Abstract

We present experimental results on the propagation of an interference pattern of two He–Ne laser beams of unequal amplitudes through a photorefractive Bi12TiO20 crystal in the presence of drift nonlinearity. The phenomenon that we have observed is the focusing of the fringes as the nonlinearity of the crystal is increased. We show that such a phenomenon can be quantitatively interpreted in the framework of modulation instability theory.

© 1995 Optical Society of America

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  1. V. I. Vespalov, V. I. Talanov, Sov. Phys. JETP Lett. 3, 307 (1966).
  2. A. Hasegawa, Opt. Lett. 9, 288 (1984).
    [CrossRef] [PubMed]
  3. E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, S. V. Chernikov, Opt. Lett. 14, 1008 (1989); P. V. Mamyshev, Ch. Bosshard, J. Wilson, G. I. Stegeman, J. Opt. Soc. Am. B 11, 1254 (1994).
    [CrossRef] [PubMed]
  4. G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, R. R. Neurgoankar, Phys. Rev. Lett. 71, 533 (1993).
    [CrossRef] [PubMed]
  5. M. D. Iturbe-Castillo, P. A. Márquez-Anguilar, J. J. Sánchez-Mondragón, S. Stepanov, V. Vysloukh, Appl. Phys. Lett. 64, 484 (1994).
    [CrossRef]
  6. M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, A. Yariv, Opt. Photon. News 5(12), 9 (1994).
    [CrossRef]
  7. M. D. Iturbe-Castillo, J. J. Sánchez-Mondragón, S. I. Stepanov, M. B. Klein, B. A. Wechsler, “(1 + 1)-dimensional dark spatial soliton in photorefractive Bi12TiO20 crystal,” Opt. Commun. (to be published).
  8. M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, Heidelberg, 1991), Chap. 6.
  9. Ya. B. Zel’dovich, Yu. P. Raizer, JETP Lett. 3, 86 (1966); Y. Chen, Opt. Lett. 16, 4 (1991).
  10. S. Trillo, S. Wabnitz, Opt. Lett. 16, 986 (1991).
    [CrossRef] [PubMed]

1994 (2)

M. D. Iturbe-Castillo, P. A. Márquez-Anguilar, J. J. Sánchez-Mondragón, S. Stepanov, V. Vysloukh, Appl. Phys. Lett. 64, 484 (1994).
[CrossRef]

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, A. Yariv, Opt. Photon. News 5(12), 9 (1994).
[CrossRef]

1993 (1)

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, R. R. Neurgoankar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

1991 (1)

1989 (1)

1984 (1)

1966 (2)

Ya. B. Zel’dovich, Yu. P. Raizer, JETP Lett. 3, 86 (1966); Y. Chen, Opt. Lett. 16, 4 (1991).

V. I. Vespalov, V. I. Talanov, Sov. Phys. JETP Lett. 3, 307 (1966).

Chernikov, S. V.

Crosignani, B.

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, A. Yariv, Opt. Photon. News 5(12), 9 (1994).
[CrossRef]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, R. R. Neurgoankar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Di Porto, P.

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, A. Yariv, Opt. Photon. News 5(12), 9 (1994).
[CrossRef]

Dianov, E. M.

DiPorto, P.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, R. R. Neurgoankar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Duree, G.

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, A. Yariv, Opt. Photon. News 5(12), 9 (1994).
[CrossRef]

Duree, G. C.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, R. R. Neurgoankar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Hasegawa, A.

Iturbe-Castillo, M. D.

M. D. Iturbe-Castillo, P. A. Márquez-Anguilar, J. J. Sánchez-Mondragón, S. Stepanov, V. Vysloukh, Appl. Phys. Lett. 64, 484 (1994).
[CrossRef]

M. D. Iturbe-Castillo, J. J. Sánchez-Mondragón, S. I. Stepanov, M. B. Klein, B. A. Wechsler, “(1 + 1)-dimensional dark spatial soliton in photorefractive Bi12TiO20 crystal,” Opt. Commun. (to be published).

Khomenko, A. V.

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, Heidelberg, 1991), Chap. 6.

Klein, M. B.

M. D. Iturbe-Castillo, J. J. Sánchez-Mondragón, S. I. Stepanov, M. B. Klein, B. A. Wechsler, “(1 + 1)-dimensional dark spatial soliton in photorefractive Bi12TiO20 crystal,” Opt. Commun. (to be published).

Mamyshev, P. V.

Márquez-Anguilar, P. A.

M. D. Iturbe-Castillo, P. A. Márquez-Anguilar, J. J. Sánchez-Mondragón, S. Stepanov, V. Vysloukh, Appl. Phys. Lett. 64, 484 (1994).
[CrossRef]

Morin, M.

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, A. Yariv, Opt. Photon. News 5(12), 9 (1994).
[CrossRef]

Neurgoankar, R. R.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, R. R. Neurgoankar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Petrov, M. P.

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, Heidelberg, 1991), Chap. 6.

Prokhorov, A. M.

Raizer, Yu. P.

Ya. B. Zel’dovich, Yu. P. Raizer, JETP Lett. 3, 86 (1966); Y. Chen, Opt. Lett. 16, 4 (1991).

Salamo, G.

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, A. Yariv, Opt. Photon. News 5(12), 9 (1994).
[CrossRef]

Salamo, G. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, R. R. Neurgoankar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Sánchez-Mondragón, J. J.

M. D. Iturbe-Castillo, P. A. Márquez-Anguilar, J. J. Sánchez-Mondragón, S. Stepanov, V. Vysloukh, Appl. Phys. Lett. 64, 484 (1994).
[CrossRef]

M. D. Iturbe-Castillo, J. J. Sánchez-Mondragón, S. I. Stepanov, M. B. Klein, B. A. Wechsler, “(1 + 1)-dimensional dark spatial soliton in photorefractive Bi12TiO20 crystal,” Opt. Commun. (to be published).

Segev, M.

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, A. Yariv, Opt. Photon. News 5(12), 9 (1994).
[CrossRef]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, R. R. Neurgoankar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Sharp, E. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, R. R. Neurgoankar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Shultz, J. L.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, R. R. Neurgoankar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Stepanov, S.

M. D. Iturbe-Castillo, P. A. Márquez-Anguilar, J. J. Sánchez-Mondragón, S. Stepanov, V. Vysloukh, Appl. Phys. Lett. 64, 484 (1994).
[CrossRef]

Stepanov, S. I.

M. D. Iturbe-Castillo, J. J. Sánchez-Mondragón, S. I. Stepanov, M. B. Klein, B. A. Wechsler, “(1 + 1)-dimensional dark spatial soliton in photorefractive Bi12TiO20 crystal,” Opt. Commun. (to be published).

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, Heidelberg, 1991), Chap. 6.

Talanov, V. I.

V. I. Vespalov, V. I. Talanov, Sov. Phys. JETP Lett. 3, 307 (1966).

Trillo, S.

Vespalov, V. I.

V. I. Vespalov, V. I. Talanov, Sov. Phys. JETP Lett. 3, 307 (1966).

Vysloukh, V.

M. D. Iturbe-Castillo, P. A. Márquez-Anguilar, J. J. Sánchez-Mondragón, S. Stepanov, V. Vysloukh, Appl. Phys. Lett. 64, 484 (1994).
[CrossRef]

Wabnitz, S.

Wechsler, B. A.

M. D. Iturbe-Castillo, J. J. Sánchez-Mondragón, S. I. Stepanov, M. B. Klein, B. A. Wechsler, “(1 + 1)-dimensional dark spatial soliton in photorefractive Bi12TiO20 crystal,” Opt. Commun. (to be published).

Yariv, A.

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, A. Yariv, Opt. Photon. News 5(12), 9 (1994).
[CrossRef]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, R. R. Neurgoankar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Zel’dovich, Ya. B.

Ya. B. Zel’dovich, Yu. P. Raizer, JETP Lett. 3, 86 (1966); Y. Chen, Opt. Lett. 16, 4 (1991).

Appl. Phys. Lett. (1)

M. D. Iturbe-Castillo, P. A. Márquez-Anguilar, J. J. Sánchez-Mondragón, S. Stepanov, V. Vysloukh, Appl. Phys. Lett. 64, 484 (1994).
[CrossRef]

JETP Lett. (1)

Ya. B. Zel’dovich, Yu. P. Raizer, JETP Lett. 3, 86 (1966); Y. Chen, Opt. Lett. 16, 4 (1991).

Opt. Lett. (3)

Opt. Photon. News (1)

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, A. Yariv, Opt. Photon. News 5(12), 9 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, R. R. Neurgoankar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Sov. Phys. JETP Lett. (1)

V. I. Vespalov, V. I. Talanov, Sov. Phys. JETP Lett. 3, 307 (1966).

Other (2)

M. D. Iturbe-Castillo, J. J. Sánchez-Mondragón, S. I. Stepanov, M. B. Klein, B. A. Wechsler, “(1 + 1)-dimensional dark spatial soliton in photorefractive Bi12TiO20 crystal,” Opt. Commun. (to be published).

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, Heidelberg, 1991), Chap. 6.

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Figures (4)

Fig. 1
Fig. 1

Diagram of the experimental setup. M1, M2, mirrors; NDF, neutral-density filter.

Fig. 2
Fig. 2

Experimental output profiles at the indicated voltages when the initial interference pattern has 14 fringes/mm.

Fig. 3
Fig. 3

Experimental (open circles), numerical (solid curve), and theoretical (dashed curve) results for the output fringe peak intensity as a function of the voltage applied to the BTO crystal. The input profile has 14 fringes/mm.

Fig. 4
Fig. 4

Numerical result calculated with Eqs. (4) and (5) of modeling the propagation of an interference pattern with 14 fringes/mm through a 9-mm-long BTO crystal. The parameters used were T = 1.423, μ = 1, R = 25.67, a0 = 0.28, and b = 20.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

i A Z = 1 2 2 A X 2 + k 0 L D δ n A ,
E sc = J 0 σ 0 [ I 0 + I ( X ) ] .
δ n = ± δ n 0 ( 1 - A 2 / I 0 1 + A 2 / I 0 ) ,
i q Z = 1 2 2 q X 2 + R μ q 2 1 + μ q 2 q ,
q ( x , 0 ) = [ 1 + a 0 cos ( 2 π X / T ) ] exp ( - X 6 / 2 b 6 ) ,
i δ q Z = 1 2 2 δ q X 2 + 2 R f ( μ ) Re ( δ q ) ,
δ q = a 0 cosh ( α Z / 2 ) cos ( Ω X ) - i ( a 0 α / 2 Ω 2 ) × sinh ( α Z / 2 ) cos ( Ω X ) .

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