Abstract

We present both steady-state and dynamical studies of multigrating competition effects in photorefractive mutually pumped phase conjugation. It is shown that in the case of a single interaction region the conical ring, resulting from the scattering by multiple gratings, will collapse to the plane-wave component that has the highest gain. The coupling between the scattered beams is also considered. Both theoretical and experimental results are presented and discussed.

© 1992 Optical Society of America

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  1. S. Weiss, S. Sternklar, B. Fischer, Opt. Lett. 12, 114 (1987).
    [CrossRef]
  2. A. M. C. Smout, R. W. Eason, Opt. Lett. 12, 498 (1987).
    [CrossRef] [PubMed]
  3. M. D. Ewbank, Opt. Lett. 13, 47 (1987).
    [CrossRef]
  4. P. Yeh, T. Y. Chang, M. D. Ewbank, J. Opt. Soc. Am. B 5, 1743 (1988).
    [CrossRef]
  5. A. A. Zozulya, A. V. Mamaev, Sov. Phys. JETP 70, 56 (1990).
  6. Q. C. He, J. G. Duthie, Opt. Commun. 75, 311 (1990).
    [CrossRef]
  7. Q. C. He, J. Shamir, J. G. Duthie, Appl. Opt. 28, 306 (1989).
    [CrossRef] [PubMed]
  8. S. Sternklar, S. Weiss, B. Fischer, Opt. Eng. 26, 423 (1987).
    [CrossRef]
  9. S. Sternklar, S. Weiss, M. Segev, B. Fischer, Opt. Lett. 11, 528 (1986).
    [CrossRef] [PubMed]
  10. G. Dunning, Y. Owechko, B. H. Soffer, OSA Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), paper WU3.
  11. S. Sternklar, S. Weiss, M. Segev, B. Fischer, Appl. Opt. 25, 4518 (1986).
    [CrossRef] [PubMed]
  12. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
    [CrossRef]
  13. Q. C. He, IEEE J. Quantum Electron. 24, 2507 (1988).
    [CrossRef]
  14. P. Yeh, Appl. Opt. 28, 1961 (1989).
    [CrossRef] [PubMed]
  15. M. Cronin-Golomb, Opt. Lett. 15, 897 (1990).
    [CrossRef] [PubMed]
  16. V. Voronov, I. Dorosh, Yu. Kuz’minov, N. Tkachenko, Sov. J. Quantum Electron. 10, 1346 (1981).
    [CrossRef]
  17. D. Statman, B. Liby, J. Opt. Soc. Am. B 6, 1884 (1989).
    [CrossRef]
  18. A. Yariv, S. K. Kwong, Opt. Lett. 10, 454 (1985).
    [CrossRef] [PubMed]
  19. D. Z. Anderson, R. Saxena, J. Opt. Soc. Am. B 2, 164 (1987).
    [CrossRef]
  20. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
    [CrossRef]
  21. J. M. Heaton, L. Solymar, IEEE J. Quantum Electron. 24, 558 (1988).
    [CrossRef]
  22. H. Zhang, X. He, E. Chen, Y. Liu, S. Tang, D. Shen, D. Jiang, Appl. Phys. Lett. 57, 1298 (1990).
    [CrossRef]
  23. G. L. Wood, W. W. Clark, M. J. Miller, E. J. Sharp, G. J. Salamo, R. R. Neurgaonkar, IEEE J. Quantum Electron. QE-23, 2126 (1987).
    [CrossRef]

1990 (4)

A. A. Zozulya, A. V. Mamaev, Sov. Phys. JETP 70, 56 (1990).

Q. C. He, J. G. Duthie, Opt. Commun. 75, 311 (1990).
[CrossRef]

M. Cronin-Golomb, Opt. Lett. 15, 897 (1990).
[CrossRef] [PubMed]

H. Zhang, X. He, E. Chen, Y. Liu, S. Tang, D. Shen, D. Jiang, Appl. Phys. Lett. 57, 1298 (1990).
[CrossRef]

1989 (3)

1988 (3)

P. Yeh, T. Y. Chang, M. D. Ewbank, J. Opt. Soc. Am. B 5, 1743 (1988).
[CrossRef]

Q. C. He, IEEE J. Quantum Electron. 24, 2507 (1988).
[CrossRef]

J. M. Heaton, L. Solymar, IEEE J. Quantum Electron. 24, 558 (1988).
[CrossRef]

1987 (6)

D. Z. Anderson, R. Saxena, J. Opt. Soc. Am. B 2, 164 (1987).
[CrossRef]

S. Weiss, S. Sternklar, B. Fischer, Opt. Lett. 12, 114 (1987).
[CrossRef]

A. M. C. Smout, R. W. Eason, Opt. Lett. 12, 498 (1987).
[CrossRef] [PubMed]

M. D. Ewbank, Opt. Lett. 13, 47 (1987).
[CrossRef]

S. Sternklar, S. Weiss, B. Fischer, Opt. Eng. 26, 423 (1987).
[CrossRef]

G. L. Wood, W. W. Clark, M. J. Miller, E. J. Sharp, G. J. Salamo, R. R. Neurgaonkar, IEEE J. Quantum Electron. QE-23, 2126 (1987).
[CrossRef]

1986 (2)

1985 (1)

1984 (1)

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

1981 (1)

V. Voronov, I. Dorosh, Yu. Kuz’minov, N. Tkachenko, Sov. J. Quantum Electron. 10, 1346 (1981).
[CrossRef]

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Anderson, D. Z.

D. Z. Anderson, R. Saxena, J. Opt. Soc. Am. B 2, 164 (1987).
[CrossRef]

Chang, T. Y.

Chen, E.

H. Zhang, X. He, E. Chen, Y. Liu, S. Tang, D. Shen, D. Jiang, Appl. Phys. Lett. 57, 1298 (1990).
[CrossRef]

Clark, W. W.

G. L. Wood, W. W. Clark, M. J. Miller, E. J. Sharp, G. J. Salamo, R. R. Neurgaonkar, IEEE J. Quantum Electron. QE-23, 2126 (1987).
[CrossRef]

Cronin-Golomb, M.

M. Cronin-Golomb, Opt. Lett. 15, 897 (1990).
[CrossRef] [PubMed]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Dorosh, I.

V. Voronov, I. Dorosh, Yu. Kuz’minov, N. Tkachenko, Sov. J. Quantum Electron. 10, 1346 (1981).
[CrossRef]

Dunning, G.

G. Dunning, Y. Owechko, B. H. Soffer, OSA Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), paper WU3.

Duthie, J. G.

Eason, R. W.

Ewbank, M. D.

Fischer, B.

He, Q. C.

Q. C. He, J. G. Duthie, Opt. Commun. 75, 311 (1990).
[CrossRef]

Q. C. He, J. Shamir, J. G. Duthie, Appl. Opt. 28, 306 (1989).
[CrossRef] [PubMed]

Q. C. He, IEEE J. Quantum Electron. 24, 2507 (1988).
[CrossRef]

He, X.

H. Zhang, X. He, E. Chen, Y. Liu, S. Tang, D. Shen, D. Jiang, Appl. Phys. Lett. 57, 1298 (1990).
[CrossRef]

Heaton, J. M.

J. M. Heaton, L. Solymar, IEEE J. Quantum Electron. 24, 558 (1988).
[CrossRef]

Jiang, D.

H. Zhang, X. He, E. Chen, Y. Liu, S. Tang, D. Shen, D. Jiang, Appl. Phys. Lett. 57, 1298 (1990).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Kuz’minov, Yu.

V. Voronov, I. Dorosh, Yu. Kuz’minov, N. Tkachenko, Sov. J. Quantum Electron. 10, 1346 (1981).
[CrossRef]

Kwong, S. K.

Liby, B.

Liu, Y.

H. Zhang, X. He, E. Chen, Y. Liu, S. Tang, D. Shen, D. Jiang, Appl. Phys. Lett. 57, 1298 (1990).
[CrossRef]

Mamaev, A. V.

A. A. Zozulya, A. V. Mamaev, Sov. Phys. JETP 70, 56 (1990).

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Miller, M. J.

G. L. Wood, W. W. Clark, M. J. Miller, E. J. Sharp, G. J. Salamo, R. R. Neurgaonkar, IEEE J. Quantum Electron. QE-23, 2126 (1987).
[CrossRef]

Neurgaonkar, R. R.

G. L. Wood, W. W. Clark, M. J. Miller, E. J. Sharp, G. J. Salamo, R. R. Neurgaonkar, IEEE J. Quantum Electron. QE-23, 2126 (1987).
[CrossRef]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Owechko, Y.

G. Dunning, Y. Owechko, B. H. Soffer, OSA Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), paper WU3.

Salamo, G. J.

G. L. Wood, W. W. Clark, M. J. Miller, E. J. Sharp, G. J. Salamo, R. R. Neurgaonkar, IEEE J. Quantum Electron. QE-23, 2126 (1987).
[CrossRef]

Saxena, R.

D. Z. Anderson, R. Saxena, J. Opt. Soc. Am. B 2, 164 (1987).
[CrossRef]

Segev, M.

Shamir, J.

Sharp, E. J.

G. L. Wood, W. W. Clark, M. J. Miller, E. J. Sharp, G. J. Salamo, R. R. Neurgaonkar, IEEE J. Quantum Electron. QE-23, 2126 (1987).
[CrossRef]

Shen, D.

H. Zhang, X. He, E. Chen, Y. Liu, S. Tang, D. Shen, D. Jiang, Appl. Phys. Lett. 57, 1298 (1990).
[CrossRef]

Smout, A. M. C.

Soffer, B. H.

G. Dunning, Y. Owechko, B. H. Soffer, OSA Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), paper WU3.

Solymar, L.

J. M. Heaton, L. Solymar, IEEE J. Quantum Electron. 24, 558 (1988).
[CrossRef]

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Statman, D.

Sternklar, S.

Tang, S.

H. Zhang, X. He, E. Chen, Y. Liu, S. Tang, D. Shen, D. Jiang, Appl. Phys. Lett. 57, 1298 (1990).
[CrossRef]

Tkachenko, N.

V. Voronov, I. Dorosh, Yu. Kuz’minov, N. Tkachenko, Sov. J. Quantum Electron. 10, 1346 (1981).
[CrossRef]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Voronov, V.

V. Voronov, I. Dorosh, Yu. Kuz’minov, N. Tkachenko, Sov. J. Quantum Electron. 10, 1346 (1981).
[CrossRef]

Weiss, S.

White, J. O.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Wood, G. L.

G. L. Wood, W. W. Clark, M. J. Miller, E. J. Sharp, G. J. Salamo, R. R. Neurgaonkar, IEEE J. Quantum Electron. QE-23, 2126 (1987).
[CrossRef]

Yariv, A.

A. Yariv, S. K. Kwong, Opt. Lett. 10, 454 (1985).
[CrossRef] [PubMed]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Yeh, P.

Zhang, H.

H. Zhang, X. He, E. Chen, Y. Liu, S. Tang, D. Shen, D. Jiang, Appl. Phys. Lett. 57, 1298 (1990).
[CrossRef]

Zozulya, A. A.

A. A. Zozulya, A. V. Mamaev, Sov. Phys. JETP 70, 56 (1990).

Appl. Opt. (3)

Appl. Phys. Lett. (1)

H. Zhang, X. He, E. Chen, Y. Liu, S. Tang, D. Shen, D. Jiang, Appl. Phys. Lett. 57, 1298 (1990).
[CrossRef]

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

IEEE J. Quantum Electron. (4)

J. M. Heaton, L. Solymar, IEEE J. Quantum Electron. 24, 558 (1988).
[CrossRef]

G. L. Wood, W. W. Clark, M. J. Miller, E. J. Sharp, G. J. Salamo, R. R. Neurgaonkar, IEEE J. Quantum Electron. QE-23, 2126 (1987).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Q. C. He, IEEE J. Quantum Electron. 24, 2507 (1988).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

Q. C. He, J. G. Duthie, Opt. Commun. 75, 311 (1990).
[CrossRef]

Opt. Eng. (1)

S. Sternklar, S. Weiss, B. Fischer, Opt. Eng. 26, 423 (1987).
[CrossRef]

Opt. Lett. (6)

Sov. J. Quantum Electron. (1)

V. Voronov, I. Dorosh, Yu. Kuz’minov, N. Tkachenko, Sov. J. Quantum Electron. 10, 1346 (1981).
[CrossRef]

Sov. Phys. JETP (1)

A. A. Zozulya, A. V. Mamaev, Sov. Phys. JETP 70, 56 (1990).

Other (1)

G. Dunning, Y. Owechko, B. H. Soffer, OSA Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), paper WU3.

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Figures (11)

Fig. 1
Fig. 1

(a) Schematic drawing of MPPC. (b) Vector diagram of optical waves and shared gratings.

Fig. 2
Fig. 2

Steady-state reflectivity as a function of mutual coupling constant γ3L when γ1L = 2.8, γ2L = 3.0, and q = 1. The circles represent calculated phase-conjugate reflectivities |A30/A40|2. The squares represent calculated non-phase-conjugate component reflectivities |A30′/A40|2.

Fig. 3
Fig. 3

Typical transient process of photorefractive MPPC. Curves (a), (b), and (c) represent the phase-conjugate beam |A1L|2, the pump beam |A4L|2, and the non-phase-conjugate beam |A1L′|2, respectively.

Fig. 4
Fig. 4

Transient processes of phase-conjugate and non-phase-conjugate outputs with different γ2L, where γ1L = 3.0, γ3L = 0, and q = 1. Curves (a) and (d) represent phase-conjugate |A1L|2 and non-phase-conjugate |A1L′|2 beams at γ2L = 2.9, respectively. Curves (b) and (c) represent phase-conjugate |A1L|2 and non-phase-conjugate |A1L′|2 beams at γ2L = 2.98, respectively.

Fig. 5
Fig. 5

Transient processes of non-phase-conjugate outputs |A1L′|2 with different γ3L, where γ1L = 3, γ2L = 2.9, and q = 1. (a) γ3L = 0, (b) γ3L = 0.4, (c) γ3L = 0.6.

Fig. 6
Fig. 6

Transient processes of phase-conjugate and non-phase-conjugate outputs with different γ3L, where γ1L = 2.8, γ2L = 3, and q = 1. Curves (a) and (f) represent |A1L′|2 and |A1L|2 at γ3L = 0.8, respectively. Curves (b) and (e) represent |A1L′|2 and |A1L|2 at γ3L = 0.92, respectively. Curves (c) and (d) represent |A1L′|2 and |A1L|2 at γ3L = 1, respectively.

Fig. 7
Fig. 7

Transient processes of non-phase-conjugate outputs |A30′|2 with different q, where γ1L = 3, γ2L = 2.9, and γ3L = 0. (a) q = 1, (b) q = 2, (c) q = 5.

Fig. 8
Fig. 8

Seeding effect on the transient process of MPPC with = 10−3, γ1L = 3, γ2L = 2.9, γ3L = 0, and q = 1. Curves (a) and (d) represent |A1L|2 and |A1L′|2 without seeding, respectively. Curves (b) and (c) represent |A1L|2 and |A1L′|2 with seeding, respectively.

Fig. 9
Fig. 9

Transient process of MPPC when coupling is below the threshold, γ1L = 1.9, γ2L = 1.85, γ3L = 0, and q = 1. Curves (a) and (b) represent |A1L|2 and |A1L′|2, respectively.

Fig. 10
Fig. 10

Schematic drawing of the incidence configuration for the observation of noncoplanar oscillation in the photorefractive Rh–SBN:60 crystal.

Fig. 11
Fig. 11

Photographs of (a) partial conical ring output, (b) decaying arc, and (c) noncoplanar oscillation.

Equations (29)

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K 1 = k 1 - k 4 = k 3 - k 2 ,
K 2 = k 1 - k 4 = k 3 - k 2 ,
K 3 = k 1 - k 1 = k 3 - k 3 .
d A 1 d z = γ 1 I 0 ( A 1 A 4 * + A 2 * A 3 ) A 4 + γ 3 I 0 ( A 1 A 1 * + A 3 * A 3 ) A 1 ,
d A 2 * d z = γ 1 I 0 ( A 1 A 4 * + A 2 * A 3 ) A 3 * + γ 2 I 0 ( A 1 A 4 * + A 2 * A 3 ) A 3 * ,
d A 3 d z = - γ 1 I 0 ( A 1 A 4 * + A 2 * A 3 ) A 2 - γ 3 I 0 ( A 1 A 1 * + A 3 * A 3 ) A 3 ,
d A 4 * d z = - γ 1 I 0 ( A 1 A 4 * + A 2 * A 3 ) A 1 * - γ 2 I 0 ( A 1 A 4 * + A 2 * A 3 ) A 1 * ,
d A 1 d z = γ 2 I 0 ( A 1 A 4 * + A 2 * A 3 ) A 4 - γ 3 * I 0 ( A 1 A 1 * + A 3 * A 3 ) A 1 ,
d A 3 d z = - γ 2 I 0 ( A 1 A 4 * + A 2 * A 3 ) A 2 + γ 3 * I 0 ( A 1 A 1 * + A 3 * A 3 ) A 3 ,
A 1 ( 0 ) = A 1 ( 0 ) = A 3 ( L ) = A 3 ( L ) = 0 ,
A 4 ( 0 ) = A 40 ,             A 2 ( L ) = A 2 L ,             q = A 40 2 / A 2 L 2 ,
A 1 ( 0 ) = A 1 ( 0 ) = A 3 ( L ) = A 3 ( L ) = ,
A 4 ( 0 ) = A 40 ,             A 2 ( L ) = A 2 L ,             q = A 40 2 / A 2 L 2 ,
A 1 z = i Γ 1 ( E 1 E q 1 ) A 4 + i Γ 3 ( E 3 E q 3 ) A 1 ,
A 2 * z = i Γ 1 ( E 1 E q 1 ) A 3 * + i Γ 2 ( E 2 E q 2 ) A 3 * ,
A 3 z = - i Γ 1 ( E 1 E q 1 ) A 2 - i Γ 3 ( E 3 E q 3 ) A 3 ,
A 4 * z = - i Γ 1 ( E 1 E q 1 ) A 1 * - i Γ 2 ( E 2 E q 2 ) A 1 * ,
A 1 z = i Γ 2 ( E 2 E q 2 ) A 4 + i Γ 3 ( E 3 E q 3 ) * A 1 ,
A 3 z = - i Γ 2 ( E 2 E q 2 ) A 2 - i Γ 3 ( E 3 E q 3 ) * A 3
t N ( E 1 E q 1 ) + A K 1 ( E 1 E q 1 ) = B 1 A 1 A 4 * + A 2 * A 3 I 0 ,
t N ( E 2 E q 2 ) + A K 2 ( E 2 E q 2 ) = B 2 A 1 A 4 * + A 2 * A 3 I 0 ,
t N ( E 3 E q 3 ) + A K 3 ( E 3 E q 3 ) = B 3 A 1 A 1 * + A 3 * A 3 I 0 ,
A K j = 1 D j ( 1 + E d j E q j + i E 0 E q j ) , B j = 1 D j ( - E 0 E q j + i E d j E q j ) , D j = 1 + E d j E m j + i E 0 E m j ,
γ 1 = i Γ 1 B 1 A K 1 ,             γ 2 = i Γ 2 B 2 A K 2 ,             γ 3 = i Γ 3 B 3 A K 3 .
A 1 ( 0 , t N ) = 0 , A 3 ( L , t N ) = 0 , A 1 ( 0 , t N ) = 0 , A 3 ( L , t N ) = 0             ( unseeded case )
A 1 ( 0 , t N ) = A 40 , A 3 ( L , t N ) = A 2 L , A 1 ( 0 , t N ) = A 40 , A 3 ( L , t N ) = A 2 L             ( seeded case ) ,
A 2 ( L , t N ) = A 2 L ,             A 4 ( 0 , t N ) = A 40 .
A 1 ( z , Δ t N ) z 0 = A 1 ( z , Δ t N ) z 0 = A 40 ,
A 3 ( z , Δ t N ) z L = A 3 ( z , Δ t N ) z L = A 2 L ,

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