Abstract

A theory based on the Kukhtarev–Vinetskii model is developed that provides the evolution equation of one-dimensional optical spatial solitons in photorefractive media. In the steady-state regime and under appropriate external bias conditions, our analysis indicates that the underlying wave equation can exhibit bright and dark as well as gray spatial soliton states. The characteristics of these self-trapped optical beams are discussed in detail.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. 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]
  2. M. D. Castillo, P. 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]
  3. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923 (1992).
    [CrossRef] [PubMed]
  4. B. Crosignani, M. Segev, D. Engin, P. D. Porto, A. Yariv, and G. Salamo, "Self-trapping of optical beams in photorefractive media," J. Opt. Soc. Am. B 10, 446 (1993).
    [CrossRef]
  5. P. Gunter and J. P. Huignard, eds., Photorefractive Materials and Their Applications I and II (Springer-Verlag, Berlin, 1988); P. Yeh, Photorefractive Nonlinear Optics (Wiley, New York, 1993).
    [CrossRef]
  6. 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]
  7. M. Segev, B. Crosignani, P. D. Porto, A. Yariv, G. Duree, G. Salamo, and E. Sharp, "Stability of photorefractive spatial solitons," Opt. Lett. 19, 1296 (1994).
    [CrossRef] [PubMed]
  8. G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, and E. Sharp, "Dimensionality and size of photorefractive spatial solitons," Opt. Lett. 19, 1195 (1994).
    [CrossRef] [PubMed]
  9. 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); V. O. Vinetskii and N. V. Kukhtarev, "Theory of the conductivity induced by recording holographic gratings in nonmetallic crystals," Sov. Phys. Solid State 16, 2414 (1975).
    [CrossRef]
  10. M. Morin, G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. Sharp, and R. Neurgaonkar, "Photorefractive dark solitons," presented at Optical Society of America Annual Meeting, Dallas, TX, October 2–7, 1994.
  11. M. D. Castillo, P. A. Aguilar, J. J. Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, "Spatial dark solitons in photorefractive Bi12TiO20 crystal," presented at Optical Society of America Annual Meeting, Dallas, TX, October 2–7, 1994.
  12. R. A. Vazquez, R. R. Neurgaonkar, and M. D. Ewbank, "Photorefractive properties of SBN:60 systematically doped with rhodium," J. Opt. Soc. Am. B 9, 1416 (1992).
    [CrossRef]
  13. This approximation as well as the neglect of diffusion effects can be justified more physically in terms of the inequality Ed « Esc « Eq, where Eq and Ed are the limiting space-charge field and the diffusion field, respectively, with both evaluated at the soliton length scale.
  14. S. Gatz and J. Herrmann, "Soliton propagation in materials with saturable nonlinearity," J. Opt. Soc. Am. B 8, 2296 (1991).
    [CrossRef]
  15. V. E. Zakharov and P. B. Shabat, "Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media," Sov. Phys. JETP 34, 62 (1972).
  16. G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass., 1989).
  17. Y. Kodama and A. Hasegawa, "Nonlinear pulse propagation in a monomode dielectric guide," IEEE J. Quantum Electron. 23, 510 (1987).
    [CrossRef]
  18. K. J. Blow, N. J. Doran, and D. Wood, "Suppression of the soliton self-frequency shift by bandwidth-limited amplification," J. Opt. Soc. Am. B 5, 1301 (1988).
    [CrossRef]
  19. A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion," Appl. Phys. Lett. 23, 171 (1973).
    [CrossRef]
  20. Note that the dark irradiance Id can be elevated artificially, as done in Ref. 2.
  21. M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, and A. Yariv, "Steady-state spatial screening solitons in photorefractive materials with external applied field," Phys. Rev. Lett. 73, 3211 (1994).
    [CrossRef] [PubMed]

1994 (5)

M. D. Castillo, P. 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]

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

M. Segev, B. Crosignani, P. D. Porto, A. Yariv, G. Duree, G. Salamo, and E. Sharp, "Stability of photorefractive spatial solitons," Opt. Lett. 19, 1296 (1994).
[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]

1993 (2)

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. 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. D. Porto, A. Yariv, and G. Salamo, "Self-trapping of optical beams in photorefractive media," J. Opt. Soc. Am. B 10, 446 (1993).
[CrossRef]

1992 (2)

R. A. Vazquez, R. R. Neurgaonkar, and M. D. Ewbank, "Photorefractive properties of SBN:60 systematically doped with rhodium," J. Opt. Soc. Am. B 9, 1416 (1992).
[CrossRef]

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

1991 (1)

1988 (1)

1987 (1)

Y. Kodama and A. Hasegawa, "Nonlinear pulse propagation in a monomode dielectric guide," IEEE J. Quantum Electron. 23, 510 (1987).
[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); V. O. Vinetskii and N. V. Kukhtarev, "Theory of the conductivity induced by recording holographic gratings in nonmetallic crystals," Sov. Phys. Solid State 16, 2414 (1975).
[CrossRef]

1973 (1)

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion," Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

1972 (1)

V. E. Zakharov and P. B. Shabat, "Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media," Sov. Phys. JETP 34, 62 (1972).

Agrawal, G. P.

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

Aguilar, P. A.

M. D. Castillo, P. 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]

M. D. Castillo, P. A. Aguilar, J. J. Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, "Spatial dark solitons in photorefractive Bi12TiO20 crystal," presented at Optical Society of America Annual Meeting, Dallas, TX, October 2–7, 1994.

Blow, K. J.

Carvalho, M. I.

Castillo, M. D.

M. D. Castillo, P. 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]

M. D. Castillo, P. A. Aguilar, J. J. Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, "Spatial dark solitons in photorefractive Bi12TiO20 crystal," presented at Optical Society of America Annual Meeting, Dallas, TX, October 2–7, 1994.

Christodoulides, D. N.

Crosignani, B.

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

M. Segev, B. Crosignani, P. D. Porto, A. Yariv, G. Duree, G. Salamo, and E. Sharp, "Stability of photorefractive spatial solitons," Opt. Lett. 19, 1296 (1994).
[CrossRef] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. 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. D. 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]

M. Morin, G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. Sharp, and R. Neurgaonkar, "Photorefractive dark solitons," presented at Optical Society of America Annual Meeting, Dallas, TX, October 2–7, 1994.

Doran, N. J.

Duree, G.

Duree, G. C.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. 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.

Ewbank, M. D.

Fischer, B.

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

Gatz, S.

Hasegawa, A.

Y. Kodama and A. Hasegawa, "Nonlinear pulse propagation in a monomode dielectric guide," IEEE J. Quantum Electron. 23, 510 (1987).
[CrossRef]

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion," Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Herrmann, J.

Klein, M. B.

M. D. Castillo, P. A. Aguilar, J. J. Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, "Spatial dark solitons in photorefractive Bi12TiO20 crystal," presented at Optical Society of America Annual Meeting, Dallas, TX, October 2–7, 1994.

Kodama, Y.

Y. Kodama and A. Hasegawa, "Nonlinear pulse propagation in a monomode dielectric guide," IEEE J. Quantum Electron. 23, 510 (1987).
[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); V. O. Vinetskii and N. V. Kukhtarev, "Theory of the conductivity induced by recording holographic gratings in nonmetallic crystals," Sov. Phys. Solid State 16, 2414 (1975).
[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); V. O. Vinetskii and N. V. Kukhtarev, "Theory of the conductivity induced by recording holographic gratings in nonmetallic crystals," Sov. Phys. Solid State 16, 2414 (1975).
[CrossRef]

Mondragon, J. J.

M. D. Castillo, P. 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]

M. D. Castillo, P. A. Aguilar, J. J. Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, "Spatial dark solitons in photorefractive Bi12TiO20 crystal," presented at Optical Society of America Annual Meeting, Dallas, TX, October 2–7, 1994.

Morin, M.

M. Morin, G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. Sharp, and R. Neurgaonkar, "Photorefractive dark solitons," presented at Optical Society of America Annual Meeting, Dallas, TX, October 2–7, 1994.

Neurgaonkar, R.

M. Morin, G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. Sharp, and R. Neurgaonkar, "Photorefractive dark solitons," presented at Optical Society of America Annual Meeting, Dallas, TX, October 2–7, 1994.

Neurgaonkar, R. R.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. 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]

R. A. Vazquez, R. R. Neurgaonkar, and M. D. Ewbank, "Photorefractive properties of SBN:60 systematically doped with rhodium," J. Opt. Soc. Am. B 9, 1416 (1992).
[CrossRef]

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); V. O. Vinetskii and N. V. Kukhtarev, "Theory of the conductivity induced by recording holographic gratings in nonmetallic crystals," Sov. Phys. Solid State 16, 2414 (1975).
[CrossRef]

Porto, P. D.

M. Segev, G. C. Valley, B. Crosignani, P. D. 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, P. D. Porto, A. Yariv, G. Duree, G. Salamo, and E. Sharp, "Stability of photorefractive spatial solitons," Opt. Lett. 19, 1296 (1994).
[CrossRef] [PubMed]

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

B. Crosignani, M. Segev, D. Engin, P. D. Porto, A. Yariv, and G. Salamo, "Self-trapping of optical beams in photorefractive media," J. Opt. Soc. Am. B 10, 446 (1993).
[CrossRef]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. 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]

M. Morin, G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. Sharp, and R. Neurgaonkar, "Photorefractive dark solitons," presented at Optical Society of America Annual Meeting, Dallas, TX, October 2–7, 1994.

Salamo, G.

Salamo, G. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. 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]

Segev, M.

M. Segev, B. Crosignani, P. D. Porto, A. Yariv, G. Duree, G. Salamo, and E. Sharp, "Stability of photorefractive spatial solitons," Opt. Lett. 19, 1296 (1994).
[CrossRef] [PubMed]

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. 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. D. Porto, and A. Yariv, "Steady-state spatial screening solitons in photorefractive materials with external applied field," Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

B. Crosignani, M. Segev, D. Engin, P. D. Porto, A. Yariv, and G. Salamo, "Self-trapping of optical beams in photorefractive media," J. Opt. Soc. Am. B 10, 446 (1993).
[CrossRef]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. 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]

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

M. Morin, G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. Sharp, and R. Neurgaonkar, "Photorefractive dark solitons," presented at Optical Society of America Annual Meeting, Dallas, TX, October 2–7, 1994.

Shabat, P. B.

V. E. Zakharov and P. B. Shabat, "Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media," Sov. Phys. JETP 34, 62 (1972).

Sharp, E.

Sharp, E. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. 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]

Shultz, J. L.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. 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]

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); V. O. Vinetskii and N. V. Kukhtarev, "Theory of the conductivity induced by recording holographic gratings in nonmetallic crystals," Sov. Phys. Solid State 16, 2414 (1975).
[CrossRef]

Stepanov, S.

M. D. Castillo, P. 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. Castillo, P. A. Aguilar, J. J. Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, "Spatial dark solitons in photorefractive Bi12TiO20 crystal," presented at Optical Society of America Annual Meeting, Dallas, TX, October 2–7, 1994.

Tappert, F.

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion," Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Valley, G. C.

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

Vazquez, R. A.

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); V. O. Vinetskii and N. V. Kukhtarev, "Theory of the conductivity induced by recording holographic gratings in nonmetallic crystals," Sov. Phys. Solid State 16, 2414 (1975).
[CrossRef]

Vysloukh, V.

M. D. Castillo, P. 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. Castillo, P. A. Aguilar, J. J. Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, "Spatial dark solitons in photorefractive Bi12TiO20 crystal," presented at Optical Society of America Annual Meeting, Dallas, TX, October 2–7, 1994.

Wood, D.

Yariv, A.

M. Segev, B. Crosignani, P. D. Porto, A. Yariv, G. Duree, G. Salamo, and E. Sharp, "Stability of photorefractive spatial solitons," Opt. Lett. 19, 1296 (1994).
[CrossRef] [PubMed]

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. 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. D. Porto, and A. Yariv, "Steady-state spatial screening solitons in photorefractive materials with external applied field," Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

B. Crosignani, M. Segev, D. Engin, P. D. Porto, A. Yariv, and G. Salamo, "Self-trapping of optical beams in photorefractive media," J. Opt. Soc. Am. B 10, 446 (1993).
[CrossRef]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. 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]

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

M. Morin, G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. Sharp, and R. Neurgaonkar, "Photorefractive dark solitons," presented at Optical Society of America Annual Meeting, Dallas, TX, October 2–7, 1994.

Zakharov, V. E.

V. E. Zakharov and P. B. Shabat, "Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media," Sov. Phys. JETP 34, 62 (1972).

Appl. Phys. Lett. (2)

M. D. Castillo, P. 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]

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion," Appl. Phys. Lett. 23, 171 (1973).
[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); V. O. Vinetskii and N. V. Kukhtarev, "Theory of the conductivity induced by recording holographic gratings in nonmetallic crystals," Sov. Phys. Solid State 16, 2414 (1975).
[CrossRef]

IEEE J. Quantum Electron. (1)

Y. Kodama and A. Hasegawa, "Nonlinear pulse propagation in a monomode dielectric guide," IEEE J. Quantum Electron. 23, 510 (1987).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Lett. (3)

Phys. Rev. Lett. (3)

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. 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]

M. Segev, G. C. Valley, B. Crosignani, P. D. 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]

Sov. Phys. JETP (1)

V. E. Zakharov and P. B. Shabat, "Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media," Sov. Phys. JETP 34, 62 (1972).

Other (6)

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

This approximation as well as the neglect of diffusion effects can be justified more physically in terms of the inequality Ed « Esc « Eq, where Eq and Ed are the limiting space-charge field and the diffusion field, respectively, with both evaluated at the soliton length scale.

P. Gunter and J. P. Huignard, eds., Photorefractive Materials and Their Applications I and II (Springer-Verlag, Berlin, 1988); P. Yeh, Photorefractive Nonlinear Optics (Wiley, New York, 1993).
[CrossRef]

M. Morin, G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. Sharp, and R. Neurgaonkar, "Photorefractive dark solitons," presented at Optical Society of America Annual Meeting, Dallas, TX, October 2–7, 1994.

M. D. Castillo, P. A. Aguilar, J. J. Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, "Spatial dark solitons in photorefractive Bi12TiO20 crystal," presented at Optical Society of America Annual Meeting, Dallas, TX, October 2–7, 1994.

Note that the dark irradiance Id can be elevated artificially, as done in Ref. 2.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Normalized intensity profiles of bright spatial solitons for β = 173, x0 = 40 μm, and r = 10, 1, and 0.1.

Fig. 2
Fig. 2

Intensity FWHM of bright spatial photorefractive solitons versus r in units of x ^ 0 = 8000(E0)−1/2, where x ^ 0 is in units of micrometers and E0 is in units of volts per meter. The system parameters are taken here to be λ0 = 0.5 μm, ne = 2.35, and r33 = 224 pm/V.

Fig. 3
Fig. 3

Normalized field profile of a dark solitary wave when β = −103, x0 = 40 μm, and ρ = 1.

Fig. 4
Fig. 4

Normalized intensity versus s for a gray spatial soliton state when x0 = 40 μm, ρ = 5, β = −34.5, and m = 0.4.

Fig. 5
Fig. 5

Correction factor hB for bright photorefractive solitons versus r.

Fig. 6
Fig. 6

Correction factor hD for dark photorefractive solitons versus ρ.

Equations (39)

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

2 E + ( k 0 n e ) 2 E = 0 ,
i ϕ z + 1 2 k ϕ x x - k 0 2 ( n e 3 r 33 E sc ) ϕ = 0 ,
γ R n N D + = s i ( I + I d ) ( N D - N D + ) ,
J = e μ ( n E sc + K B T e n x ) ,
J x = 0             or             J = constant ,
E sc x = e ɛ 0 ɛ r ( N D + - N A - n ) .
N D + = N A ( 1 + ɛ 0 ɛ r e N A E sc x ) ,
n = s i ( N D - N A ) γ R N A ( I + I d ) ( 1 + ɛ 0 ɛ r e N A E sc x ) - 1 .
n 0 = s i ( N D - N A ) γ R N A ( I + I d ) .
E sc = n 0 E 0 n - K B T e 1 n n x .
E sc = E 0 ( I + I d ) ( I + I d ) ( 1 + ɛ 0 ɛ r e N A E sc x ) - K B T e ( I / x ) ( I + I d ) + K B T e ɛ 0 ɛ r e N A ( 1 + ɛ 0 ɛ r e N A E sc x ) - 1 2 E sc x 2 .
E sc = E 0 ( I + I d ) ( I + I d ) .
i U ξ + 1 2 U s s - β ( 1 + ρ ) U 1 + U 2 = 0 ,
β - W 2 x 0 W 2 x 0 d s ( 1 + ρ ) 1 + U 2 = k 0 2 x 0 2 n e 4 r 33 V .
i u ξ + 1 2 u s s + β ( 1 + ρ ) ( u 2 1 + u 2 ) u = 0.
i U ξ + 1 2 U s s - β U 1 + U 2 = 0.
L = i 2 ( U U ξ * - U * U ξ ) + 1 2 U s U s * + β ln ( 1 + U 2 ) ,
P = - d s U 2 ,
Q = - d s [ ( U s 2 / 2 ) + β ln ( 1 + U 2 ) ] ,
y ¨ - 2 ν y - 2 β y 1 + r y 2 = 0 ,
ν = - ( β / r ) ln ( 1 + r ) ,
( y ˙ ) 2 = ( 2 β / r ) [ ln ( 1 + r y 2 ) - y 2 ln ( 1 + r ) ] .
( 2 β ) 1 / 2 s = ± y 1 r 1 / 2 d y [ ln ( 1 + r y 2 ) - y 2 ln ( 1 + r ) ] 1 / 2 ,
i U ξ + ½ U s s - β U + β U 2 U = 0 ,
i U ξ + ½ U s s - β U + β U 2 U + γ ( U 2 ) s U = 0 ,
i U ξ + 1 2 U s s - β ( 1 + ρ ) U 1 + U 2 = 0.
y ¨ - 2 ν y - 2 β ( 1 + ρ ) y 1 + ρ y 2 = 0 ,
ν = - β .
( y ˙ ) 2 = ( - 2 β ) [ ( y 2 - 1 ) - ( 1 + ρ ) ρ ln ( 1 + ρ y 2 1 + ρ ) ] ,
i U ξ + ½ U s s - β ( 1 + ρ ) ( 1 - U 2 ) U = 0 ,
U = ρ 1 / 2 y ( s ) exp [ i ( ν ξ + s J d s y 2 ( s ) ) ] ,
y ¨ - 2 ν y - J 2 y 3 - 2 β ( 1 + ρ ) y 1 + ρ y 2 = 0.
J 2 = - 2 ( ν + β ) ,
ν = ( - β ) ( m - 1 ) 2 [ m ( 1 + ρ ) ρ ln ( 1 + ρ m 1 + ρ ) + ( 1 - m ) ] ,
( y ˙ ) 2 = 2 ν ( y 2 - 1 ) + 2 β ρ ( 1 + ρ ) ln ( 1 + ρ y 2 1 + ρ ) + 2 ( ν + β ) ( 1 - y 2 y 2 ) .
i U ζ + 1 2 U η η ( 1 + ρ ) U 1 + U 2 = 0.
V = 2 E 0 α [ 0 η ^ ( 1 + ρ ) d η 1 + U 2 + ( α W 2 - η ^ ) ] .
h = 2 7.34 × 10 2 [ 0 η ^ ( 1 + ρ ) d η 1 + U 2 - η ^ ] .
E 0 = ( - h + h 2 + 4 W V 2 W ) 2 .

Metrics