Abstract

A free-space optical logic technique is presented that utilizes a two-dimensional array of diffractive optical elements. Each optical element focuses light to multiple, separate positions in the output focal plane. The focal spots from different optical elements are allowed to overlap spatially, resulting in interference. By changing the phase shift between the optical elements, one can create different optical logic operations in the focal plane. The technique is demonstrated by the use of two input beams incident onto a multiplexed optical element written onto a programmable spatial light modulator. The optical element simultaneously creates both and and xor logic functions in the output plane.

© 1995 Optical Society of America

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References

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  1. T. H. Barnes, T. Eiju, K. Matsuda, H. Ichikawa, M. R. Taghizadeh, J. Turunen, “Reconfigurable free-space optical interconnections with a phase-only liquid crystal spatial light modulator,” Appl. Opt. 31, 5527–5535 (1992).
    [CrossRef] [PubMed]
  2. H. Ichikawa, T. H. Barnes, M. R. Taghizadeh, J. Turunen, T. Eiju, K. Matsuda, “Dynamic space-variant optical interconnections using liquid crystal spatial light modulators,” Opt. Commun. 93, 145–150 (1992).
    [CrossRef]
  3. H. Yamazaki, M. Yamaguchi, “Experiments on a multichannel holographic optical switch with the use of a liquid-crystal display,” Opt. Lett. 17, 1228–1230 (1992).
    [CrossRef] [PubMed]
  4. H. Dammann, K. Gortler, “High efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
    [CrossRef]
  5. D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel hybrid optical bistable switch: the quantum well self-electro-optic effect device,” Appl. Phys. Lett. 45, 13–15 (1984).
    [CrossRef]
  6. A. C. Walker, “Reflection bistable etalons with absorbed transmission,” Opt. Commun. 59, 145–150 (1986).
    [CrossRef]
  7. J. A. Davis, D. M. Cottrell, C. A. Maley, M. R. Crivello, “Subdiffraction-limited focusing lens,” Appl. Opt. 33, 4128–4131 (1994).
    [CrossRef] [PubMed]
  8. B. Vinas, Z. Jaroszewicz, A. Kolodziejczyk, M. Sypek, “Zone plates with black focal spots,” Appl. Opt. 31, 192–198 (1992).
    [CrossRef] [PubMed]
  9. J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
    [CrossRef] [PubMed]
  10. J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
    [CrossRef]
  11. J. A. Davis, D. M. Cottrell, “Random mask encoding of multiplexed phase-only and binary phase-only filters,” Opt. Lett. 19, 496–498 (1994).
    [CrossRef] [PubMed]
  12. W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).
  13. J. A. Davis, D. M. Cottrell, R.. A. Lilly, S. W. Connely, “Multiplexed phase-encoded lenses written on spatial light modulators,” Opt. Lett. 14, 420–422 (1989).
    [CrossRef] [PubMed]

1994 (2)

1992 (4)

1990 (1)

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

1989 (1)

1986 (1)

A. C. Walker, “Reflection bistable etalons with absorbed transmission,” Opt. Commun. 59, 145–150 (1986).
[CrossRef]

1984 (2)

J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
[CrossRef] [PubMed]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel hybrid optical bistable switch: the quantum well self-electro-optic effect device,” Appl. Phys. Lett. 45, 13–15 (1984).
[CrossRef]

1983 (1)

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).

1971 (1)

H. Dammann, K. Gortler, “High efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Anderson, R. H.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).

Barnes, T. H.

H. Ichikawa, T. H. Barnes, M. R. Taghizadeh, J. Turunen, T. Eiju, K. Matsuda, “Dynamic space-variant optical interconnections using liquid crystal spatial light modulators,” Opt. Commun. 93, 145–150 (1992).
[CrossRef]

T. H. Barnes, T. Eiju, K. Matsuda, H. Ichikawa, M. R. Taghizadeh, J. Turunen, “Reconfigurable free-space optical interconnections with a phase-only liquid crystal spatial light modulator,” Appl. Opt. 31, 5527–5535 (1992).
[CrossRef] [PubMed]

Bunch, R. M.

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Burrus, C. A.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel hybrid optical bistable switch: the quantum well self-electro-optic effect device,” Appl. Phys. Lett. 45, 13–15 (1984).
[CrossRef]

Chemla, D. S.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel hybrid optical bistable switch: the quantum well self-electro-optic effect device,” Appl. Phys. Lett. 45, 13–15 (1984).
[CrossRef]

Connely, S. W.

Cottrell, D. M.

Crivello, M. R.

Damen, T. C.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel hybrid optical bistable switch: the quantum well self-electro-optic effect device,” Appl. Phys. Lett. 45, 13–15 (1984).
[CrossRef]

Dammann, H.

H. Dammann, K. Gortler, “High efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Davis, J. A.

Eiju, T.

H. Ichikawa, T. H. Barnes, M. R. Taghizadeh, J. Turunen, T. Eiju, K. Matsuda, “Dynamic space-variant optical interconnections using liquid crystal spatial light modulators,” Opt. Commun. 93, 145–150 (1992).
[CrossRef]

T. H. Barnes, T. Eiju, K. Matsuda, H. Ichikawa, M. R. Taghizadeh, J. Turunen, “Reconfigurable free-space optical interconnections with a phase-only liquid crystal spatial light modulator,” Appl. Opt. 31, 5527–5535 (1992).
[CrossRef] [PubMed]

Gianino, P. D.

Gortler, K.

H. Dammann, K. Gortler, “High efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Gossard, A. C.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel hybrid optical bistable switch: the quantum well self-electro-optic effect device,” Appl. Phys. Lett. 45, 13–15 (1984).
[CrossRef]

Horner, J. L.

Ichikawa, H.

H. Ichikawa, T. H. Barnes, M. R. Taghizadeh, J. Turunen, T. Eiju, K. Matsuda, “Dynamic space-variant optical interconnections using liquid crystal spatial light modulators,” Opt. Commun. 93, 145–150 (1992).
[CrossRef]

T. H. Barnes, T. Eiju, K. Matsuda, H. Ichikawa, M. R. Taghizadeh, J. Turunen, “Reconfigurable free-space optical interconnections with a phase-only liquid crystal spatial light modulator,” Appl. Opt. 31, 5527–5535 (1992).
[CrossRef] [PubMed]

Jaroszewicz, Z.

Kolodziejczyk, A.

Lilly, R.. A.

Maley, C. A.

Matsuda, K.

T. H. Barnes, T. Eiju, K. Matsuda, H. Ichikawa, M. R. Taghizadeh, J. Turunen, “Reconfigurable free-space optical interconnections with a phase-only liquid crystal spatial light modulator,” Appl. Opt. 31, 5527–5535 (1992).
[CrossRef] [PubMed]

H. Ichikawa, T. H. Barnes, M. R. Taghizadeh, J. Turunen, T. Eiju, K. Matsuda, “Dynamic space-variant optical interconnections using liquid crystal spatial light modulators,” Opt. Commun. 93, 145–150 (1992).
[CrossRef]

Merrill, E. A.

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Miller, D. A. B.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel hybrid optical bistable switch: the quantum well self-electro-optic effect device,” Appl. Phys. Lett. 45, 13–15 (1984).
[CrossRef]

Psaltis, D.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).

Ross, W. E.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).

Sypek, M.

Taghizadeh, M. R.

H. Ichikawa, T. H. Barnes, M. R. Taghizadeh, J. Turunen, T. Eiju, K. Matsuda, “Dynamic space-variant optical interconnections using liquid crystal spatial light modulators,” Opt. Commun. 93, 145–150 (1992).
[CrossRef]

T. H. Barnes, T. Eiju, K. Matsuda, H. Ichikawa, M. R. Taghizadeh, J. Turunen, “Reconfigurable free-space optical interconnections with a phase-only liquid crystal spatial light modulator,” Appl. Opt. 31, 5527–5535 (1992).
[CrossRef] [PubMed]

Turunen, J.

T. H. Barnes, T. Eiju, K. Matsuda, H. Ichikawa, M. R. Taghizadeh, J. Turunen, “Reconfigurable free-space optical interconnections with a phase-only liquid crystal spatial light modulator,” Appl. Opt. 31, 5527–5535 (1992).
[CrossRef] [PubMed]

H. Ichikawa, T. H. Barnes, M. R. Taghizadeh, J. Turunen, T. Eiju, K. Matsuda, “Dynamic space-variant optical interconnections using liquid crystal spatial light modulators,” Opt. Commun. 93, 145–150 (1992).
[CrossRef]

Vinas, B.

Walker, A. C.

A. C. Walker, “Reflection bistable etalons with absorbed transmission,” Opt. Commun. 59, 145–150 (1986).
[CrossRef]

Wiegmann, W.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel hybrid optical bistable switch: the quantum well self-electro-optic effect device,” Appl. Phys. Lett. 45, 13–15 (1984).
[CrossRef]

Wood, T. H.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel hybrid optical bistable switch: the quantum well self-electro-optic effect device,” Appl. Phys. Lett. 45, 13–15 (1984).
[CrossRef]

Yamaguchi, M.

Yamazaki, H.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel hybrid optical bistable switch: the quantum well self-electro-optic effect device,” Appl. Phys. Lett. 45, 13–15 (1984).
[CrossRef]

Opt. Commun. (3)

A. C. Walker, “Reflection bistable etalons with absorbed transmission,” Opt. Commun. 59, 145–150 (1986).
[CrossRef]

H. Ichikawa, T. H. Barnes, M. R. Taghizadeh, J. Turunen, T. Eiju, K. Matsuda, “Dynamic space-variant optical interconnections using liquid crystal spatial light modulators,” Opt. Commun. 93, 145–150 (1992).
[CrossRef]

H. Dammann, K. Gortler, “High efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Opt. Eng. (2)

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).

Opt. Lett. (3)

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Figures (15)

Fig. 1
Fig. 1

a, Centered light beam is focused onto the center axis of the lens; b, the focused spot is laterally shifted when the center of the incident beam is shifted relative to the center axis of the lens.

Fig. 2
Fig. 2

Optical interconnect logic technique in which a, different input beams are sent to different output locations, and b, output locations coincide.

Fig. 3
Fig. 3

Interference-based truth table for a, and logic function and b, xor logic function.

Fig. 4
Fig. 4

Two-channel logic technique in which two input beams simultaneously form two output logic functions. More energy is sent to the xor output relative to the and output.

Fig. 5
Fig. 5

Patterns that are written to the magneto-optic spatial light modulator (MOSLM), using rectangular windows that show a, the pattern controlling beam 1 on the left side while blocking beam 2 on the right side; b, the pattern controlling beam 2 that uses a 0-rad phase shift (beam 1 is blocked); c, the pattern controlling beam 2 that uses a π-rad phase shift (beam 1 is blocked).

Fig. 6
Fig. 6

Output intensity from computer simulations, using input lens functions from Fig. 5: a, beam 1 is turned on, using the pattern of Fig. 5a (output is the same if beam 2 is turned on); b, both beams are turned on and beam 2 has a 0-rad phase shift as in Fig. 5b (output forms and logic function); c, both beams are turned on and beam 2 has a π-rad phase shift to form xor logic function as in Fig. 5c (note that the output intensity is larger than in Fig. 6a and xor logic function does not work). Area represented by the figure is 5f λ/D on a side.

Fig. 7
Fig. 7

Patterns that are written to the MOSLM, using diagonal windows that show a, the pattern controlling beam 1 on left side while blocking beam 2 on right side; b, the pattern controlling beam 2 that uses a 0-rad phase shift (beam 1 is blocked); c, the pattern controlling beam 2 that uses a π-rad phase shift (beam 1 is blocked).

Fig. 8
Fig. 8

Output intensity from computer simulations, using input lens functions from Fig. 7: a, beam 1 is turned on, using the pattern of Fig. 7a (output is the same if beam 2 is turned on); b, both beams are turned on and beam 2 has a 0-rad phase shift as in Fig. 7b (output forms and logic function); c, both beams are turned on and beam 2 has a π-rad phase shift to form xor logic function as in Fig. 7c (note that the output intensity is smaller than in Fig. 8a and the xor logic function now works). Area represented by the figure is 5fλ/D on a side.

Fig. 9
Fig. 9

Representative Fresnel lens patterns that show phase shifts of a, 0 rad; b, π rad; c, π/3 rad.

Fig. 10
Fig. 10

Patterns that are written to the MOSLM, using random multiplexing and rectangular window channels that simultaneously produce a scaled and logic function in one output location and an xor logic function at another location: a, the pattern controlling beam 1 on left side while blocking beam 2 on the right side; b, the pattern controlling beam 2 on right side while blocking beam 1 on the left side.

Fig. 11
Fig. 11

Experimental outputs measured with a diode detector array mounted in the focal plane, using inputs of Fig. 10: a, input beam 1 is turned on; b, input beam 2 is turned on; c, both input beams are turned on (note the xor logic function does not work). The xor output is formed on the left and the and output is formed on the right.

Fig. 12
Fig. 12

Patterns that are written to the MOSLM, using random multiplexing and diagonal window channels that simultaneously produce a scaled and logic function in one output location and an xor logic function at another location: a, the pattern controlling beam 1 on the left side while blocking beam 2 on the right side; b, the pattern controlling beam 2 on the right side while blocking beam 1 on the left side.

Fig. 13
Fig. 13

Experimental outputs measured with a diode detector array mounted in the focal plane, using inputs of Fig. 12: a, input beam 1 is turned on; b, input beam 2 is turned on; c, both input beams are turned on (note the xor logic function works). The xor logic function is formed on the left and the and logic function is formed on the right.

Fig. 14
Fig. 14

Patterns that are written to the MOSLM, using a random multiplexing pattern for each input and random multiplexing for scaling that simultaneously produce a scaled and logic function in one output location and an xor logic function at another location: a, the pattern controlling beam 1 while blocking beam 2; b, the pattern controlling beam 2 while blocking beam 1.

Fig. 15
Fig. 15

Experimental outputs measured with a diode detector array mounted in the focal plane, using inputs of Fig. 14: a, input beam 1 is turned on; b, input beam 2 is turned on; c, both input beams are turned on (note the xor logic function works perfectly). The xor logic function is formed on the left and the and logic function is formed on the right.

Equations (20)

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L A ( x ) = exp [ - i π ( x - A ) 2 λ f ] .
L 1 = W 1 L A ,
L 2 = W 2 L B ,
L 1 = W 1 L A exp ( - i ϕ ) ,
L 2 = W 2 L A .
E A = E 1 exp ( - i ϕ ) + E 2 .
I A = 2 ( 1 + cos ϕ ) .
L 1 = W 1 [ α L A exp ( - i ϕ ) + β L B exp ( - i δ ) ] ,
L 2 = W 2 ( α L A + β L B ) .
E A = α E 1 exp ( - i ϕ ) + α E 2 ,
E B = β E 1 exp ( - i δ ) + β E 2 .
I A = 2 α 2 ( 1 + cos ϕ ) ,
I B = 2 β 2 ( 1 + cos δ ) .
L ˜ ( x ) = L ( x ) L ( x ) .
L ˜ 1 = W 1 [ α L A exp ( - i ϕ ) + β L B exp ( - i δ ) ] α L A exp ( - i ϕ ) + β L B exp ( - i δ ) ,
= W 1 [ α L A exp ( - i ϕ ) ] α L A exp ( - i ϕ ) + β L B exp ( - i δ ) + W 1 [ β L B exp ( - i δ ) ] α L A exp ( - i ϕ + β L B exp ( - i δ ) ) .
L ˜ 1 = W 1 R [ L A exp ( - i ϕ ) ] L A + W 1 R ¯ [ L B exp ( - i δ ) ] L B ,
L ˜ 2 = W 2 R ( L A ) L A + W 2 R ¯ ( L B ) ] L B ,
L ˜ 1 = R 1 R [ L A exp ( - i ϕ ) ] L A + R 1 R ¯ [ L B exp ( - i δ ) ] L B ,
L ˜ 2 = R ¯ 2 R [ L A ] L A + R ¯ 1 R ¯ ( L B ) L B .

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