Abstract

Electronic parallel processors might communicate more effectively by photons sent through glass or air than by electrons sent through wires, but quickly routing thousands of optical signals remains a problem. Previous photorefractive interconnection networks have dedicated one hologram to each input channel. Instead, we compute a control image from the entire network configuration and store it as a single color-keyed volume hologram. This lets us use hologram superposition for fast switching between multiple prestored patterns. During operation, data signals from the input modulator array, powered by a shared wavelength-tunable laser, are correlated optically with one color-matched connection hologram to produce the output array. This decouples both data rate and interconnect switching speeds from the slow photorefractive response. We can display arbitrary connection weights using simple binary-phase spatial light modulators and gracefully accommodate modulator limitations by trading off control-image bandwidth for output signal-to-noise ratio. Experimental results with color-multiplexed reflection holograms in z-cut LiNbO3 confirmed our theoretical predictions that this approach works best for densely connected networks with high fan-in to each output. We obtained an average aggregate signal-to-noise ratio of more than 200:1 for 1024 inputs and outputs.

© 1994 Optical Society of America

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  4. R. Paturi, D. T. Lu, J. E. Ford, S. C. Esener, S. H. Lee, “Parallel algorithms based on expander graphs for optical computing,” Appl. Opt. 30, 917–927 (1991).
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    [CrossRef]
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  29. J. E. Ford, Y. Fainman, S. H. Lee, “Enhanced photorefractive performance from 45°-cut BaTiO3,” Appl. Opt. 28, 4808–4815 (1989).
    [CrossRef] [PubMed]
  30. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  31. G. Rakuljic, V. Leyva, “Volume holographic narrow band optical filter,” Opt. Lett. 15, 459–461 (1993).
    [CrossRef]
  32. F. H. Mok, “Angle-multiplexed storage of 5000 holograms in lithium niobate,” Opt. Lett. 18, 915–917 (1993).
    [CrossRef] [PubMed]
  33. D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
    [CrossRef]
  34. D. Von der Linde, A. M. Glass, K. F. Rodgers, “Multiphoton photorefractive processes for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
    [CrossRef]
  35. D. Armitage, D. Kinell, “Liquid-crystal integrated silicon spatial light modulator,” Appl. Opt. 31, 3945–3949 (1992).
    [CrossRef] [PubMed]
  36. J. E. Ford, S. H. Lee, Y. Fainman, “Reconfigurable interconnection using the correlation matrix–tensor multiplier,” presented at the International Commission for Optics Topical Meeting on Optical Computing, Kobe, Japan, April 1990.
  37. H. Takahashi, D. Zaleta, J. Ma, J. Ford, Y. Fainman, S. Lee, “Packaged optical interconnection system based on photorefractive correlation,” Appl. Opt. 33, 2991–2997 (1994).
    [CrossRef] [PubMed]
  38. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Sec. 2.9, pp. 44–55.

1994 (1)

1993 (2)

G. Rakuljic, V. Leyva, “Volume holographic narrow band optical filter,” Opt. Lett. 15, 459–461 (1993).
[CrossRef]

F. H. Mok, “Angle-multiplexed storage of 5000 holograms in lithium niobate,” Opt. Lett. 18, 915–917 (1993).
[CrossRef] [PubMed]

1992 (1)

1991 (7)

1990 (5)

1989 (3)

F. Kiamilev, S. Esener, R. Paturi, Y. Fainman, P. Mercier, C. Guest, S. H. Lee, “Programmable opto-electronic multiprocessors and their comparison with symbolic substitution for digital optical computing,” Opt. Eng. 28, 396–409 (1989).

H. Lee, “Volume holographic global and local interconnecting patterns with maximal capacity and minimal first-order cross talk,” Appl. Opt. 28, 5312–5316 (1989).
[CrossRef] [PubMed]

J. E. Ford, Y. Fainman, S. H. Lee, “Enhanced photorefractive performance from 45°-cut BaTiO3,” Appl. Opt. 28, 4808–4815 (1989).
[CrossRef] [PubMed]

1988 (4)

1987 (2)

1984 (1)

J. Goodman, F. Leonberger, S. Kung, R. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

1980 (1)

J. O. White, A. Yariv, “Real-time image processing via four-wave mixing in a photorefractive media,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

1978 (1)

1975 (1)

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

1974 (1)

D. Von der Linde, A. M. Glass, K. F. Rodgers, “Multiphoton photorefractive processes for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[CrossRef]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Amodei, J. J.

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

Armitage, D.

Athale, R.

J. Goodman, F. Leonberger, S. Kung, R. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Athale, R. A.

J. A. Neff, R. A. Athale, S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 826–855 (1991).
[CrossRef]

AuYeung, J.

Brady, D.

Burke, W. J.

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

Cheng, L. J.

Chiou, A. T.

Cooper, I. R.

David, A. J.

Domash, L. H.

L. H. Domash, C. Gozewski, “Composite pattern recognition using the nonlinear triple processor,” in Optical Pattern Recognition II, H. J. Caulfield, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1134, 162–172 (1989).

Esener, S.

F. Kiamilev, S. Esener, R. Paturi, Y. Fainman, P. Mercier, C. Guest, S. H. Lee, “Programmable opto-electronic multiprocessors and their comparison with symbolic substitution for digital optical computing,” Opt. Eng. 28, 396–409 (1989).

Esener, S. C.

Fainman, Y.

H. Takahashi, D. Zaleta, J. Ma, J. Ford, Y. Fainman, S. Lee, “Packaged optical interconnection system based on photorefractive correlation,” Appl. Opt. 33, 2991–2997 (1994).
[CrossRef] [PubMed]

J. E. Ford, Y. Fainman, S. H. Lee, “Array interconnection by phase-coded optical correlation,” Opt. Lett. 15, 1088–1090 (1990).
[CrossRef] [PubMed]

J. E. Ford, Y. Fainman, S. H. Lee, “Enhanced photorefractive performance from 45°-cut BaTiO3,” Appl. Opt. 28, 4808–4815 (1989).
[CrossRef] [PubMed]

F. Kiamilev, S. Esener, R. Paturi, Y. Fainman, P. Mercier, C. Guest, S. H. Lee, “Programmable opto-electronic multiprocessors and their comparison with symbolic substitution for digital optical computing,” Opt. Eng. 28, 396–409 (1989).

The first public presentation of the LiNbO3 correlator work performed at the University of California, San Diego, was by J. Ford, Y. Fainman, S. Lee, “Reconfigurable array interconnection by photorefractive correlation,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 274.

J. E. Ford, S. H. Lee, Y. Fainman, “Reconfigurable interconnection using the correlation matrix–tensor multiplier,” presented at the International Commission for Optics Topical Meeting on Optical Computing, Kobe, Japan, April 1990.

Farhat, N.

N. Farhat, D. Psaltis, “Optical implementation of associative memory based on models of neural networks,” in Optical Signal Processing, J. Horner, ed. (Academic, New York, 1987), Sec. 23, pp. 129–162.

Fekete, D.

Fischer, B.

Ford, J.

H. Takahashi, D. Zaleta, J. Ma, J. Ford, Y. Fainman, S. Lee, “Packaged optical interconnection system based on photorefractive correlation,” Appl. Opt. 33, 2991–2997 (1994).
[CrossRef] [PubMed]

The first public presentation of the LiNbO3 correlator work performed at the University of California, San Diego, was by J. Ford, Y. Fainman, S. Lee, “Reconfigurable array interconnection by photorefractive correlation,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 274.

Ford, J. E.

R. Paturi, D. T. Lu, J. E. Ford, S. C. Esener, S. H. Lee, “Parallel algorithms based on expander graphs for optical computing,” Appl. Opt. 30, 917–927 (1991).
[CrossRef] [PubMed]

J. E. Ford, Y. Fainman, S. H. Lee, “Array interconnection by phase-coded optical correlation,” Opt. Lett. 15, 1088–1090 (1990).
[CrossRef] [PubMed]

J. E. Ford, Y. Fainman, S. H. Lee, “Enhanced photorefractive performance from 45°-cut BaTiO3,” Appl. Opt. 28, 4808–4815 (1989).
[CrossRef] [PubMed]

J. E. Ford, S. H. Lee, Y. Fainman, “Reconfigurable interconnection using the correlation matrix–tensor multiplier,” presented at the International Commission for Optics Topical Meeting on Optical Computing, Kobe, Japan, April 1990.

J. E. Ford, “Reconfigurable array interconnection by photorefractive volume holography,” Ph.D. dissertation (University of California, San Diego, La Jolla, Calif., 1992).

Gheen, G.

Glass, A. M.

D. Von der Linde, A. M. Glass, K. F. Rodgers, “Multiphoton photorefractive processes for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[CrossRef]

Goodman, J.

J. Goodman, F. Leonberger, S. Kung, R. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Sec. 2.9, pp. 44–55.

Gozewski, C.

L. H. Domash, C. Gozewski, “Composite pattern recognition using the nonlinear triple processor,” in Optical Pattern Recognition II, H. J. Caulfield, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1134, 162–172 (1989).

Gregory, D. A.

F. T. S. Yu, S. Wu, A. Mayers, S. Rajan, D. A. Gregory, “Color holographic storage in LiNbO3,” Opt. Commun. 81, 348–352 (1991).
[CrossRef]

S. Wu, Q. Song, A. Mayers, D. A. Gregory, F. T. S. Yu, “Reconfigurable interconnections using photorefractive holograms,” Appl. Opt. 29, 1118–1125 (1990).
[CrossRef] [PubMed]

Gu, C.

Guest, C.

F. Kiamilev, S. Esener, R. Paturi, Y. Fainman, P. Mercier, C. Guest, S. H. Lee, “Programmable opto-electronic multiprocessors and their comparison with symbolic substitution for digital optical computing,” Opt. Eng. 28, 396–409 (1989).

Habiby, S. F.

A. Marrakchi, W. M. Hubbard, S. F. Habiby, J. S. Patel, “Dynamic holographic interconnects with analog weights in photorefractive crystals,” Opt. Eng. 29, 215–224 (1990).
[CrossRef]

Hong, J.

Hubbard, W. M.

A. Marrakchi, W. M. Hubbard, S. F. Habiby, J. S. Patel, “Dynamic holographic interconnects with analog weights in photorefractive crystals,” Opt. Eng. 29, 215–224 (1990).
[CrossRef]

Johnson, K. M.

E. S. Maniloff, K. M. Johnson, “Dynamic holographic interconnects using static holograms,” Opt. Eng. 29, 225–229 (1990).
[CrossRef]

Keyes, R. W.

R. W. Keyes, The Physics of VLSI Systems (Addison-Wesley, Reading, Mass., 1987), Chap. 7, pp. 146–170.

Kiamilev, F.

F. Kiamilev, S. Esener, R. Paturi, Y. Fainman, P. Mercier, C. Guest, S. H. Lee, “Programmable opto-electronic multiprocessors and their comparison with symbolic substitution for digital optical computing,” Opt. Eng. 28, 396–409 (1989).

Kinell, D.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Kung, S.

J. Goodman, F. Leonberger, S. Kung, R. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Lee, H.

Lee, S.

H. Takahashi, D. Zaleta, J. Ma, J. Ford, Y. Fainman, S. Lee, “Packaged optical interconnection system based on photorefractive correlation,” Appl. Opt. 33, 2991–2997 (1994).
[CrossRef] [PubMed]

The first public presentation of the LiNbO3 correlator work performed at the University of California, San Diego, was by J. Ford, Y. Fainman, S. Lee, “Reconfigurable array interconnection by photorefractive correlation,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 274.

Lee, S. H.

J. A. Neff, R. A. Athale, S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 826–855 (1991).
[CrossRef]

R. Paturi, D. T. Lu, J. E. Ford, S. C. Esener, S. H. Lee, “Parallel algorithms based on expander graphs for optical computing,” Appl. Opt. 30, 917–927 (1991).
[CrossRef] [PubMed]

J. E. Ford, Y. Fainman, S. H. Lee, “Array interconnection by phase-coded optical correlation,” Opt. Lett. 15, 1088–1090 (1990).
[CrossRef] [PubMed]

J. E. Ford, Y. Fainman, S. H. Lee, “Enhanced photorefractive performance from 45°-cut BaTiO3,” Appl. Opt. 28, 4808–4815 (1989).
[CrossRef] [PubMed]

F. Kiamilev, S. Esener, R. Paturi, Y. Fainman, P. Mercier, C. Guest, S. H. Lee, “Programmable opto-electronic multiprocessors and their comparison with symbolic substitution for digital optical computing,” Opt. Eng. 28, 396–409 (1989).

J. E. Ford, S. H. Lee, Y. Fainman, “Reconfigurable interconnection using the correlation matrix–tensor multiplier,” presented at the International Commission for Optics Topical Meeting on Optical Computing, Kobe, Japan, April 1990.

Leonberger, F.

J. Goodman, F. Leonberger, S. Kung, R. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Leyva, V.

G. Rakuljic, V. Leyva, “Volume holographic narrow band optical filter,” Opt. Lett. 15, 459–461 (1993).
[CrossRef]

Lu, D. T.

Ma, J.

Maniloff, E. S.

E. S. Maniloff, K. M. Johnson, “Dynamic holographic interconnects using static holograms,” Opt. Eng. 29, 225–229 (1990).
[CrossRef]

Marrakchi, A.

A. Marrakchi, W. M. Hubbard, S. F. Habiby, J. S. Patel, “Dynamic holographic interconnects with analog weights in photorefractive crystals,” Opt. Eng. 29, 215–224 (1990).
[CrossRef]

Mayers, A.

F. T. S. Yu, S. Wu, A. Mayers, S. Rajan, D. A. Gregory, “Color holographic storage in LiNbO3,” Opt. Commun. 81, 348–352 (1991).
[CrossRef]

S. Wu, Q. Song, A. Mayers, D. A. Gregory, F. T. S. Yu, “Reconfigurable interconnections using photorefractive holograms,” Appl. Opt. 29, 1118–1125 (1990).
[CrossRef] [PubMed]

Mayers, A. W.

F. T. S. Yu, S. Wu, A. W. Mayers, S. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
[CrossRef]

McCall, M. W.

Mercier, P.

F. Kiamilev, S. Esener, R. Paturi, Y. Fainman, P. Mercier, C. Guest, S. H. Lee, “Programmable opto-electronic multiprocessors and their comparison with symbolic substitution for digital optical computing,” Opt. Eng. 28, 396–409 (1989).

Mok, F. H.

Neff, J. A.

J. A. Neff, R. A. Athale, S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 826–855 (1991).
[CrossRef]

Nicholson, M. G.

Owechko, Y.

Paek, E. G.

E. G. Paek, D. Psaltis, “Optical associative memory using Fourier transform holograms,” Opt. Eng. 26, 428–433 (1987).

Patel, J. S.

A. Marrakchi, W. M. Hubbard, S. F. Habiby, J. S. Patel, “Dynamic holographic interconnects with analog weights in photorefractive crystals,” Opt. Eng. 29, 215–224 (1990).
[CrossRef]

Paturi, R.

R. Paturi, D. T. Lu, J. E. Ford, S. C. Esener, S. H. Lee, “Parallel algorithms based on expander graphs for optical computing,” Appl. Opt. 30, 917–927 (1991).
[CrossRef] [PubMed]

F. Kiamilev, S. Esener, R. Paturi, Y. Fainman, P. Mercier, C. Guest, S. H. Lee, “Programmable opto-electronic multiprocessors and their comparison with symbolic substitution for digital optical computing,” Opt. Eng. 28, 396–409 (1989).

Pepper, D. M.

Petts, C. R.

Phillips, W.

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

Psaltis, D.

D. Psaltis, D. Brady, K. Wagner, “Adaptive optical networks using photorefractive crystals,” Appl. Opt. 27, 1752–1759 (1988).
[CrossRef]

E. G. Paek, D. Psaltis, “Optical associative memory using Fourier transform holograms,” Opt. Eng. 26, 428–433 (1987).

N. Farhat, D. Psaltis, “Optical implementation of associative memory based on models of neural networks,” in Optical Signal Processing, J. Horner, ed. (Academic, New York, 1987), Sec. 23, pp. 129–162.

Rajan, S.

F. T. S. Yu, S. Wu, A. W. Mayers, S. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
[CrossRef]

F. T. S. Yu, S. Wu, A. Mayers, S. Rajan, D. A. Gregory, “Color holographic storage in LiNbO3,” Opt. Commun. 81, 348–352 (1991).
[CrossRef]

Rakuljic, G.

G. Rakuljic, V. Leyva, “Volume holographic narrow band optical filter,” Opt. Lett. 15, 459–461 (1993).
[CrossRef]

Rodgers, K. F.

D. Von der Linde, A. M. Glass, K. F. Rodgers, “Multiphoton photorefractive processes for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[CrossRef]

Saleh, B. E. A.

Segev, M.

Slinger, C.

Soffer, B. H.

Song, Q.

Staebler, D. L.

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

Sternklar, S.

Takahashi, H.

Von der Linde, D.

D. Von der Linde, A. M. Glass, K. F. Rodgers, “Multiphoton photorefractive processes for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[CrossRef]

Wagner, K.

Weiss, S.

White, J. O.

J. O. White, A. Yariv, “Real-time image processing via four-wave mixing in a photorefractive media,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

Wu, S.

F. T. S. Yu, S. Wu, A. Mayers, S. Rajan, D. A. Gregory, “Color holographic storage in LiNbO3,” Opt. Commun. 81, 348–352 (1991).
[CrossRef]

F. T. S. Yu, S. Wu, A. W. Mayers, S. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
[CrossRef]

S. Wu, Q. Song, A. Mayers, D. A. Gregory, F. T. S. Yu, “Reconfigurable interconnections using photorefractive holograms,” Appl. Opt. 29, 1118–1125 (1990).
[CrossRef] [PubMed]

Yariv, A.

J. O. White, A. Yariv, “Real-time image processing via four-wave mixing in a photorefractive media,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

D. M. Pepper, J. AuYeung, D. Fekete, A. Yariv, “Spatial convolution and correlation of optical fields via degenerate four-wave mixing,” Opt. Lett. 3, 7–9 (1978).
[CrossRef] [PubMed]

Yeh, P.

Yu, F. T. S.

F. T. S. Yu, S. Wu, A. W. Mayers, S. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Programmable optoelectronic multiprocessor system, combining local electronic processing with global optical interconnection. Reconfigurable interconnects between the two processing planes are controlled externally.

Fig. 2
Fig. 2

Conceptual construction of the algorithm in three steps: (a) Correlation of the input array with the control image produces the output at sites imbedded in a field of noise. (b) Phase coding the input and the control images cuts background noise relative to the signal. (c) The final control image, H(x, y), is produced by compression (overlapping) of W′(x, y), reducing control SBP at the cost of superimposing noise on the signal sites.

Fig. 3
Fig. 3

Predicted scaling of the control-image SPB necessary to maintain a constant SNR = 20 as a function of input array size N 2 = M 2. The SBP necessary to maintain a one-to-one connection increases dramatically with N 2, while the SBP necessary for a dense connection (in the plot, with F = 0.5N 2) rises much more slowly. The SBP necessary to build a conventional vector–matrix multiplier, N 4, lies between these extremes. The horizontal line is the SBP of a 1000 × 1000 binary SLM.

Fig. 4
Fig. 4

Average output SNR from a computer simulation of the algorithm as a function of k for 16 inputs and 16 outputs with a hypercube connection pattern. To minimize statistical fluctuation (largest for small N, F, and k), we averaged at least 200 runs for each point. The plot shows the average SNR over all 16 output sites and runs, the average minimum SNR, and the prediction of Eq. (1).

Fig. 5
Fig. 5

Photorefractive correlator system. Inputs u 1, u 2, and u 4 are Fourier transformed into the crystal to generate the output u 3. For correlation a point source is placed at u 2. The first correlator experiments used this configuration with all inputs present simultaneously. f, focal lengths; B.S. beam splitter; F-T lenses, Fourier-transform lens.

Fig. 6
Fig. 6

Preprogrammed photorefractive correlator that uses reflection holograms recorded in z-cut LiNbO3. Several interconnections are superimposed by recording of a series of holograms, each with a unique wavelength address. During operation the input, coded by wavelength (and by the unchanging phase code), reads one reference pattern.

Fig. 7
Fig. 7

Experimental test of the photorefractive-correlator accuracy. The autocorrelation and cross correlation of a 50 × 50 pixel random phase code was detected on a CCD camera. The plot shows the theoretical autocorrelation peak (amplitude scaled for best fit).

Fig. 8
Fig. 8

Experimental CMTM optical interconnection system that uses wavelength-multiplexed reflection holograms in LiNbO3.

Fig. 9
Fig. 9

Degenerate-four-wave-mixing CMTM system output. The output for two inputs is shown. The control image was an uncompressed pattern with five outputs for each input pixel (N = 5 and k = 3). The average SNR for all connections was 25.

Fig. 10
Fig. 10

Prestored CMTM system output that uses the uncompressed control image; the output for illumination by each of four of the 25 inputs pixels is shown. The average SNR for all connections was 71. Broadcast and one-to-one output points had equal intensities.

Fig. 11
Fig. 11

Readout of three color-multiplexed interconnections. Three interconnections were stored at (a) 476 nm (broadcast), (b) 488 nm (irregular), and (c) 496 nm (broadcast). Interconnected output from a single input pixel is shown at each wavelength. No cross talk is visible.

Fig. 12
Fig. 12

Output for sparse versus dense interconnections. The control image (upper) and the resulting output (lower) for a one-to-one interconnection are shown at left, while those for a dense (25%-filled) interconnection are shown at right. All experimental parameters are equal except for readout intensity, which was increased for the sparse output to show detail.

Fig. 13
Fig. 13

Effect of phase-code density on output SNR. Phase-code pixel size was constant at 20 μm; thus as k increases, the array size also increases. At left, all inputs are on. At right, half the inputs are masked. Signal intensity and uniformity increase as k grows. N = 16; (a) k = 8, (b) k = 16, and (c) k = 32.

Fig. 14
Fig. 14

Effect of array size on output SNR. We held the control-image SBP at roughly 1000 × 1000 by decreasing k linearly with N. At left, all inputs are on. At right, half the inputs are masked. Output SNR decreases as N 2 grows from 256 to 1024 to 4096. (a) N = 16, k = 32; (b) N = 32, k = 16; (c) N = 64, k = 8.

Tables (1)

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Table 1 Experimental Scaling of the Signal-to-Noise Ratio

Equations (12)

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SNR = 1 + G k 2 F N 2 M 4 16 N 4 - M 3 2 N 3 + M 2 N 2 - 1 N 2 - M 2 4 N 4 + M 2 N 3 + 1 16 N 4 ,
SNR 1 + G ( k / N ) 2 F .
u 3 ( x , y ) Ψ u 1 ( x , y ) * u 2 ( x , y ) u 4 ( x , y ) ,
I n = A n 2 = 1 Q T 2 = T 2 Q ,
I s = A s 2 = ( G T k 2 F ) 2 .
SNR = I s + I n I n .
Q p q = G k 2 F N 2 × { [ μ = 1 M ν = 1 M ( N - p - μ ) ( N - q - ν ) ] - N 2 } .
μ = 1 M ( N - p - μ ) = [ - p 2 + ( M + 1 ) p + M ( N - 1 2 ) - M 2 2 ] .
SNR p q = 1 + G k 2 F N 2 [ - p 2 + ( M + 1 ) p + M ( N - 1 2 ) - M 2 2 ] [ - q 2 + ( M + 1 ) q + M ( N - 1 2 ) - M 2 2 ] .
SNR = 1 + G k 2 F N 2 M 4 16 N 4 - M 3 2 N 3 + M 2 N 2 - 1 N 2 - M 2 4 N 4 + M 2 N 3 + 1 16 N 4 .
SNR = 1 + G k 2 F N 2 M 4 16 N 4 - M 3 2 N 3 + M 2 N 2 .
SNR = 1 + 8 G k 2 N 2 F 9 - 12 N 2 + 1 N 4 .

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