Abstract

It is shown that the propagation of steady-state spatial solitons in a bismuth titanium oxide (Bi12TiO20) photorefractive crystal is strongly affected by the presence of concomitant natural optical activity. We assume that the Bi12TiO20 crystal is (110) cut and that the external bias field is along the [001¯] axis. Such orientation introduces self-focusing in one polarization of an optical wave front, whereas it has no effect whatsoever on the component orthogonal to it. Under these conditions, the equations that describe the coupled evolution of the two polarizations of an optical planar beam are derived. Our numerical study of the interaction dynamics shows that, even though the optical beam experiences periodic diffraction in one of the polarization components, it can still recover significantly at particular distances within the crystal. Moreover, it is initially capable of maintaining its solitonlike form over a certain distance of propagation. Relevant examples are provided.

© 1996 Optical Society of America

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  1. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923 (1992).
    [Crossref] [PubMed]
  2. 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 (1993).
    [Crossref]
  3. D. N. Christodoulides and M. I. Carvalho, “Compression, self-bending and collapse of Gaussian beams in photorefractive crystals,” Opt. Lett. 19, 1714 (1994).
    [Crossref] [PubMed]
  4. 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 (1993).
    [Crossref] [PubMed]
  5. G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, D. Porto, and E. Sharp, “Dimensionality and size of photorefractive spatial solitons,” Opt. Lett. 19, 1195 (1994).
    [Crossref] [PubMed]
  6. M. D. Castillo, A. Aguilar, J. J. Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408 (1994).
    [Crossref]
  7. G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457 (1994).
    [Crossref] [PubMed]
  8. 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 (1994).
    [Crossref] [PubMed]
  9. D. N. Christodoulides and M. I. Carvalho, “Bright, dark and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12, 1628 (1995).
    [Crossref]
  10. M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826 (1995).
    [Crossref]
  11. M. D. I. Castillo, J. J. Sanchez-Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, “(1 + 1)-dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515 (1995).
    [Crossref]
  12. A. M. Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165 (1995).
    [Crossref]
  13. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
  14. M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, “Vector photorefractive spatial solitons,” Opt. Lett. 20, 1764 (1995).
    [Crossref] [PubMed]
  15. S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, “Vector interactions of steady-state planar solitons in biased photorefractive media,” Opt. Lett. 20, 2177 (1995).
    [Crossref] [PubMed]
  16. N. V. Kukhtarev, G. E. Dovgalenko, and V. N. Starkov, “Influence of the optical activity on hologram formation in photorefractive crystals,” Appl. Phys. A 33, 227 (1984).
    [Crossref]
  17. A. Marrakchi, R. V. Johnson, and A. R. Tanguay, “Polarization properties of photorefractive diffraction in electrooptic and optically active sillenite crystals (Bragg regime),” J. Opt. Soc. Am. B 3, 321 (1986).
    [Crossref]
  18. M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, Berlin, 1991).
    [Crossref]
  19. V. L. Vinetskii and N. Kukhtarev, “Theory of the conductivity induced by recording holographic gratings in nonmetallic crystals,” Sov. Phys. 16, 2414 (1975).
  20. N. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949 (1979).
    [Crossref]
  21. G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass, 1989).
  22. In Eq. (11) we have ignored any self-bending effects arising from diffusion that may lead to a walk-off between the X and Y components. In this system, even for beam widths as small as 28 μ m, the X self-deflection was found to be less than 1 μ m at z = 2 cm and can thus be neglected. See also M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright solitons in biased photorefractive crystals,” Opt. Commun. 120, 311 (1995).
    [Crossref]
  23. S. R. Singh and D. N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569 (1995).
    [Crossref]

1995 (8)

D. N. Christodoulides and M. I. Carvalho, “Bright, dark and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12, 1628 (1995).
[Crossref]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826 (1995).
[Crossref]

M. D. I. Castillo, J. J. Sanchez-Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, “(1 + 1)-dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515 (1995).
[Crossref]

A. M. Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165 (1995).
[Crossref]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, “Vector photorefractive spatial solitons,” Opt. Lett. 20, 1764 (1995).
[Crossref] [PubMed]

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, “Vector interactions of steady-state planar solitons in biased photorefractive media,” Opt. Lett. 20, 2177 (1995).
[Crossref] [PubMed]

In Eq. (11) we have ignored any self-bending effects arising from diffusion that may lead to a walk-off between the X and Y components. In this system, even for beam widths as small as 28 μ m, the X self-deflection was found to be less than 1 μ m at z = 2 cm and can thus be neglected. See also M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright solitons in biased photorefractive crystals,” Opt. Commun. 120, 311 (1995).
[Crossref]

S. R. Singh and D. N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569 (1995).
[Crossref]

1994 (5)

D. N. Christodoulides and M. I. Carvalho, “Compression, self-bending and collapse of Gaussian beams in photorefractive crystals,” Opt. Lett. 19, 1714 (1994).
[Crossref] [PubMed]

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

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

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457 (1994).
[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 (1994).
[Crossref] [PubMed]

1993 (2)

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 (1993).
[Crossref] [PubMed]

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 (1993).
[Crossref]

1992 (1)

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923 (1992).
[Crossref] [PubMed]

1986 (1)

1984 (1)

N. V. Kukhtarev, G. E. Dovgalenko, and V. N. Starkov, “Influence of the optical activity on hologram formation in photorefractive crystals,” Appl. Phys. A 33, 227 (1984).
[Crossref]

1979 (1)

N. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949 (1979).
[Crossref]

1975 (1)

V. L. Vinetskii and N. Kukhtarev, “Theory of the conductivity induced by recording holographic gratings in nonmetallic crystals,” Sov. Phys. 16, 2414 (1975).

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass, 1989).

Aguilar, A.

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

Aguilar, A. M.

A. M. Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165 (1995).
[Crossref]

Bashaw, M. C.

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457 (1994).
[Crossref] [PubMed]

Bloch, G.

A. M. Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165 (1995).
[Crossref]

Carvalho, M. I.

Castillo, M. D.

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

Castillo, M. D. I.

M. D. I. Castillo, J. J. Sanchez-Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, “(1 + 1)-dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515 (1995).
[Crossref]

Christodoulides, D. N.

In Eq. (11) we have ignored any self-bending effects arising from diffusion that may lead to a walk-off between the X and Y components. In this system, even for beam widths as small as 28 μ m, the X self-deflection was found to be less than 1 μ m at z = 2 cm and can thus be neglected. See also M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright solitons in biased photorefractive crystals,” Opt. Commun. 120, 311 (1995).
[Crossref]

S. R. Singh and D. N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569 (1995).
[Crossref]

D. N. Christodoulides and M. I. Carvalho, “Bright, dark and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12, 1628 (1995).
[Crossref]

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, “Vector interactions of steady-state planar solitons in biased photorefractive media,” Opt. Lett. 20, 2177 (1995).
[Crossref] [PubMed]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, “Vector photorefractive spatial solitons,” Opt. Lett. 20, 1764 (1995).
[Crossref] [PubMed]

D. N. Christodoulides and M. I. Carvalho, “Compression, self-bending and collapse of Gaussian beams in photorefractive crystals,” Opt. Lett. 19, 1714 (1994).
[Crossref] [PubMed]

Crosignani, B.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826 (1995).
[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 (1994).
[Crossref] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457 (1994).
[Crossref] [PubMed]

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, D. Porto, and E. Sharp, “Dimensionality and size of photorefractive spatial solitons,” Opt. Lett. 19, 1195 (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 (1993).
[Crossref] [PubMed]

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 (1993).
[Crossref]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923 (1992).
[Crossref] [PubMed]

Di Porto, P.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826 (1995).
[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 (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 (1993).
[Crossref] [PubMed]

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 (1993).
[Crossref]

Dovgalenko, G. E.

N. V. Kukhtarev, G. E. Dovgalenko, and V. N. Starkov, “Influence of the optical activity on hologram formation in photorefractive crystals,” Appl. Phys. A 33, 227 (1984).
[Crossref]

Duree, G.

Duree, G. C.

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 (1993).
[Crossref] [PubMed]

Engin, D.

Fejer, M. M.

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457 (1994).
[Crossref] [PubMed]

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923 (1992).
[Crossref] [PubMed]

Johnson, R. V.

Khomenko, A. V.

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

Klein, M. B.

M. D. I. Castillo, J. J. Sanchez-Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, “(1 + 1)-dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515 (1995).
[Crossref]

Kukhtarev, N.

N. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949 (1979).
[Crossref]

V. L. Vinetskii and N. Kukhtarev, “Theory of the conductivity induced by recording holographic gratings in nonmetallic crystals,” Sov. Phys. 16, 2414 (1975).

Kukhtarev, N. V.

N. V. Kukhtarev, G. E. Dovgalenko, and V. N. Starkov, “Influence of the optical activity on hologram formation in photorefractive crystals,” Appl. Phys. A 33, 227 (1984).
[Crossref]

Markov, V. B.

N. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949 (1979).
[Crossref]

Marrakchi, A.

Mondragon, J. J.

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

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 (1993).
[Crossref] [PubMed]

Odulov, S. G.

N. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949 (1979).
[Crossref]

Petrov, M. P.

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

Porto, D.

Salamo, G.

Salamo, G. J.

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 (1993).
[Crossref] [PubMed]

Sanchez-Mondragon, J. J.

A. M. Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165 (1995).
[Crossref]

M. D. I. Castillo, J. J. Sanchez-Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, “(1 + 1)-dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515 (1995).
[Crossref]

Segev, M.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826 (1995).
[Crossref]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, “Vector photorefractive spatial solitons,” Opt. Lett. 20, 1764 (1995).
[Crossref] [PubMed]

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

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457 (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 (1993).
[Crossref] [PubMed]

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 (1993).
[Crossref]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923 (1992).
[Crossref] [PubMed]

Sharp, E.

Sharp, E. J.

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 (1993).
[Crossref] [PubMed]

Shih, M.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826 (1995).
[Crossref]

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 (1993).
[Crossref] [PubMed]

Singh, S. R.

S. R. Singh and D. N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569 (1995).
[Crossref]

In Eq. (11) we have ignored any self-bending effects arising from diffusion that may lead to a walk-off between the X and Y components. In this system, even for beam widths as small as 28 μ m, the X self-deflection was found to be less than 1 μ m at z = 2 cm and can thus be neglected. See also M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright solitons in biased photorefractive crystals,” Opt. Commun. 120, 311 (1995).
[Crossref]

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, “Vector interactions of steady-state planar solitons in biased photorefractive media,” Opt. Lett. 20, 2177 (1995).
[Crossref] [PubMed]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, “Vector photorefractive spatial solitons,” Opt. Lett. 20, 1764 (1995).
[Crossref] [PubMed]

Soskin, M. S.

N. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949 (1979).
[Crossref]

Starkov, V. N.

N. V. Kukhtarev, G. E. Dovgalenko, and V. N. Starkov, “Influence of the optical activity on hologram formation in photorefractive crystals,” Appl. Phys. A 33, 227 (1984).
[Crossref]

Stepanov, S.

A. M. Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165 (1995).
[Crossref]

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

Stepanov, S. I.

M. D. I. Castillo, J. J. Sanchez-Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, “(1 + 1)-dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515 (1995).
[Crossref]

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

Tanguay, A. R.

Valley, G. C.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826 (1995).
[Crossref]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, “Vector photorefractive spatial solitons,” Opt. Lett. 20, 1764 (1995).
[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 (1994).
[Crossref] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457 (1994).
[Crossref] [PubMed]

Vinetskii, V. L.

N. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949 (1979).
[Crossref]

V. L. Vinetskii and N. Kukhtarev, “Theory of the conductivity induced by recording holographic gratings in nonmetallic crystals,” Sov. Phys. 16, 2414 (1975).

Vysloukh, V.

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

Wechsler, B. A.

M. D. I. Castillo, J. J. Sanchez-Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, “(1 + 1)-dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515 (1995).
[Crossref]

Yariv, A.

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 (1994).
[Crossref] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457 (1994).
[Crossref] [PubMed]

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, D. Porto, and E. Sharp, “Dimensionality and size of photorefractive spatial solitons,” Opt. Lett. 19, 1195 (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 (1993).
[Crossref] [PubMed]

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 (1993).
[Crossref]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923 (1992).
[Crossref] [PubMed]

Yeh, P.

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

Appl. Phys. A (1)

N. V. Kukhtarev, G. E. Dovgalenko, and V. N. Starkov, “Influence of the optical activity on hologram formation in photorefractive crystals,” Appl. Phys. A 33, 227 (1984).
[Crossref]

Appl. Phys. Lett. (1)

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

Electron. Lett. (1)

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826 (1995).
[Crossref]

Ferroelectrics (1)

N. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949 (1979).
[Crossref]

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

Opt. Commun. (4)

M. D. I. Castillo, J. J. Sanchez-Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, “(1 + 1)-dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515 (1995).
[Crossref]

A. M. Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165 (1995).
[Crossref]

In Eq. (11) we have ignored any self-bending effects arising from diffusion that may lead to a walk-off between the X and Y components. In this system, even for beam widths as small as 28 μ m, the X self-deflection was found to be less than 1 μ m at z = 2 cm and can thus be neglected. See also M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright solitons in biased photorefractive crystals,” Opt. Commun. 120, 311 (1995).
[Crossref]

S. R. Singh and D. N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569 (1995).
[Crossref]

Opt. Lett. (4)

Phys. Rev. A (1)

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457 (1994).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

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 (1994).
[Crossref] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923 (1992).
[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 (1993).
[Crossref] [PubMed]

Sov. Phys. (1)

V. L. Vinetskii and N. Kukhtarev, “Theory of the conductivity induced by recording holographic gratings in nonmetallic crystals,” Sov. Phys. 16, 2414 (1975).

Other (3)

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

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass, 1989).

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Figures (5)

Fig. 1
Fig. 1

Light-propagation coordinate system. The BTO crystal is cut along the (110) plane, and the external field is applied parallel to [ 00 1 ¯ ].

Fig. 2
Fig. 2

Coupled evolution of the (a) X and (b) Y components when the x-polarized input is an r = 3 soliton obtained at E0 = 12.5 kV/cm.

Fig. 3
Fig. 3

Propagation of the (a) X and (b) Y components when the input is x polarized and is a low-intensity r = 0.1 soliton at E0 = 12.5 kV/cm.

Fig. 4
Fig. 4

Evolution of the (a) X and (b) Y components when the input is x-polarized and is an r = 20 soliton at E0 = 12.5 kV/cm.

Fig. 5
Fig. 5

Normalized intensity X profiles (|X|2/|Xmax|2) when the x-polarized input is an r = 3 soliton at E0 = 12.5 kV/cm, for different applied electric field strengths, i.e., E0 = 0, −12.5, +12.5, +15 kV/cm. The output beams at z = 1 cm are compared with that at the input.

Equations (19)

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2 E + k 0 2 0 D = 0 ,
D = E + Δ E + i G × E ,
Δ = Δ η 0 .
Δ i j = 0 n 4 Δ η i j .
T = [ 1 2 1 2 0 0 0 1 1 2 1 2 0 ] .
Δ = 0 [ Δ 1 0 0 0 0 0 0 0 Δ 1 ] ,
D = 0 [ ( n 2 Δ 1 ) i G i G n 2 ] [ E x E y ] ,
i U z + 1 2 k U y y i G k 0 2 2 k V k 0 2 n 4 r 41 E s y 2 k U = 0 ,
i V z + 1 2 k V y y + i G k 0 2 2 k U = 0 ,
E s y ( y , z ) = E 0 I d [ I ( y , z ) + I d ] .
i X ξ + X s s 2 i κ Y β X 1 + | X | 2 + | Y | 2 = 0 ,
i Y ξ + Y s s 2 i κ X = 0 ,
i X ξ + ½ X s s i κ Y = 0 ,
i Y ξ + ½ Y s s + i κ X = 0 ,
X = f 1 ( ξ , s ) cos ( κ ξ ) + f 2 ( ξ , s ) sin ( κ ξ ) ,
Y = f 2 ( ξ , s ) cos ( κ ξ ) f 1 ( ξ , s ) sin ( κ ξ ) ,
i f 1 , 2 ξ + 1 2 2 f 1 , 2 s 2 = 0 .
X = exp ( i γ 2 ξ ) [ X 0 cos ( κ F ξ ) + F ( Y 0 + i γ 2 κ X 0 ) × sin ( κ F ξ ) ] ,
Y = exp ( i γ 2 ξ ) [ Y 0 cos ( κ F ξ ) F ( X 0 + i γ 2 κ Y 0 ) × sin ( κ F ξ ) ] ,

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