Abstract

The coupling effect between phase and intensity in photorefractive two-wave mixing in a Bi12SiO20 crystal is demonstrated. By using interference fringe-shifting techniques that are executed by a Mach–Zehnder interferometer, an optical parallel logic operation system that is based on the coupling effect is implemented.

© 1992 Optical Society of America

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References

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  1. M. T. Fatehi, K. C. Wasmundt, S. A. Collins, “Optical logic gates using liquid crystal light valve: implementation and application example,” Appl. Opt. 20, 2250–2256 (1981).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. Y. Imai, Y. Ohtsuka, “Optical multiple-output and multiple-valued logic operation based on fringe shifting techniques using a spatial light modulator,” Appl. Opt. 26, 274–277 (1987).
    [CrossRef] [PubMed]
  4. S.-K. Kwong, G. A. Rakuljic, A. Yariv, “Real-time image subtraction and exclusive or operation using a self-pumped phase-conjugate mirror,” Appl. Phys. Lett. 48, 201–202 (1986).
    [CrossRef]
  5. A. E. Chiou, P. Yeh, “Parallel image subtraction using a phase-conjugate Michelson interferometer,” Opt. Lett. 11, 306–308 (1986).
    [CrossRef] [PubMed]
  6. Y. Fainman, C. C. Guest, S. H. Lee, “Optical digital logic operations by two-beam coupling in photorefractive material,” Appl. Opt. 25, 1598–1603 (1986).
    [CrossRef] [PubMed]
  7. N. A. Vainos, J. A. Khoury, R. W. Eason, “Real-time parallel optical logic in photorefractive bismuth silicon oxide,” Opt. Lett. 13, 503–505 (1988).
    [CrossRef] [PubMed]
  8. K. Xu, H. Xu, J. Hong, “Observation of optical wave phase and wave-front-correction in photorefractive two-wave mixing,” Opt. Commun. 69, 429–432 (1989).
    [CrossRef]
  9. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I: Steady state,” Ferroelectrics 22, 949–960 (1979).
    [CrossRef]
  10. Y. H. Ja, “Beam coupling and decoupling in degenerate two-wave mixing in a reflection geometry with photorefractive Bi12GeO20 crystals,” Opt. Quantum Electron. 16, 399–404 (1984).
    [CrossRef]
  11. P. N. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
    [CrossRef]

1989 (1)

K. Xu, H. Xu, J. Hong, “Observation of optical wave phase and wave-front-correction in photorefractive two-wave mixing,” Opt. Commun. 69, 429–432 (1989).
[CrossRef]

1988 (1)

1987 (2)

1986 (3)

1984 (1)

Y. H. Ja, “Beam coupling and decoupling in degenerate two-wave mixing in a reflection geometry with photorefractive Bi12GeO20 crystals,” Opt. Quantum Electron. 16, 399–404 (1984).
[CrossRef]

1982 (1)

P. N. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[CrossRef]

1981 (1)

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I: Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Chiou, A. E.

Collins, S. A.

Eason, R. W.

Fainman, Y.

Fatehi, M. T.

Guest, C. C.

Günter, P. N.

P. N. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[CrossRef]

Hong, J.

K. Xu, H. Xu, J. Hong, “Observation of optical wave phase and wave-front-correction in photorefractive two-wave mixing,” Opt. Commun. 69, 429–432 (1989).
[CrossRef]

Imai, Y.

Ja, Y. H.

Y. H. Ja, “Beam coupling and decoupling in degenerate two-wave mixing in a reflection geometry with photorefractive Bi12GeO20 crystals,” Opt. Quantum Electron. 16, 399–404 (1984).
[CrossRef]

Khoury, J. A.

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I: Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Kwong, S.-K.

S.-K. Kwong, G. A. Rakuljic, A. Yariv, “Real-time image subtraction and exclusive or operation using a self-pumped phase-conjugate mirror,” Appl. Phys. Lett. 48, 201–202 (1986).
[CrossRef]

Lee, S. H.

Lu, X. J.

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I: Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I: Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Ohtsuka, Y.

Rakuljic, G. A.

S.-K. Kwong, G. A. Rakuljic, A. Yariv, “Real-time image subtraction and exclusive or operation using a self-pumped phase-conjugate mirror,” Appl. Phys. Lett. 48, 201–202 (1986).
[CrossRef]

Song, Q. W.

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I: Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Vainos, N. A.

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I: Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Wasmundt, K. C.

Xu, H.

K. Xu, H. Xu, J. Hong, “Observation of optical wave phase and wave-front-correction in photorefractive two-wave mixing,” Opt. Commun. 69, 429–432 (1989).
[CrossRef]

Xu, K.

K. Xu, H. Xu, J. Hong, “Observation of optical wave phase and wave-front-correction in photorefractive two-wave mixing,” Opt. Commun. 69, 429–432 (1989).
[CrossRef]

Yariv, A.

S.-K. Kwong, G. A. Rakuljic, A. Yariv, “Real-time image subtraction and exclusive or operation using a self-pumped phase-conjugate mirror,” Appl. Phys. Lett. 48, 201–202 (1986).
[CrossRef]

Yeh, P.

Yu, F. T. S.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

S.-K. Kwong, G. A. Rakuljic, A. Yariv, “Real-time image subtraction and exclusive or operation using a self-pumped phase-conjugate mirror,” Appl. Phys. Lett. 48, 201–202 (1986).
[CrossRef]

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I: Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Opt. Commun. (1)

K. Xu, H. Xu, J. Hong, “Observation of optical wave phase and wave-front-correction in photorefractive two-wave mixing,” Opt. Commun. 69, 429–432 (1989).
[CrossRef]

Opt. Lett. (3)

Opt. Quantum Electron. (1)

Y. H. Ja, “Beam coupling and decoupling in degenerate two-wave mixing in a reflection geometry with photorefractive Bi12GeO20 crystals,” Opt. Quantum Electron. 16, 399–404 (1984).
[CrossRef]

Phys. Rep. (1)

P. N. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[CrossRef]

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Figures (16)

Fig. 1
Fig. 1

Conventional photorefractive two-wave mixing configuration.

Fig. 2
Fig. 2

Theoretical curves of phase variation Δϕ versus intensity beam ratio β under various applied fields E0.

Fig. 3
Fig. 3

Theoretical curve of phase variation Δϕ versus applied field E0 (β = 30, 2θ = 7.0°).

Fig. 4
Fig. 4

Experimental setup for implementing a logic operation by using photorefractive mixing and interference fringe-shift techniques: M1–M6, mirrors; BS1–BS5, beam splitters.

Fig. 5
Fig. 5

(a) Input patterns, (b) output interference fringe corresponding to input state (0, 0).

Fig. 6
Fig. 6

Realization of logic gates xor and XOR ¯: D, dark fringe; B, bright fringe.

Fig. 7
Fig. 7

Realization of logic gates A B ¯, ĀB, Ā + B and A + B ¯.

Fig. 8
Fig. 8

Implementation of logic operations or, nor, and, and nand.

Fig. 9
Fig. 9

Implementation of logic operations A, Ā, xor, and XOR ¯.

Fig. 10
Fig. 10

Logic gates B, B ¯, xor, and XOR ¯.

Fig. 11
Fig. 11

Logic gates F, T, or, and nor.

Fig. 12
Fig. 12

Experimental results of beam intensity ratio β dependence on phase variation Δϕ under various applied fields E0 in Bi12SiO20.

Fig. 13
Fig. 13

Experimental curve of phase variation Δϕ versus applied field E0 (β = 28.0, 2θ = 7.0°).

Fig. 14
Fig. 14

(a) Output interference fringe from an interferometer without input pattern (0, 0) and (b) the binarized result.

Fig. 15
Fig. 15

Input patterns IA and IB in the experiment.

Fig. 16
Fig. 16

Experimental results of realizing logic gates or, nor, and, and nand simultaneously.

Tables (1)

Tables Icon

Table 1 16 Possible Functions of Two Binary Variables

Equations (7)

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Δ ϕ = ϕ - 1 - ϕ - 10 = γ Γ ln [ ( 1 + β - 1 ) exp ( Γ x ) 1 + β - 1 exp ( Γ x ) ] ,
Γ = 2 δ E D 1 + ( E D / E Q ) + ( E 0 2 / E D E Q ) ( 1 + E D / E Q ) 2 + ( E 0 / E Q ) 2 ,
Φ g = arctan ( E D / E O ) ,
E D = 2 π k B T / Λ e ,
E Q = e N A Λ / 2 π 0 ,
δ = - π n 0 r 41 λ cos θ .
I 0 = I - 1 + I - 10 + 2 ( I - 1 I - 10 ) 1 / 2 cos ( Δ ϕ ) .

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