Abstract

We report experimental results on the dynamics of formation of a photoinduced lens produced by a two-dimensional cw He–Ne Gaussian laser beam (633 nm) in a cubic Bi12TiO20 photorefractive crystal under an external dc electric field. The main features of the effect, namely, astigmatism of the dynamic lens formed, the pulse shape of the far-field response after switching on of the focused beam, inverse linear dependence of time of its growth on the beam intensity, and approximate constancy of its peak level, are explained in the framework of the analytical model for a one-dimensional Gaussian beam and numerical calculations for a two-dimensional one.

© 1996 Optical Society of America

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  1. G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
    [Crossref] [PubMed]
  2. M. D. Iturbe Castillo, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
    [Crossref]
  3. G. C. Duree, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, and E. J. Sharp, “Dimensionality and size of photorefractive spatial solitons,” Opt. Lett. 19, 1195–1197 (1994).
    [Crossref] [PubMed]
  4. M. C. Bashaw, M. Taya, M. M. Feier, M. Segev, and G. C. Valley, “Observation and waveguide properties of photovoltaic spatial solitons,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 391–394.
  5. M. D. Iturbe Castillo, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, M. B. Klein, and B. A. Wechsler, “Probe beam wave-guiding by spatial dark soliton in photorefractive Bi12TiO20 crystal,” in Digest of Conference of Lasers and Electro-Optics/Europe (Optical Society America, Washington, D.C., 1994), pp. 236–237; M. D. Iturbe Castillo, J. J. Sánchez Mondragón, S. Stepanov, M. B. Klein, and B. A. Wechsler, “(1 + 1)-dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515–519 (1995).
    [Crossref]
  6. M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, and A. Yariv, “Photorefractive dark and vortex solitons,” Opt. Photonics News 5, 9–10 (1994).
    [Crossref]
  7. G. Salamo, G. Duree, M. Morin, M. Segev, B. Crosignani, and P. Di Porto, “Dark, bright and vortex photorefractive quasi-steady-state spatial solitons,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 399–402.
  8. M. Segev, B. Crosignani, A. Yariv, and B. Fisher, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992); B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B 10, 446–453 (1993).
    [Crossref] [PubMed]
  9. M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
    [Crossref] [PubMed]
  10. A. A. Zozulya and D. Z. Anderson, “Nonstationary self-focusing in photorefractive media,” Opt. Lett. 20, 837–839 (1995).
    [Crossref] [PubMed]
  11. A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520–1531 (1995).
    [Crossref] [PubMed]
  12. C. M. Gómez, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Astimagtism of steady-state photoinduced drift photorefractive lenses,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 387–390; J. Mod. Opt. 43, 311–321 (1995).
  13. P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165–174 (1995).
    [Crossref]
  14. M. Petrov, S. Stepanov, and A. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer, Berlin, 1991).
    [Crossref]
  15. C. Hu and J. R. Whinnery, “New thermo-optical measurement method and a comparison with other methods,” Appl. Opt. 12, 72–79 (1973).
    [Crossref] [PubMed]
  16. M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
    [Crossref] [PubMed]
  17. G. S. García Quirino, M. D. Iturbe Castillo, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Interferometric measurements of the photoinduced refractive index profiles in photorefractive Bi12TiO20 crystals,” Opt. Commun. 123, 597–602 (1996).
    [Crossref]

1996 (1)

G. S. García Quirino, M. D. Iturbe Castillo, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Interferometric measurements of the photoinduced refractive index profiles in photorefractive Bi12TiO20 crystals,” Opt. Commun. 123, 597–602 (1996).
[Crossref]

1995 (3)

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520–1531 (1995).
[Crossref] [PubMed]

P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165–174 (1995).
[Crossref]

A. A. Zozulya and D. Z. Anderson, “Nonstationary self-focusing in photorefractive media,” Opt. Lett. 20, 837–839 (1995).
[Crossref] [PubMed]

1994 (4)

M. D. Iturbe Castillo, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[Crossref]

G. C. Duree, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, and E. J. Sharp, “Dimensionality and size of photorefractive spatial solitons,” Opt. Lett. 19, 1195–1197 (1994).
[Crossref] [PubMed]

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, and A. Yariv, “Photorefractive dark and vortex solitons,” Opt. Photonics News 5, 9–10 (1994).
[Crossref]

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[Crossref] [PubMed]

1993 (1)

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

1992 (1)

M. Segev, B. Crosignani, A. Yariv, and B. Fisher, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992); B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B 10, 446–453 (1993).
[Crossref] [PubMed]

1989 (1)

1973 (1)

Anderson, D. Z.

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520–1531 (1995).
[Crossref] [PubMed]

A. A. Zozulya and D. Z. Anderson, “Nonstationary self-focusing in photorefractive media,” Opt. Lett. 20, 837–839 (1995).
[Crossref] [PubMed]

Bashaw, M. C.

M. C. Bashaw, M. Taya, M. M. Feier, M. Segev, and G. C. Valley, “Observation and waveguide properties of photovoltaic spatial solitons,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 391–394.

Bloch, G.

P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165–174 (1995).
[Crossref]

Crosignani, B.

G. C. Duree, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, and E. J. Sharp, “Dimensionality and size of photorefractive spatial solitons,” Opt. Lett. 19, 1195–1197 (1994).
[Crossref] [PubMed]

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, and A. Yariv, “Photorefractive dark and vortex solitons,” Opt. Photonics News 5, 9–10 (1994).
[Crossref]

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[Crossref] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fisher, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992); B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B 10, 446–453 (1993).
[Crossref] [PubMed]

G. Salamo, G. Duree, M. Morin, M. Segev, B. Crosignani, and P. Di Porto, “Dark, bright and vortex photorefractive quasi-steady-state spatial solitons,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 399–402.

Di Porto, P.

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[Crossref] [PubMed]

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, and A. Yariv, “Photorefractive dark and vortex solitons,” Opt. Photonics News 5, 9–10 (1994).
[Crossref]

G. C. Duree, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, and E. J. Sharp, “Dimensionality and size of photorefractive spatial solitons,” Opt. Lett. 19, 1195–1197 (1994).
[Crossref] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

G. Salamo, G. Duree, M. Morin, M. Segev, B. Crosignani, and P. Di Porto, “Dark, bright and vortex photorefractive quasi-steady-state spatial solitons,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 399–402.

Duree, G.

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, and A. Yariv, “Photorefractive dark and vortex solitons,” Opt. Photonics News 5, 9–10 (1994).
[Crossref]

G. Salamo, G. Duree, M. Morin, M. Segev, B. Crosignani, and P. Di Porto, “Dark, bright and vortex photorefractive quasi-steady-state spatial solitons,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 399–402.

Duree, G. C.

G. C. Duree, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, and E. J. Sharp, “Dimensionality and size of photorefractive spatial solitons,” Opt. Lett. 19, 1195–1197 (1994).
[Crossref] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

Feier, M. M.

M. C. Bashaw, M. Taya, M. M. Feier, M. Segev, and G. C. Valley, “Observation and waveguide properties of photovoltaic spatial solitons,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 391–394.

Fisher, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fisher, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992); B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B 10, 446–453 (1993).
[Crossref] [PubMed]

García Quirino, G. S.

G. S. García Quirino, M. D. Iturbe Castillo, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Interferometric measurements of the photoinduced refractive index profiles in photorefractive Bi12TiO20 crystals,” Opt. Commun. 123, 597–602 (1996).
[Crossref]

Gómez, C. M.

C. M. Gómez, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Astimagtism of steady-state photoinduced drift photorefractive lenses,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 387–390; J. Mod. Opt. 43, 311–321 (1995).

Hu, C.

Iturbe Castillo, M. D.

G. S. García Quirino, M. D. Iturbe Castillo, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Interferometric measurements of the photoinduced refractive index profiles in photorefractive Bi12TiO20 crystals,” Opt. Commun. 123, 597–602 (1996).
[Crossref]

M. D. Iturbe Castillo, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[Crossref]

M. D. Iturbe Castillo, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, M. B. Klein, and B. A. Wechsler, “Probe beam wave-guiding by spatial dark soliton in photorefractive Bi12TiO20 crystal,” in Digest of Conference of Lasers and Electro-Optics/Europe (Optical Society America, Washington, D.C., 1994), pp. 236–237; M. D. Iturbe Castillo, J. J. Sánchez Mondragón, S. Stepanov, M. B. Klein, and B. A. Wechsler, “(1 + 1)-dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515–519 (1995).
[Crossref]

Khomenko, A.

M. Petrov, S. Stepanov, and A. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer, Berlin, 1991).
[Crossref]

Klein, M. B.

M. D. Iturbe Castillo, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, M. B. Klein, and B. A. Wechsler, “Probe beam wave-guiding by spatial dark soliton in photorefractive Bi12TiO20 crystal,” in Digest of Conference of Lasers and Electro-Optics/Europe (Optical Society America, Washington, D.C., 1994), pp. 236–237; M. D. Iturbe Castillo, J. J. Sánchez Mondragón, S. Stepanov, M. B. Klein, and B. A. Wechsler, “(1 + 1)-dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515–519 (1995).
[Crossref]

Márquez Aguilar, P. A.

P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165–174 (1995).
[Crossref]

M. D. Iturbe Castillo, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[Crossref]

C. M. Gómez, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Astimagtism of steady-state photoinduced drift photorefractive lenses,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 387–390; J. Mod. Opt. 43, 311–321 (1995).

M. D. Iturbe Castillo, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, M. B. Klein, and B. A. Wechsler, “Probe beam wave-guiding by spatial dark soliton in photorefractive Bi12TiO20 crystal,” in Digest of Conference of Lasers and Electro-Optics/Europe (Optical Society America, Washington, D.C., 1994), pp. 236–237; M. D. Iturbe Castillo, J. J. Sánchez Mondragón, S. Stepanov, M. B. Klein, and B. A. Wechsler, “(1 + 1)-dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515–519 (1995).
[Crossref]

Morin, M.

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, and A. Yariv, “Photorefractive dark and vortex solitons,” Opt. Photonics News 5, 9–10 (1994).
[Crossref]

G. Salamo, G. Duree, M. Morin, M. Segev, B. Crosignani, and P. Di Porto, “Dark, bright and vortex photorefractive quasi-steady-state spatial solitons,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 399–402.

Neurgaonkar, R. R.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

Petrov, M.

M. Petrov, S. Stepanov, and A. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer, Berlin, 1991).
[Crossref]

Said, A. A.

Salamo, G.

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, and A. Yariv, “Photorefractive dark and vortex solitons,” Opt. Photonics News 5, 9–10 (1994).
[Crossref]

G. Salamo, G. Duree, M. Morin, M. Segev, B. Crosignani, and P. Di Porto, “Dark, bright and vortex photorefractive quasi-steady-state spatial solitons,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 399–402.

Salamo, G. J.

G. C. Duree, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, and E. J. Sharp, “Dimensionality and size of photorefractive spatial solitons,” Opt. Lett. 19, 1195–1197 (1994).
[Crossref] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

Sánchez Mondragón, J. J.

G. S. García Quirino, M. D. Iturbe Castillo, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Interferometric measurements of the photoinduced refractive index profiles in photorefractive Bi12TiO20 crystals,” Opt. Commun. 123, 597–602 (1996).
[Crossref]

P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165–174 (1995).
[Crossref]

M. D. Iturbe Castillo, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[Crossref]

C. M. Gómez, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Astimagtism of steady-state photoinduced drift photorefractive lenses,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 387–390; J. Mod. Opt. 43, 311–321 (1995).

M. D. Iturbe Castillo, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, M. B. Klein, and B. A. Wechsler, “Probe beam wave-guiding by spatial dark soliton in photorefractive Bi12TiO20 crystal,” in Digest of Conference of Lasers and Electro-Optics/Europe (Optical Society America, Washington, D.C., 1994), pp. 236–237; M. D. Iturbe Castillo, J. J. Sánchez Mondragón, S. Stepanov, M. B. Klein, and B. A. Wechsler, “(1 + 1)-dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515–519 (1995).
[Crossref]

Segev, M.

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, and A. Yariv, “Photorefractive dark and vortex solitons,” Opt. Photonics News 5, 9–10 (1994).
[Crossref]

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[Crossref] [PubMed]

G. C. Duree, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, and E. J. Sharp, “Dimensionality and size of photorefractive spatial solitons,” Opt. Lett. 19, 1195–1197 (1994).
[Crossref] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fisher, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992); B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B 10, 446–453 (1993).
[Crossref] [PubMed]

G. Salamo, G. Duree, M. Morin, M. Segev, B. Crosignani, and P. Di Porto, “Dark, bright and vortex photorefractive quasi-steady-state spatial solitons,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 399–402.

M. C. Bashaw, M. Taya, M. M. Feier, M. Segev, and G. C. Valley, “Observation and waveguide properties of photovoltaic spatial solitons,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 391–394.

Sharp, E. J.

G. C. Duree, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, and E. J. Sharp, “Dimensionality and size of photorefractive spatial solitons,” Opt. Lett. 19, 1195–1197 (1994).
[Crossref] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

Sheik-Bahae, M.

Shultz, J. L.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

Stepanov, S.

G. S. García Quirino, M. D. Iturbe Castillo, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Interferometric measurements of the photoinduced refractive index profiles in photorefractive Bi12TiO20 crystals,” Opt. Commun. 123, 597–602 (1996).
[Crossref]

P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165–174 (1995).
[Crossref]

M. D. Iturbe Castillo, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[Crossref]

C. M. Gómez, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Astimagtism of steady-state photoinduced drift photorefractive lenses,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 387–390; J. Mod. Opt. 43, 311–321 (1995).

M. Petrov, S. Stepanov, and A. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer, Berlin, 1991).
[Crossref]

M. D. Iturbe Castillo, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, M. B. Klein, and B. A. Wechsler, “Probe beam wave-guiding by spatial dark soliton in photorefractive Bi12TiO20 crystal,” in Digest of Conference of Lasers and Electro-Optics/Europe (Optical Society America, Washington, D.C., 1994), pp. 236–237; M. D. Iturbe Castillo, J. J. Sánchez Mondragón, S. Stepanov, M. B. Klein, and B. A. Wechsler, “(1 + 1)-dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515–519 (1995).
[Crossref]

Taya, M.

M. C. Bashaw, M. Taya, M. M. Feier, M. Segev, and G. C. Valley, “Observation and waveguide properties of photovoltaic spatial solitons,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 391–394.

Valley, G. C.

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[Crossref] [PubMed]

M. C. Bashaw, M. Taya, M. M. Feier, M. Segev, and G. C. Valley, “Observation and waveguide properties of photovoltaic spatial solitons,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 391–394.

Van Stryland, E. W.

Vysloukh, V.

G. S. García Quirino, M. D. Iturbe Castillo, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Interferometric measurements of the photoinduced refractive index profiles in photorefractive Bi12TiO20 crystals,” Opt. Commun. 123, 597–602 (1996).
[Crossref]

M. D. Iturbe Castillo, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[Crossref]

C. M. Gómez, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Astimagtism of steady-state photoinduced drift photorefractive lenses,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 387–390; J. Mod. Opt. 43, 311–321 (1995).

Wechsler, B. A.

M. D. Iturbe Castillo, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, M. B. Klein, and B. A. Wechsler, “Probe beam wave-guiding by spatial dark soliton in photorefractive Bi12TiO20 crystal,” in Digest of Conference of Lasers and Electro-Optics/Europe (Optical Society America, Washington, D.C., 1994), pp. 236–237; M. D. Iturbe Castillo, J. J. Sánchez Mondragón, S. Stepanov, M. B. Klein, and B. A. Wechsler, “(1 + 1)-dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515–519 (1995).
[Crossref]

Whinnery, J. R.

Yariv, A.

G. C. Duree, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, and E. J. Sharp, “Dimensionality and size of photorefractive spatial solitons,” Opt. Lett. 19, 1195–1197 (1994).
[Crossref] [PubMed]

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, and A. Yariv, “Photorefractive dark and vortex solitons,” Opt. Photonics News 5, 9–10 (1994).
[Crossref]

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[Crossref] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fisher, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992); B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B 10, 446–453 (1993).
[Crossref] [PubMed]

Zozulya, A. A.

A. A. Zozulya and D. Z. Anderson, “Nonstationary self-focusing in photorefractive media,” Opt. Lett. 20, 837–839 (1995).
[Crossref] [PubMed]

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520–1531 (1995).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. D. Iturbe Castillo, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[Crossref]

Opt. Commun. (2)

G. S. García Quirino, M. D. Iturbe Castillo, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Interferometric measurements of the photoinduced refractive index profiles in photorefractive Bi12TiO20 crystals,” Opt. Commun. 123, 597–602 (1996).
[Crossref]

P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165–174 (1995).
[Crossref]

Opt. Lett. (3)

Opt. Photonics News (1)

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. Di Porto, and A. Yariv, “Photorefractive dark and vortex solitons,” Opt. Photonics News 5, 9–10 (1994).
[Crossref]

Phys. Rev. A (1)

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520–1531 (1995).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[Crossref] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fisher, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992); B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B 10, 446–453 (1993).
[Crossref] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[Crossref] [PubMed]

Other (5)

G. Salamo, G. Duree, M. Morin, M. Segev, B. Crosignani, and P. Di Porto, “Dark, bright and vortex photorefractive quasi-steady-state spatial solitons,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 399–402.

M. C. Bashaw, M. Taya, M. M. Feier, M. Segev, and G. C. Valley, “Observation and waveguide properties of photovoltaic spatial solitons,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 391–394.

M. D. Iturbe Castillo, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, M. B. Klein, and B. A. Wechsler, “Probe beam wave-guiding by spatial dark soliton in photorefractive Bi12TiO20 crystal,” in Digest of Conference of Lasers and Electro-Optics/Europe (Optical Society America, Washington, D.C., 1994), pp. 236–237; M. D. Iturbe Castillo, J. J. Sánchez Mondragón, S. Stepanov, M. B. Klein, and B. A. Wechsler, “(1 + 1)-dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515–519 (1995).
[Crossref]

C. M. Gómez, P. A. Márquez Aguilar, J. J. Sánchez Mondragón, S. Stepanov, and V. Vysloukh, “Astimagtism of steady-state photoinduced drift photorefractive lenses,” in Photorefractive Materials, Effects, and Devices (University of Colorado, Boulder, Colo., 1995), pp. 387–390; J. Mod. Opt. 43, 311–321 (1995).

M. Petrov, S. Stepanov, and A. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer, Berlin, 1991).
[Crossref]

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Figures (11)

Fig. 1
Fig. 1

Experimental configuration used for observation of the dynamics of the self-focusing/defocusing in the far field. The inset shows the orientation of the BTO sample in the setup. BS stands for beam splitter, and H.V. means high-voltage.

Fig. 2
Fig. 2

(a) Time evolution of the far-field on-axis output intensity after switching on of the focused light beam. U0 =1.5 kV, µ2.8 (1), µ28 (2) and the line shows the output intensity without application of the electric field. (b) Time evolution of the far-field wing (points a and b) output intensity after switching on of the focused light beam. U0=1.5 kV, µ 2.8 (1), µ28 (2), and the line shows the output intensity without application of the electric field. The inset shows the position of the measurement points in the wings of the beam.

Fig. 3
Fig. 3

Time evolution of the near-field intensity distribution in the output focused beam (a) along and (b) perpendicular to the applied electric field. U0=2.0 kV, there is no uniform illumination, and the time from the moment of application of the field, counted in seconds, is shown by the symbol key.

Fig. 4
Fig. 4

Steady-state depth of modulation of the Z-scan curve versus contrast parameter μ: far field, U0=1.5 kV.

Fig. 5
Fig. 5

Time evolution of the far-field on-axis output light intensity after switching on of the focused light beam. U0 =1.5 kV, there is no uniform illumination, and the lines show the corresponding output light intensities without application of the electric field.

Fig. 6
Fig. 6

(a) Dependence of the relative pulse (Fig. 5) amplitude on the focused-beam intensity. (b) Dependence of the inverse time delay of the maximum of the pulse (Fig. 5) on focused-beam intensity. U0=1.5 kV, no uniform illumination.

Fig. 7
Fig. 7

Spatial distributions of the normalized refractive index (numerical calculations): µ=10, (a) t/τM=0.18, (b) t/τM=0.8.

Fig. 8
Fig. 8

Temporal behavior of the normalized curvatures of the refractive index profile (numerical calculations) for (a) moderate contrast ratio µ=2 and (b) high contrast ratio µ=10; time is normalized to τM.

Fig. 9
Fig. 9

Normalized curvatures of the steady-state refractive index profile versus contrast parameter μ (numerical calculations).

Fig. 10
Fig. 10

Spatial spectrum of the laser beam after the sample: (a) under focusing voltage, (b) under defocusing voltage, (c) without voltage applied. φmax=π/2, µ=2, t/τM=0.5, and spatial frequencies Kx and Ky are normalized to a0.

Fig. 11
Fig. 11

Dependence of the stationary zero component of the output spatial spectrum Q(0, 0) on the maximal value of the nonlinear phase shift φmax normalized to π/2.

Equations (25)

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Fphst=(1+μ)24µ(8a02Uλ/2/λdE0)=(1+μ)24µFphst,max.
I(x)=Imax exp(-x2/a02),
T=Fphz02+(Fph-z)2,
T1+z0/Fph.
Est(x)=E0/[1+μ exp(-x2/a02)].
τM(x)=τM/[1+μ exp(-x2/a02)],
E(x, t)E0 exp{-t[1+μ exp(-x2/a02)]/τM}.
A=122E(x, t)x2x=0=E0tμτMa02exp[-t(1+μ)/τM].
AmaxE0a02e,
t=τp=τM/(1+μ),
Fphtr,min=2ea02Uλ/2/λdE0,
σ(x, y, t)=αI(x, y, t),
ρt+div(σE)=0,
ε div E=4πρ.
ε4πtΔv+div[αI grad(v)]=0,
v=-xE0+μu.
IΣ(x, y, t)=I0[1+μf(x, y, t)].
τM t(Δu)+(1+μf)Δu+μ fxux+μ fyuy
=E0 fx,
δn=12rn3μ ux,
f(x, y, t)=exp(-x2-y2)H(t),
i qz=12Δq.
T(x, y, t)=exp(-iKδnd).
Q(kx, ky)=|q(kx, ky)|2,
q(kx, ky)=1(2π)2- - q(x, y)×exp[-i(kxx+kyy)]dxdy,

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