Abstract

We propose and demonstrate the use of a Fourier transform to achieve maximum energy efficiency in a photorefractive optical interconnection. The results of experimental investigations on reconfigurable optical interconnections using photorefractive holograms in a barium titanate crystal are presented and discussed. High energy efficiency is achieved by matched amplification at the Fourier plane.

© 1990 Optical Society of America

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References

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  1. See, for example, J. W. Goodman, F. I. Leonberger, S. Y. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850–866 (1984).
    [CrossRef]
  2. See, for example, J. A. Neff, Ed., Optical Computing, Proc. Soc. Photo-Opt. Instrum. Eng.625, 109–172 (1986).
  3. C. Mead, “Potential and Limitation of VLSI,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1985), paper MA2.
  4. A. A. Sawchuk, B. K. Jenkins, “Dynamic Optical Interconnections for Parallel Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143–153 (1986).
  5. A. A. Sawchuk, B. K. Jenkins, C. S. Raghavendra, A. Varma, “Optical Crossbar Networks,” IEEE Trans. Comput. C-20, No. 6, 50–60 (1987).
  6. J. W. Goodman, A. R. Dias, L. M. Woody, “Fully Parallel, High-Speed Incoherent Optical Method for Performing Discrete Fourier Transforms,” Opt. Lett. 2, 1–3 (1978).
    [CrossRef] [PubMed]
  7. W. T. Rhodes, “Optical Matrix–Vector Processors: Basic Concepts,” Proc. Soc. Photo-Opt. Instrum. Eng. 614, 146–152 (1986).
  8. R. A. Athale, “Optical Matrix Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 96–111 (1986).
  9. P. Yeh, A. E. T. Chiou, J. Hong, “Optical Interconnection Using Photorefractive Dynamic Holograms,” Appl. Opt. 27, 2093–2096 (1988).
    [CrossRef] [PubMed]
  10. A. E. Chiou, P. Yeh, J. Hong, “Energy Efficient Optical Interconnection Using Dynamic Holograms in Photorefractive Media,” OSA Annual Meeting, 1988Technical Digest Series, Vol. 11 (Optical Society of America, Washington, DC, 1988), p. 178.
  11. A. E. Chiou, P. Yeh, “Energy Efficiency of Optical Interconnection Using Photorefractive Dynamic Holograms,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), p. 128.
  12. N. V. Kukhtarev et al., “Holographic Storage in Electrooptic Crystal. I: Steady State,” Ferroelectrics 22, 949–960 (1979).
    [CrossRef]
  13. P. Gunter, “Holography, Coherent Light Amplification and Optical Phase Conjugation with Photorefractive Materials,” Phys. Rep. 93, 199–299 (1982).
    [CrossRef]
  14. N. V. Kukhtarev et al., “Holographic Storage in Electrooptic Crystal. II. Beam Coupling—Light Amplification,” Ferroelectrics 22, 961–964 (1979).
    [CrossRef]
  15. J. P. Huignard, A. Marrakchi, “Coherent Signal Beam Amplification in Two-Wave Mixing Experiments with Photorefractive Bi12SiO20 Crystals,” Opt. Commun. 38, 249–253 (1981).
    [CrossRef]
  16. A. E. Chiou, P. Yeh, “Beam Cleanup Using Photorefractive Two-Wave Mixing,” Opt. Lett. 10, 621–623 (1985).
    [CrossRef] [PubMed]
  17. A. D. Fisher, J. N. Lee, “The Current Status of Two-Dimensional Spatial Light Modulator Technology,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 352–371 (1986).
  18. C. Warde, A. D. Fisher, “Spatial Light Modulators: Applications and Functional Capabilities,” in Optical Signal Processing, J. Horner, Ed. (Academic, New York, 1987).
  19. J. Feinberg, “Asymmetric Self-Defocusing of an Optical Beam from the Photorefractive Effect,” J. Opt. Soc. Am. 72, 46–51 (1982).
    [CrossRef]
  20. D. Malacara, “Diffraction and Scattering,” in Physical Optics and Light Measurement, Methods of Experimental Physics, Vol. 26, D. Malacara, Ed. (Academic, New York, 1988).

1988 (1)

1987 (1)

A. A. Sawchuk, B. K. Jenkins, C. S. Raghavendra, A. Varma, “Optical Crossbar Networks,” IEEE Trans. Comput. C-20, No. 6, 50–60 (1987).

1986 (4)

A. A. Sawchuk, B. K. Jenkins, “Dynamic Optical Interconnections for Parallel Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143–153 (1986).

W. T. Rhodes, “Optical Matrix–Vector Processors: Basic Concepts,” Proc. Soc. Photo-Opt. Instrum. Eng. 614, 146–152 (1986).

R. A. Athale, “Optical Matrix Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 96–111 (1986).

A. D. Fisher, J. N. Lee, “The Current Status of Two-Dimensional Spatial Light Modulator Technology,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 352–371 (1986).

1985 (1)

1984 (1)

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

1982 (2)

J. Feinberg, “Asymmetric Self-Defocusing of an Optical Beam from the Photorefractive Effect,” J. Opt. Soc. Am. 72, 46–51 (1982).
[CrossRef]

P. Gunter, “Holography, Coherent Light Amplification and Optical Phase Conjugation with Photorefractive Materials,” Phys. Rep. 93, 199–299 (1982).
[CrossRef]

1981 (1)

J. P. Huignard, A. Marrakchi, “Coherent Signal Beam Amplification in Two-Wave Mixing Experiments with Photorefractive Bi12SiO20 Crystals,” Opt. Commun. 38, 249–253 (1981).
[CrossRef]

1979 (2)

N. V. Kukhtarev et al., “Holographic Storage in Electrooptic Crystal. II. Beam Coupling—Light Amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

N. V. Kukhtarev et al., “Holographic Storage in Electrooptic Crystal. I: Steady State,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

1978 (1)

Athale, R. A.

R. A. Athale, “Optical Matrix Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 96–111 (1986).

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

Chiou, A. E.

A. E. Chiou, P. Yeh, “Beam Cleanup Using Photorefractive Two-Wave Mixing,” Opt. Lett. 10, 621–623 (1985).
[CrossRef] [PubMed]

A. E. Chiou, P. Yeh, J. Hong, “Energy Efficient Optical Interconnection Using Dynamic Holograms in Photorefractive Media,” OSA Annual Meeting, 1988Technical Digest Series, Vol. 11 (Optical Society of America, Washington, DC, 1988), p. 178.

A. E. Chiou, P. Yeh, “Energy Efficiency of Optical Interconnection Using Photorefractive Dynamic Holograms,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), p. 128.

Chiou, A. E. T.

Dias, A. R.

Feinberg, J.

Fisher, A. D.

A. D. Fisher, J. N. Lee, “The Current Status of Two-Dimensional Spatial Light Modulator Technology,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 352–371 (1986).

C. Warde, A. D. Fisher, “Spatial Light Modulators: Applications and Functional Capabilities,” in Optical Signal Processing, J. Horner, Ed. (Academic, New York, 1987).

Goodman, J. W.

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

J. W. Goodman, A. R. Dias, L. M. Woody, “Fully Parallel, High-Speed Incoherent Optical Method for Performing Discrete Fourier Transforms,” Opt. Lett. 2, 1–3 (1978).
[CrossRef] [PubMed]

Gunter, P.

P. Gunter, “Holography, Coherent Light Amplification and Optical Phase Conjugation with Photorefractive Materials,” Phys. Rep. 93, 199–299 (1982).
[CrossRef]

Hong, J.

P. Yeh, A. E. T. Chiou, J. Hong, “Optical Interconnection Using Photorefractive Dynamic Holograms,” Appl. Opt. 27, 2093–2096 (1988).
[CrossRef] [PubMed]

A. E. Chiou, P. Yeh, J. Hong, “Energy Efficient Optical Interconnection Using Dynamic Holograms in Photorefractive Media,” OSA Annual Meeting, 1988Technical Digest Series, Vol. 11 (Optical Society of America, Washington, DC, 1988), p. 178.

Huignard, J. P.

J. P. Huignard, A. Marrakchi, “Coherent Signal Beam Amplification in Two-Wave Mixing Experiments with Photorefractive Bi12SiO20 Crystals,” Opt. Commun. 38, 249–253 (1981).
[CrossRef]

Jenkins, B. K.

A. A. Sawchuk, B. K. Jenkins, C. S. Raghavendra, A. Varma, “Optical Crossbar Networks,” IEEE Trans. Comput. C-20, No. 6, 50–60 (1987).

A. A. Sawchuk, B. K. Jenkins, “Dynamic Optical Interconnections for Parallel Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143–153 (1986).

Kukhtarev, N. V.

N. V. Kukhtarev et al., “Holographic Storage in Electrooptic Crystal. I: Steady State,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

N. V. Kukhtarev et al., “Holographic Storage in Electrooptic Crystal. II. Beam Coupling—Light Amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

Kung, S. Y.

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

Lee, J. N.

A. D. Fisher, J. N. Lee, “The Current Status of Two-Dimensional Spatial Light Modulator Technology,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 352–371 (1986).

Leonberger, F. I.

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

Malacara, D.

D. Malacara, “Diffraction and Scattering,” in Physical Optics and Light Measurement, Methods of Experimental Physics, Vol. 26, D. Malacara, Ed. (Academic, New York, 1988).

Marrakchi, A.

J. P. Huignard, A. Marrakchi, “Coherent Signal Beam Amplification in Two-Wave Mixing Experiments with Photorefractive Bi12SiO20 Crystals,” Opt. Commun. 38, 249–253 (1981).
[CrossRef]

Mead, C.

C. Mead, “Potential and Limitation of VLSI,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1985), paper MA2.

Raghavendra, C. S.

A. A. Sawchuk, B. K. Jenkins, C. S. Raghavendra, A. Varma, “Optical Crossbar Networks,” IEEE Trans. Comput. C-20, No. 6, 50–60 (1987).

Rhodes, W. T.

W. T. Rhodes, “Optical Matrix–Vector Processors: Basic Concepts,” Proc. Soc. Photo-Opt. Instrum. Eng. 614, 146–152 (1986).

Sawchuk, A. A.

A. A. Sawchuk, B. K. Jenkins, C. S. Raghavendra, A. Varma, “Optical Crossbar Networks,” IEEE Trans. Comput. C-20, No. 6, 50–60 (1987).

A. A. Sawchuk, B. K. Jenkins, “Dynamic Optical Interconnections for Parallel Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143–153 (1986).

Varma, A.

A. A. Sawchuk, B. K. Jenkins, C. S. Raghavendra, A. Varma, “Optical Crossbar Networks,” IEEE Trans. Comput. C-20, No. 6, 50–60 (1987).

Warde, C.

C. Warde, A. D. Fisher, “Spatial Light Modulators: Applications and Functional Capabilities,” in Optical Signal Processing, J. Horner, Ed. (Academic, New York, 1987).

Woody, L. M.

Yeh, P.

P. Yeh, A. E. T. Chiou, J. Hong, “Optical Interconnection Using Photorefractive Dynamic Holograms,” Appl. Opt. 27, 2093–2096 (1988).
[CrossRef] [PubMed]

A. E. Chiou, P. Yeh, “Beam Cleanup Using Photorefractive Two-Wave Mixing,” Opt. Lett. 10, 621–623 (1985).
[CrossRef] [PubMed]

A. E. Chiou, P. Yeh, J. Hong, “Energy Efficient Optical Interconnection Using Dynamic Holograms in Photorefractive Media,” OSA Annual Meeting, 1988Technical Digest Series, Vol. 11 (Optical Society of America, Washington, DC, 1988), p. 178.

A. E. Chiou, P. Yeh, “Energy Efficiency of Optical Interconnection Using Photorefractive Dynamic Holograms,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), p. 128.

Appl. Opt. (1)

Ferroelectrics (2)

N. V. Kukhtarev et al., “Holographic Storage in Electrooptic Crystal. I: Steady State,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

N. V. Kukhtarev et al., “Holographic Storage in Electrooptic Crystal. II. Beam Coupling—Light Amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

IEEE Trans. Comput. (1)

A. A. Sawchuk, B. K. Jenkins, C. S. Raghavendra, A. Varma, “Optical Crossbar Networks,” IEEE Trans. Comput. C-20, No. 6, 50–60 (1987).

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

J. P. Huignard, A. Marrakchi, “Coherent Signal Beam Amplification in Two-Wave Mixing Experiments with Photorefractive Bi12SiO20 Crystals,” Opt. Commun. 38, 249–253 (1981).
[CrossRef]

Opt. Lett. (2)

Phys. Rep. (1)

P. Gunter, “Holography, Coherent Light Amplification and Optical Phase Conjugation with Photorefractive Materials,” Phys. Rep. 93, 199–299 (1982).
[CrossRef]

Proc. IEEE (1)

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

Proc. Soc. Photo-Opt. Instrum. Eng. (4)

W. T. Rhodes, “Optical Matrix–Vector Processors: Basic Concepts,” Proc. Soc. Photo-Opt. Instrum. Eng. 614, 146–152 (1986).

R. A. Athale, “Optical Matrix Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 96–111 (1986).

A. D. Fisher, J. N. Lee, “The Current Status of Two-Dimensional Spatial Light Modulator Technology,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 352–371 (1986).

A. A. Sawchuk, B. K. Jenkins, “Dynamic Optical Interconnections for Parallel Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143–153 (1986).

Other (6)

C. Warde, A. D. Fisher, “Spatial Light Modulators: Applications and Functional Capabilities,” in Optical Signal Processing, J. Horner, Ed. (Academic, New York, 1987).

D. Malacara, “Diffraction and Scattering,” in Physical Optics and Light Measurement, Methods of Experimental Physics, Vol. 26, D. Malacara, Ed. (Academic, New York, 1988).

See, for example, J. A. Neff, Ed., Optical Computing, Proc. Soc. Photo-Opt. Instrum. Eng.625, 109–172 (1986).

C. Mead, “Potential and Limitation of VLSI,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1985), paper MA2.

A. E. Chiou, P. Yeh, J. Hong, “Energy Efficient Optical Interconnection Using Dynamic Holograms in Photorefractive Media,” OSA Annual Meeting, 1988Technical Digest Series, Vol. 11 (Optical Society of America, Washington, DC, 1988), p. 178.

A. E. Chiou, P. Yeh, “Energy Efficiency of Optical Interconnection Using Photorefractive Dynamic Holograms,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989), p. 128.

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram illustrating the basic idea of a reconfigurable optical interconnection using a photorefractive crystal in conjunction with a spatial light modulator.

Fig. 2
Fig. 2

Schematic diagram illustrating the basic idea of using a Fourier transform to achieve the spatial overlap of the pump beam and signal beam.

Fig. 3
Fig. 3

Experimental configuration for measuring the energy efficiency in photorefractive two-beam coupling.

Fig. 4
Fig. 4

Energy efficiency η of two-beam coupling in a photorefractive barium titanate crystal as a function of pump-to-signal power ratio m. The symbols □, ◇, ○, and △ represent the cases without a neutral density filter, neutral density filters NDF1, NDF2, and NDF3, respectively, in the signal input arm. The percentage transmittances of the three neutral density filters are 12.2, 0.74, and 0.12%, respectively. The orientation of the crystal relative to the beam is given in the inset.

Fig. 5
Fig. 5

Energy efficiency η of the photorefractive two-beam coupling in a barium titanate sample as a function of the transmittance of a neutral density filter placed in the signal input arm. The transmittance is labeled 1/N to relate it to the fanout loss of an N × N permutation crossbar network. The orientation of the crystal relative to the beam is given in the inset.

Fig. 6
Fig. 6

Experimental configuration for a 1-to-N × N (for N = 10) broadcasting network using photorefractive holograms at the Fourier domain.

Fig. 7
Fig. 7

Intensity patterns of the masks for the probe and pump beams at the image and Fourier planes.

Fig. 8
Fig. 8

Energy efficiency as η function of the number of signal channels N in a 1-to-N × N broadcasting configuration using photorefractive holograms in a barium titanate sample.

Fig. 9
Fig. 9

A 10 × 10 intensity pattern at the output image plane in various conditions: (a) with the crystal removed; (b) with the crystal in place and the pump beam off, total power = 400 μW, e-polarization; (c) same as in (b) but with o-polarization; (d) same as in (b) but with total power = 3 μW; (e) amplified output signal, total signal input = 3 μW, pump input = 600 μW.

Fig. 10
Fig. 10

Intensity distribution of a selected row of 10 out of the l0 × 10 channels shown in Fig. 9: (a) with the crystal removed; (b) with the crystal in place and the pump beam off; total input power = 10 μW; (c) with the crystal in place and the pump beam on, input pump power = 400 μW. The vertical scale (per division) in the pictures are 50, 10, and 100 mV, respectively.

Fig. 11
Fig. 11

Intensity patterns of the masks for the probe and pump beams at the image plane and the crystal plane for a 6 × 6 generalized crossbar network.

Equations (2)

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pump :             P ( u , v ) = σ ( u , v ) ,
signal :             S ( u , v ) = n σ ( u , v ) exp [ i ϕ n ( u , v ) ] ,

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