. Opt. Soc. Am. 4, 699 (1987).
[CrossRef]

Proc. IEEE (2)

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

P. M. Solomon, “Comparison of Semiconductor Devices for High-Speed Logic,” Proc. IEEE 70, 489 (1982).
[CrossRef]

Sci. Am. (1)

A. J. Blodgett, “Microelectronic Packaging,” Sci. Am. 249, 86 (1983).
[CrossRef]

Other (2)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), Chap. 9.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 65.

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Figures (12)

Fig. 1
Fig. 1

Schematic layout of integrated circuits mounted on chip carriers and boards. Inset shows the expanded view of wire connections between the integrated circuit and chip carrier.

Fig. 2
Fig. 2

Schematic of a two-image holographic interconnection: Xs, source position; X1, X2, detector positions; Dh, hologram diameter, Zi hologram–substrate separation; Xh, hologram position. θ01, θ02, the angles between the receiving ICs and the hologram.

Fig. 3
Fig. 3

Hologram and image coordinates used in calculating the image aberrations (Xq,Xqa, and Xq).

Fig. 4
Fig. 4

Multiple-image hologram designs: (A) faceted hologram design; (B) single aperture.

Fig. 5
Fig. 5

Faceted hologram image resolution as a function of the detector separation from the source, X1 and X2: ——, Dh/Zi = (0.1cm)/(1.0 cm); – – –, Dh/Zi = (0.05 cm)/(1.0 cm); – · –, Dh/Zi = (0.1cm)/(0.5 cm); the horizontal dashed curve shows 100-μm resolution.

Fig. 6
Fig. 6

Single-aperture hologram image spot size as a function of detector separation from the source. X1 and X2 are assumed on opposite sides of the source at X = 0: Dh/Zi = (0.2 cm)/(2.0 cm); ——, Xr = −1 mm; – – –, Xr = −2 mm; – · –, Dh/Zi = (0.1 cm)/(0.5 cm); the horizontal dashed curve shows 100-μm resolution.

Fig. 7
Fig. 7

Two-image single-aperture hologram formation. The transmitting IC is located at R, and S1 and S2 correspond to the positions of the receiving integrated circuits. θa and θb correspond to two reconstruction angles.

Fig. 8
Fig. 8

Knife-edge plots of image S2 at two reconstruction angles: θa, ——, and θb, – – –, corresponding to a 2.4-mm separation between reconstruction sources on the IC substrate. The spot size of both images is ∼50 μm (i.e., knife-edge travel to change the relative intensity from 20 to 80%.

Fig. 9
Fig. 9

Knife-edge plots of image S1 at two reconstruction angles: θa, ——, and θb, – – –, corresponding to a 2.4-mm separation between reconstruction sources on the IC substrate. The spot size in this case is significantly greater than the images of S2.

Fig. 10
Fig. 10

Formation of multifaceted hologram with mask coded object beams. Each mask has a different set of apertures corresponding to the location of detectors on the receiving integrated circuits.

Fig. 11
Fig. 11

Reconstruction of mask encoded multifaceted holograms: (A) illumination of a single facet showing the three-point image of the mask code; (B) six-point image formed by illuminating two facets.

Fig. 12
Fig. 12

Knife-edge trace of one of the point images from the multifaceted hologram evaluated at, ——, Zi = 1.4 cm and, – – –, Zi = 2.8 cm with Dh ∼1.5 mm.

Equations (11)

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Δ X = ( X 1 X 2 ) = f ( D h , Z i , M , Δ d 1 , 2 = 100 μ m ) .
Δ d j = Δ d dj + Δ d aj .
Δ d j = 2.44 λ r j D h cos 2 ( θ oj ) , j = 1 , 2 .
X 1 X h = Z i tan θ o 1 , X 2 X h = Z i tan θ o 2 ,
r j = Z i cos ( θ oj ) .
l 1 q = K xq 2 π / λ + l rq ,
x qa = x q + r qa l qa ,
r qa = Z i 1 l qa 2 .
Δ d aj = x qa x pb ( x q x p ) + ( l jqa r jqa l jpb r jpb ) ,
Δ d j = Δ d dj + Δ d aj = ( x q x p ) + ( l jqa r jqa l jpb r jpb ) + 2.44 λ r j D h cos 2 ( θ oj ) , j = 1 , 2 .
1 R i = 1 R r ± λ r λ c ( 1 R o 1 R c ) , X i R i = X r R r ± λ r λ c ( X o R o X c R c ) , Y i R i = Y r R r ± λ r λ c ( Y o R o X c R c ) ,

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