Abstract

Interferometric systems with amplitude beam splitters can implement reversible operations that, on detection, become Boolean operators. Being passive, they consume no energy, do not limit the operating bandwidth, and have negligible latency. Unfortunately, conventional interferometric systems are notoriously sensitive to uncontrolled disturbances. Here the use of polarization in a common-path interferometric logic gate with and without polarization beam splitters is explored as an attractive alternative to overcome those difficulties. Two of three device configurations considered offer significant stability and lower drive modulator voltage as advantages over the previous systems. The first experimental tests of such a system are reported. Common-path interferometry lends itself to even more stability and robustness by compatibility with no-air-gap, solid optics.

© 2006 Optical Society of America

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References

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  1. H. J. Caulfield and J. Westphal, "The logic of optics and the optics of logic," Inf. Sci. 162, 21-34 (2004).
    [CrossRef]
  2. L. Qian and H. J. Caulfield, "What can we do with a linear optical logic gate?" submitted to Inf. Sci. (N.Y.).
  3. J. Shamir, H. J. Caulfield, W. Miceli, and R. J. Seymour, "Optical computing and the Fredkin gates," Appl. Opt. 25, 1604-1607 (1986).
    [CrossRef] [PubMed]
  4. T. H. Barnes, J. A. Davis, and T. G. Haskell, "Optical logic gates using grating interferometers," Opt. Rev. 1, 170-173 (1994).
  5. C.-Y. Liu and L.-W. Chen, "Tunable photonic crystal waveguide Mach-Zehnder interferometer achieved by liquid crystal phase modulation," Opt. Express 12, 2616-2624 (2004).
    [CrossRef] [PubMed]
  6. C.-J. Cheng and M.-L. Chen, "Polarization encoding for optical encryption using twisted nematic liquid crystal spatial light modulators," Opt. Commun. 237, 45-52 (2004).
    [CrossRef]
  7. H.-Y. Tu, C.-J. Cheng, and M.-L. Chen, "Optical image encryption on polarization encoding by liquid crystal spatial light modulators," J. Opt. A Pure. Appl. Opt. 6, 524-528 (2004).
    [CrossRef]
  8. G. Unnikrishnan, M. Pohit, and K. Singh, "A polarization encoded optical encryption system using ferroelectric spatial light modulator," Opt. Commun. 185, 25-31 (2000).
    [CrossRef]
  9. R. Landauer, "Computation: a fundamental physical view," Phys. Scr. 35, 88-95 (1987).
    [CrossRef]
  10. C. H. Bennett, "The thermodynamics of computing, a review," Int. J. Theor. Phys. 21, 902-940 (1982).
    [CrossRef]
  11. J. B. Brown and H. J. Caulfield, "Design of a solid optical interconnect for massive neural networks," Neural Netw. 1, Suppl. 1, 375 (1988).
    [CrossRef]
  12. J. Fu, M. P. Schamschula, and H. J. Caulfield, "Modular solid optic time delay system," Opt. Commun. 121, 8-12 (1995).
    [CrossRef]
  13. M. P. Schamschula, P. Reardon, and H. J. Caulfield, "Regular geometries for folded optical modules," Trends Opt. Eng. 1, 259-274 (1993).
  14. M. P. Schamschula and H. J. Caulfield, "Space filling modular optics: expanded Peano and collapsed Hilbert curves," Opt. Commun. 111, 219-224 (1994).
    [CrossRef]
  15. M. P. Schamschula, H. J. Caulfield, and A. Brown, "Space filling modular optics," Opt. Lett. 19, 689-691 (1994).
    [CrossRef] [PubMed]

2004 (4)

C.-Y. Liu and L.-W. Chen, "Tunable photonic crystal waveguide Mach-Zehnder interferometer achieved by liquid crystal phase modulation," Opt. Express 12, 2616-2624 (2004).
[CrossRef] [PubMed]

C.-J. Cheng and M.-L. Chen, "Polarization encoding for optical encryption using twisted nematic liquid crystal spatial light modulators," Opt. Commun. 237, 45-52 (2004).
[CrossRef]

H.-Y. Tu, C.-J. Cheng, and M.-L. Chen, "Optical image encryption on polarization encoding by liquid crystal spatial light modulators," J. Opt. A Pure. Appl. Opt. 6, 524-528 (2004).
[CrossRef]

H. J. Caulfield and J. Westphal, "The logic of optics and the optics of logic," Inf. Sci. 162, 21-34 (2004).
[CrossRef]

2000 (1)

G. Unnikrishnan, M. Pohit, and K. Singh, "A polarization encoded optical encryption system using ferroelectric spatial light modulator," Opt. Commun. 185, 25-31 (2000).
[CrossRef]

1995 (1)

J. Fu, M. P. Schamschula, and H. J. Caulfield, "Modular solid optic time delay system," Opt. Commun. 121, 8-12 (1995).
[CrossRef]

1994 (3)

M. P. Schamschula and H. J. Caulfield, "Space filling modular optics: expanded Peano and collapsed Hilbert curves," Opt. Commun. 111, 219-224 (1994).
[CrossRef]

M. P. Schamschula, H. J. Caulfield, and A. Brown, "Space filling modular optics," Opt. Lett. 19, 689-691 (1994).
[CrossRef] [PubMed]

T. H. Barnes, J. A. Davis, and T. G. Haskell, "Optical logic gates using grating interferometers," Opt. Rev. 1, 170-173 (1994).

1993 (1)

M. P. Schamschula, P. Reardon, and H. J. Caulfield, "Regular geometries for folded optical modules," Trends Opt. Eng. 1, 259-274 (1993).

1988 (1)

J. B. Brown and H. J. Caulfield, "Design of a solid optical interconnect for massive neural networks," Neural Netw. 1, Suppl. 1, 375 (1988).
[CrossRef]

1987 (1)

R. Landauer, "Computation: a fundamental physical view," Phys. Scr. 35, 88-95 (1987).
[CrossRef]

1986 (1)

1982 (1)

C. H. Bennett, "The thermodynamics of computing, a review," Int. J. Theor. Phys. 21, 902-940 (1982).
[CrossRef]

Barnes, T. H.

T. H. Barnes, J. A. Davis, and T. G. Haskell, "Optical logic gates using grating interferometers," Opt. Rev. 1, 170-173 (1994).

Bennett, C. H.

C. H. Bennett, "The thermodynamics of computing, a review," Int. J. Theor. Phys. 21, 902-940 (1982).
[CrossRef]

Brown, A.

Brown, J. B.

J. B. Brown and H. J. Caulfield, "Design of a solid optical interconnect for massive neural networks," Neural Netw. 1, Suppl. 1, 375 (1988).
[CrossRef]

Caulfield, H. J.

H. J. Caulfield and J. Westphal, "The logic of optics and the optics of logic," Inf. Sci. 162, 21-34 (2004).
[CrossRef]

J. Fu, M. P. Schamschula, and H. J. Caulfield, "Modular solid optic time delay system," Opt. Commun. 121, 8-12 (1995).
[CrossRef]

M. P. Schamschula and H. J. Caulfield, "Space filling modular optics: expanded Peano and collapsed Hilbert curves," Opt. Commun. 111, 219-224 (1994).
[CrossRef]

M. P. Schamschula, H. J. Caulfield, and A. Brown, "Space filling modular optics," Opt. Lett. 19, 689-691 (1994).
[CrossRef] [PubMed]

M. P. Schamschula, P. Reardon, and H. J. Caulfield, "Regular geometries for folded optical modules," Trends Opt. Eng. 1, 259-274 (1993).

J. B. Brown and H. J. Caulfield, "Design of a solid optical interconnect for massive neural networks," Neural Netw. 1, Suppl. 1, 375 (1988).
[CrossRef]

J. Shamir, H. J. Caulfield, W. Miceli, and R. J. Seymour, "Optical computing and the Fredkin gates," Appl. Opt. 25, 1604-1607 (1986).
[CrossRef] [PubMed]

L. Qian and H. J. Caulfield, "What can we do with a linear optical logic gate?" submitted to Inf. Sci. (N.Y.).

Chen, L.-W.

Chen, M.-L.

H.-Y. Tu, C.-J. Cheng, and M.-L. Chen, "Optical image encryption on polarization encoding by liquid crystal spatial light modulators," J. Opt. A Pure. Appl. Opt. 6, 524-528 (2004).
[CrossRef]

C.-J. Cheng and M.-L. Chen, "Polarization encoding for optical encryption using twisted nematic liquid crystal spatial light modulators," Opt. Commun. 237, 45-52 (2004).
[CrossRef]

Cheng, C.-J.

C.-J. Cheng and M.-L. Chen, "Polarization encoding for optical encryption using twisted nematic liquid crystal spatial light modulators," Opt. Commun. 237, 45-52 (2004).
[CrossRef]

H.-Y. Tu, C.-J. Cheng, and M.-L. Chen, "Optical image encryption on polarization encoding by liquid crystal spatial light modulators," J. Opt. A Pure. Appl. Opt. 6, 524-528 (2004).
[CrossRef]

Davis, J. A.

T. H. Barnes, J. A. Davis, and T. G. Haskell, "Optical logic gates using grating interferometers," Opt. Rev. 1, 170-173 (1994).

Fu, J.

J. Fu, M. P. Schamschula, and H. J. Caulfield, "Modular solid optic time delay system," Opt. Commun. 121, 8-12 (1995).
[CrossRef]

Haskell, T. G.

T. H. Barnes, J. A. Davis, and T. G. Haskell, "Optical logic gates using grating interferometers," Opt. Rev. 1, 170-173 (1994).

Landauer, R.

R. Landauer, "Computation: a fundamental physical view," Phys. Scr. 35, 88-95 (1987).
[CrossRef]

Liu, C.-Y.

Miceli, W.

Pohit, M.

G. Unnikrishnan, M. Pohit, and K. Singh, "A polarization encoded optical encryption system using ferroelectric spatial light modulator," Opt. Commun. 185, 25-31 (2000).
[CrossRef]

Qian, L.

L. Qian and H. J. Caulfield, "What can we do with a linear optical logic gate?" submitted to Inf. Sci. (N.Y.).

Reardon, P.

M. P. Schamschula, P. Reardon, and H. J. Caulfield, "Regular geometries for folded optical modules," Trends Opt. Eng. 1, 259-274 (1993).

Schamschula, M. P.

J. Fu, M. P. Schamschula, and H. J. Caulfield, "Modular solid optic time delay system," Opt. Commun. 121, 8-12 (1995).
[CrossRef]

M. P. Schamschula and H. J. Caulfield, "Space filling modular optics: expanded Peano and collapsed Hilbert curves," Opt. Commun. 111, 219-224 (1994).
[CrossRef]

M. P. Schamschula, H. J. Caulfield, and A. Brown, "Space filling modular optics," Opt. Lett. 19, 689-691 (1994).
[CrossRef] [PubMed]

M. P. Schamschula, P. Reardon, and H. J. Caulfield, "Regular geometries for folded optical modules," Trends Opt. Eng. 1, 259-274 (1993).

Seymour, R. J.

Shamir, J.

Singh, K.

G. Unnikrishnan, M. Pohit, and K. Singh, "A polarization encoded optical encryption system using ferroelectric spatial light modulator," Opt. Commun. 185, 25-31 (2000).
[CrossRef]

Tu, H.-Y.

H.-Y. Tu, C.-J. Cheng, and M.-L. Chen, "Optical image encryption on polarization encoding by liquid crystal spatial light modulators," J. Opt. A Pure. Appl. Opt. 6, 524-528 (2004).
[CrossRef]

Unnikrishnan, G.

G. Unnikrishnan, M. Pohit, and K. Singh, "A polarization encoded optical encryption system using ferroelectric spatial light modulator," Opt. Commun. 185, 25-31 (2000).
[CrossRef]

Westphal, J.

H. J. Caulfield and J. Westphal, "The logic of optics and the optics of logic," Inf. Sci. 162, 21-34 (2004).
[CrossRef]

Appl. Opt. (1)

Inf. Sci. (1)

H. J. Caulfield and J. Westphal, "The logic of optics and the optics of logic," Inf. Sci. 162, 21-34 (2004).
[CrossRef]

Int. J. Theor. Phys. (1)

C. H. Bennett, "The thermodynamics of computing, a review," Int. J. Theor. Phys. 21, 902-940 (1982).
[CrossRef]

J. Opt. A Pure. Appl. Opt. (1)

H.-Y. Tu, C.-J. Cheng, and M.-L. Chen, "Optical image encryption on polarization encoding by liquid crystal spatial light modulators," J. Opt. A Pure. Appl. Opt. 6, 524-528 (2004).
[CrossRef]

Neural Netw. (1)

J. B. Brown and H. J. Caulfield, "Design of a solid optical interconnect for massive neural networks," Neural Netw. 1, Suppl. 1, 375 (1988).
[CrossRef]

Opt. Commun. (4)

J. Fu, M. P. Schamschula, and H. J. Caulfield, "Modular solid optic time delay system," Opt. Commun. 121, 8-12 (1995).
[CrossRef]

G. Unnikrishnan, M. Pohit, and K. Singh, "A polarization encoded optical encryption system using ferroelectric spatial light modulator," Opt. Commun. 185, 25-31 (2000).
[CrossRef]

C.-J. Cheng and M.-L. Chen, "Polarization encoding for optical encryption using twisted nematic liquid crystal spatial light modulators," Opt. Commun. 237, 45-52 (2004).
[CrossRef]

M. P. Schamschula and H. J. Caulfield, "Space filling modular optics: expanded Peano and collapsed Hilbert curves," Opt. Commun. 111, 219-224 (1994).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Opt. Rev. (1)

T. H. Barnes, J. A. Davis, and T. G. Haskell, "Optical logic gates using grating interferometers," Opt. Rev. 1, 170-173 (1994).

Phys. Scr. (1)

R. Landauer, "Computation: a fundamental physical view," Phys. Scr. 35, 88-95 (1987).
[CrossRef]

Trends Opt. Eng. (1)

M. P. Schamschula, P. Reardon, and H. J. Caulfield, "Regular geometries for folded optical modules," Trends Opt. Eng. 1, 259-274 (1993).

Other (1)

L. Qian and H. J. Caulfield, "What can we do with a linear optical logic gate?" submitted to Inf. Sci. (N.Y.).

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Figures (9)

Fig. 1
Fig. 1

A simple amplitude beam splitter addressed by mutually coherent beams A and B leads to outputs C and D that can be of use in optical logic. This is a conventional amplitude beam splitter.

Fig. 2
Fig. 2

Conventional Mach–Zehnder interferometer. The logic device of Fig. 1 is its second stage. There is, however, a significant stability problem stemming from the fact that the two split paths may undergo quite different disturbances from the environment. Modulators of either beam must work in transmission.

Fig. 3
Fig. 3

In the Twyman–Green interferometer, one beam splitter plays two roles, as it operates on light traveling in two different directions at all points. It is attractive because it uses reflective modulators and hence reduced voltages. The instability problem from two separate beams, however, remains.

Fig. 4
Fig. 4

The solid optical Twyman–Green interferometer shown here might prevent and equalize disturbances, making it substantially more stable than the open system of Fig. 3. It would use reflective modulators.

Fig. 5
Fig. 5

This common-path interferometer causes the beams to remain together but to remain distinguished by their polarizations, so disturbances affect both beams identically. We choose xor or coinc by alignment of the analyzer.

Fig. 6
Fig. 6

Schematic of the orientation of the crystals and laser-light polarization in the logic device based on the transverse Pockels effect in LiNbO 3 .

Fig. 7
Fig. 7

Optical schematic of the experimental demonstration of the logic device based on the transverse Pockels effect in LiNbO 3 . The optical components are shown separately but can easily be joined into a solid optics (no-air-gap) system for stability. E-O, electro-optical.

Fig. 8
Fig. 8

Oscilloscope traces showing xor and coinc operations. The traces from the top to the bottom are the following: trace 1, result of xor operation; trace 2, result of coinc operation; trace 3, first input; trace 4, second input.

Fig. 9
Fig. 9

Integrated optical xor–coinc gate: PM fiber, polarization-maintaining fiber; Non-PM fiber, isotropic fiber; PS, polarization splitter; V, H, vertical and horizontal polarization, respectively.

Tables (1)

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Table 1 Amplitude Transformations a

Equations (2)

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( C D ) = 1 / 2 [ 1 i i 1 ] ( A B ) .
E ( E x E y ) = ( A B ) .

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