Abstract

The complete basic equations for 2+1-dimensional self-trapped beam propagation in photorefractive media are numerically solved, with the anisotropic nonlocal response, diffusion, and space-charge-field displacement effects taken into account. Initial Gaussian beams show elliptical beam shapes, self-deflection, and long-lived oscillations after propagation. The critical parameters that determine the possible damping of the transients are discussed.

© 1998 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

1997

1996

M. Shih, T. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, Opt. Lett. 21, 324 (1996).
[CrossRef] [PubMed]

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Eur. Phys. Lett. 36, 419 (1996).
[CrossRef]

1995

D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef]

A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
[CrossRef] [PubMed]

S. R. Singh and D. N. Christodoulides, Opt. Commun. 118, 569 (1995).
[CrossRef]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and D. Di Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

1994

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, D. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

1992

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

1991

Anderson, D. Z.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Eur. Phys. Lett. 36, 419 (1996).
[CrossRef]

A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
[CrossRef] [PubMed]

Carvalho, M. I.

Christodoulides, D. N.

D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef]

S. R. Singh and D. N. Christodoulides, Opt. Commun. 118, 569 (1995).
[CrossRef]

Crosignani, B.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and D. Di Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, D. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

Di Porto, D.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and D. Di Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, D. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

Garrett, M. H.

Gatz, S.

Herrmann, J.

Iturbe-Castillo, M. D.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Leach, T.

Mamaev, A. V.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Eur. Phys. Lett. 36, 419 (1996).
[CrossRef]

Marquez-Aguilar, P. A.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Saffman, M.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Eur. Phys. Lett. 36, 419 (1996).
[CrossRef]

Salamo, G.

M. Shih, T. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, Opt. Lett. 21, 324 (1996).
[CrossRef] [PubMed]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and D. Di Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

Sánchez-Mondragón, J. J.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Segev, M.

M. Shih, T. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, Opt. Lett. 21, 324 (1996).
[CrossRef] [PubMed]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and D. Di Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, D. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

Shih, M.

M. Shih, T. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, Opt. Lett. 21, 324 (1996).
[CrossRef] [PubMed]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and D. Di Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

Singh, S. R.

S. R. Singh and D. N. Christodoulides, Opt. Commun. 118, 569 (1995).
[CrossRef]

Stepanov, S.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Valley, G. C.

M. Shih, T. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, Opt. Lett. 21, 324 (1996).
[CrossRef] [PubMed]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and D. Di Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, D. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Vysloukh, V.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Yariv, A.

M. Segev, G. C. Valley, B. Crosignani, D. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

Zozulya, A. A.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Eur. Phys. Lett. 36, 419 (1996).
[CrossRef]

A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
[CrossRef] [PubMed]

Appl. Phys. Lett.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Electron. Lett.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and D. Di Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

Eur. Phys. Lett.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Eur. Phys. Lett. 36, 419 (1996).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

S. R. Singh and D. N. Christodoulides, Opt. Commun. 118, 569 (1995).
[CrossRef]

Opt. Lett.

Phys. Rev. A

A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett.

M. Segev, G. C. Valley, B. Crosignani, D. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Evolution of a Gaussian beam in the z,x plane. Parameters: γ=0.15, σ=8.4×10-3, κ=0.25, ψ0=25.

Fig. 2
Fig. 2

Top, electrostatic field and bottom, spatial beam profile after a propagation distance z=8. Parameters are as in Fig.  1.

Fig. 3
Fig. 3

Evolution of beam parameters in the propagation direction. (a) x position of the peak for the anisotropic (solid curves) and the isotropic (dashed line) models. (b) Beam radius for the anisotropic model in the x (solid curve) and the y (dotted curve) directions and for the isotropic model (dashed curve). (c) Peak intensity for the anisotropic (solid curve) and the isotropic (dashed curve) models. Parameters are as in Fig.  1.

Equations (6)

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

γRNeNDi=sI+IB+IDND-NDi,
J=eμNeEsc+μkbTNe=0,
Esc=-eNe+NA-NDi,
-iψz+122ψx2+2ψy2+1γuxψ=0,
f2ux2+2uy2+fxux+fyuy+σ2fx2+2fy2=0,
f=1+γψ21+κχ2ux2+2uy21-κ2ux2+2uy2,

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