Abstract

A phase-conjugate Michelson interferometer using an internally self-pumped barium titanate crystal as reflectors has been constructed to perform parallel image subtraction, intensity inversion, and exclusive or logic operation. These operations are independent of the optical path differences and phase aberration.

© 1986 Optical Society of America

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  1. M. D. Ewbank, P. Yeh, M. Khoshnevisan, J. Feinberg, Opt. Lett. 10, 282 (1985).
    [CrossRef] [PubMed]
  2. D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
    [CrossRef]
  3. See, for example, J. F. Ebersole, Opt. Eng. 14, 436 (1975).
  4. See, for example, G. Idebetouw, L. Bernardo, M. Miller, Appl. Opt. 19, 1218 (1980).
    [CrossRef]
  5. Y. H. Ja, Opt. Commun. 42, 377 (1982).
    [CrossRef]
  6. C. P. Grover, R. Tremblay, Appl. Opt. 21, 2666 (1982).
    [CrossRef] [PubMed]
  7. C. Warde, J. I. Thackara, Opt. Lett. 7, 344 (1982).
    [CrossRef] [PubMed]
  8. G. G. Mu, C. K. Chiang, H. K. Liu, Opt. Lett. 6, 389 (1981).
    [CrossRef] [PubMed]
  9. K. Matsuda, N. Takeya, T. Tsujiuchi, M. Shimoda, Opt. Commun. 2, 425 (1971).
    [CrossRef]
  10. K. Patroski, S. Yokozeki, T. Suzuki, Nouv. Rev. Opt. 6, 25 (1975).
    [CrossRef]
  11. W. T. Cathey, J. G. Doidge, J. Opt. Soc. Am. 56, 1139 (1966).
    [CrossRef]
  12. J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
    [CrossRef]
  13. M. Gronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
    [CrossRef]
  14. J. Feinberg, Opt. Lett. 7, 486 (1982).
    [CrossRef] [PubMed]
  15. K. R. McDonald, J. Feinberg, J. Opt. Soc. Am. 73, 458 (1983).
  16. These two beams enter the BaTiO3 phase conjugator at the same spot with approximately the same angle of incidence and are considered parts of a composite beam. Thus the assumption of a unique phase-conjugate reflectivity is legitimate. This has also been proved experimentally.
  17. Z. Knittl, Optics of Thin Films (Wiley, New York, 1976), p. 242.
  18. G. G. Stokes, Camb. Dubl. Math. J. 4, 1 (1849).
  19. S. K. Kwong, G. A. Rakuijuc, A. Yariv, Appl. Phys. Lett. 48, 201 (1985).
    [CrossRef]

1985

S. K. Kwong, G. A. Rakuijuc, A. Yariv, Appl. Phys. Lett. 48, 201 (1985).
[CrossRef]

M. D. Ewbank, P. Yeh, M. Khoshnevisan, J. Feinberg, Opt. Lett. 10, 282 (1985).
[CrossRef] [PubMed]

1983

K. R. McDonald, J. Feinberg, J. Opt. Soc. Am. 73, 458 (1983).

1982

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

M. Gronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

Y. H. Ja, Opt. Commun. 42, 377 (1982).
[CrossRef]

C. P. Grover, R. Tremblay, Appl. Opt. 21, 2666 (1982).
[CrossRef] [PubMed]

C. Warde, J. I. Thackara, Opt. Lett. 7, 344 (1982).
[CrossRef] [PubMed]

J. Feinberg, Opt. Lett. 7, 486 (1982).
[CrossRef] [PubMed]

1981

1980

1975

See, for example, J. F. Ebersole, Opt. Eng. 14, 436 (1975).

K. Patroski, S. Yokozeki, T. Suzuki, Nouv. Rev. Opt. 6, 25 (1975).
[CrossRef]

1971

K. Matsuda, N. Takeya, T. Tsujiuchi, M. Shimoda, Opt. Commun. 2, 425 (1971).
[CrossRef]

1966

1965

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

1849

G. G. Stokes, Camb. Dubl. Math. J. 4, 1 (1849).

Bernardo, L.

Brumm, D.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Cathey, W. T.

Chiang, C. K.

Cronin-Golomb, M.

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

Doidge, J. G.

Ebersole, J. F.

See, for example, J. F. Ebersole, Opt. Eng. 14, 436 (1975).

Ewbank, M. D.

Feinberg, J.

Fischer, B.

M. Gronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

Funkhouser, A.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Gabor, D.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Gronin-Golomb, M.

M. Gronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

Grover, C. P.

Idebetouw, G.

Ja, Y. H.

Y. H. Ja, Opt. Commun. 42, 377 (1982).
[CrossRef]

Khoshnevisan, M.

Knittl, Z.

Z. Knittl, Optics of Thin Films (Wiley, New York, 1976), p. 242.

Kwong, S. K.

S. K. Kwong, G. A. Rakuijuc, A. Yariv, Appl. Phys. Lett. 48, 201 (1985).
[CrossRef]

Liu, H. K.

Matsuda, K.

K. Matsuda, N. Takeya, T. Tsujiuchi, M. Shimoda, Opt. Commun. 2, 425 (1971).
[CrossRef]

McDonald, K. R.

K. R. McDonald, J. Feinberg, J. Opt. Soc. Am. 73, 458 (1983).

Miller, M.

Mu, G. G.

Patroski, K.

K. Patroski, S. Yokozeki, T. Suzuki, Nouv. Rev. Opt. 6, 25 (1975).
[CrossRef]

Rakuijuc, G. A.

S. K. Kwong, G. A. Rakuijuc, A. Yariv, Appl. Phys. Lett. 48, 201 (1985).
[CrossRef]

Restrick, R.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Shimoda, M.

K. Matsuda, N. Takeya, T. Tsujiuchi, M. Shimoda, Opt. Commun. 2, 425 (1971).
[CrossRef]

Stokes, G. G.

G. G. Stokes, Camb. Dubl. Math. J. 4, 1 (1849).

Stroke, G. W.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Suzuki, T.

K. Patroski, S. Yokozeki, T. Suzuki, Nouv. Rev. Opt. 6, 25 (1975).
[CrossRef]

Takeya, N.

K. Matsuda, N. Takeya, T. Tsujiuchi, M. Shimoda, Opt. Commun. 2, 425 (1971).
[CrossRef]

Thackara, J. I.

Tremblay, R.

Tsujiuchi, T.

K. Matsuda, N. Takeya, T. Tsujiuchi, M. Shimoda, Opt. Commun. 2, 425 (1971).
[CrossRef]

Warde, C.

White, J. O.

M. Gronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

Yariv, A.

S. K. Kwong, G. A. Rakuijuc, A. Yariv, Appl. Phys. Lett. 48, 201 (1985).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

M. Gronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

Yeh, P.

Yokozeki, S.

K. Patroski, S. Yokozeki, T. Suzuki, Nouv. Rev. Opt. 6, 25 (1975).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

S. K. Kwong, G. A. Rakuijuc, A. Yariv, Appl. Phys. Lett. 48, 201 (1985).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

M. Gronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

Camb. Dubl. Math. J.

G. G. Stokes, Camb. Dubl. Math. J. 4, 1 (1849).

J. Opt. Soc. Am.

K. R. McDonald, J. Feinberg, J. Opt. Soc. Am. 73, 458 (1983).

W. T. Cathey, J. G. Doidge, J. Opt. Soc. Am. 56, 1139 (1966).
[CrossRef]

Nouv. Rev. Opt.

K. Patroski, S. Yokozeki, T. Suzuki, Nouv. Rev. Opt. 6, 25 (1975).
[CrossRef]

Opt. Commun.

Y. H. Ja, Opt. Commun. 42, 377 (1982).
[CrossRef]

K. Matsuda, N. Takeya, T. Tsujiuchi, M. Shimoda, Opt. Commun. 2, 425 (1971).
[CrossRef]

Opt. Eng.

See, for example, J. F. Ebersole, Opt. Eng. 14, 436 (1975).

Opt. Lett.

Phys. Lett.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Other

These two beams enter the BaTiO3 phase conjugator at the same spot with approximately the same angle of incidence and are considered parts of a composite beam. Thus the assumption of a unique phase-conjugate reflectivity is legitimate. This has also been proved experimentally.

Z. Knittl, Optics of Thin Films (Wiley, New York, 1976), p. 242.

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram illustrating the basic idea of coherent image subtraction and addition by a phase-conjugate Michelson interferometer.

Fig. 2
Fig. 2

Experimental results for the image subtraction and addition by the phase-conjugate Michelson interferometer. The horizontal and the vertical bars are the images of transparencies 1 and 2, respectively, when the illuminating beam for the other arm is blocked. The checkerboard patterns at upper and lower right are the intensity distribution of the coherent subtraction and addition, respectively, of the two images.

Fig. 3
Fig. 3

Experimental results for the intensity inversion: (a) intensity distribution of the phase-conjugate beam in the first arm with the transparency removed, (b) image of the transparency in the second arm, and (c) the intensity inversion of (b). (a) I1 ∝ |T1(x, y)|2 = 1, (b) I2 ∝ |T2(x, y)|2, (c) I ∝ |T1(x, y) − T2(x, y)|2 = |1 − T2(x, y)|2.

Fig. 4
Fig. 4

Temporal fluctuation of the intensity of each image and their coherent subtraction for (a) a phase-conjugate Michelson interferometer, (b) a Mach–Zehnder interferometer with regular mirrors. Δ is the signal output at the subtraction port.

Tables (1)

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Table 1 The Logic Operations Represented by the Intensity IA

Equations (4)

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I A ( x , y ) = E 2 ρ 2 t * r T 1 ( x , y ) + r * t T 2 ( x , y ) 2 ,
r t * + r * t = 0 ,
I A ( x , y ) = E 2 ρ 2 R T T 1 ( x , y ) - T 2 ( x , y ) 2 ,
I B ( x , y ) = E 2 ρ 2 T T 1 ( x , y ) + R T 2 ( x , y ) 2 .

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