Abstract

A theory based on the paraxial propagation of laser beams in nonlinear media and on the Kukhtarev material equations is developed to explain the interaction of bright spatial screening solitons in photorefractive crystals. A numerical study in three dimensions is performed to reveal qualitative and quantitative agreement with experiment. Screening solitons display a variety of propagation effects, such as inelastic scattering, attraction and repulsion, and oscillation and spiraling. In particular, we investigate the influence of initial separation and launching directions on the propagation of incoherent solitons.

© 2000 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, 923–926 (1992).
    [CrossRef] [PubMed]
  2. G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
    [CrossRef] [PubMed]
  3. G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
    [CrossRef] [PubMed]
  4. M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, 3095–3100 (1995).
    [CrossRef] [PubMed]
  5. M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi20TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
    [CrossRef]
  6. M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
    [CrossRef] [PubMed]
  7. M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B 14, 1772–1781 (1997).
    [CrossRef]
  8. D. N. Christodoulides and M. J. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12, 1628–1633 (1995).
    [CrossRef]
  9. M. Segev, M. Shih, and G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13, 706–718 (1996).
    [CrossRef]
  10. B. Crosignani, P. DiPorto, A. Degasperis, M. Segev, and S. Trillo, “Three-dimensional optical beam propagation and solitons in photorefractive crystals,” J. Opt. Soc. Am. B 14, 3078–3090 (1997).
    [CrossRef]
  11. V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971); “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972).
  12. A. W. Snyder and Y. S. Kivshar, “Bright spatial solitons in non-Kerr media: stationary beams and dynamical evolution,” J. Opt. Soc. Am. B 14, 3025–3031 (1997).
    [CrossRef]
  13. M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
    [CrossRef]
  14. M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).
    [CrossRef] [PubMed]
  15. A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
    [CrossRef]
  16. M. Shih, M. Segev, and G. Salamo, “Circular waveguides induced by two-dimensional bright steady-state photorefractive spatial screening solitons,” Opt. Lett. 21, 931–933 (1996).
    [CrossRef] [PubMed]
  17. M. Shih, Z. Chen, M. Mitchell, M. Segev, H. Lee, S. Feigelson, and J. P. Wilde, “Waveguides induced by photorefractive screening solitons,” J. Opt. Soc. Am. B 14, 3091–3101 (1997).
    [CrossRef]
  18. B. Luther-Davies and X. Yang, “Waveguides and Y junctions formed in bulk media by using dark spatial solitons,” Opt. Lett. 17, 496–498 (1992).
    [CrossRef] [PubMed]
  19. N. N. Akhmediev and A. Ankiewicz, “Spatial soliton X-junctions and couplers,” Opt. Commun. 100, 186–192 (1993).
    [CrossRef]
  20. W. Krolikowski and S. A. Holstrom, “Fusion and birth of spatial solitons upon collision,” Opt. Lett. 22, 369–371 (1996).
    [CrossRef]
  21. M. Morin, G. Duree, G. Salamo, and M. Segev, “Waveguides formed by quasi-steady-state photorefractive spatial solitons,” Opt. Lett. 20, 2066–2068 (1995).
    [CrossRef] [PubMed]
  22. D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
    [CrossRef]
  23. Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Observation of incoherently coupled photorefractive spatial soliton pairs,” Opt. Lett. 21, 1436–1438 (1996).
    [CrossRef] [PubMed]
  24. Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, and Y. Kivshar, “Coupled photorefractive spatial soliton pairs,” J. Opt. Soc. Am. B 14, 3066–3077 (1997).
    [CrossRef]
  25. M. Shih and M. Segev, “Incoherent collisions between two-dimensional bright steady-state photorefractive spatial screening solitons,” Opt. Lett. 21, 1538–1540 (1996).
    [CrossRef] [PubMed]
  26. S. Gatz and J. Herrmann, “Soliton collision and soliton fusion in dispersive materials with a linear and quadratic intensity depending refraction index change,” IEEE J. Quantum Electron. 28, 1732–1738 (1992).
    [CrossRef]
  27. S. Gatz and J. Herrmann, “The propagation of optical beams and the properties of two-dimensional spatial solitons in media with a local saturable nonlinear refractive index,” J. Opt. Soc. Am. B 14, 1795–1806 (1997).
    [CrossRef]
  28. K. A. Gorshkov and L. A. Ostrovsky, “Interaction of solitons in nonintegrable systems: direct perturbation method and applications,” Physica D 2, 428–438 (1981).
    [CrossRef]
  29. D. J. Kaup, “Perturbation theory for solitons in optical fibers,” Phys. Rev. A 42, 5689–5694 (1990).
    [CrossRef] [PubMed]
  30. B. A. Malomed, “Polarization dynamics and interactions of solitons in a birefringent optical fiber,” Phys. Rev. A 43, 410–423 (1991).
    [CrossRef] [PubMed]
  31. A. V. Buryak and V. V. Steblina, “Soliton collisions in bulk quadratic media: analytical and numerical study,” J. Opt. Soc. Am. B 16, 245–255 (1999).
    [CrossRef]
  32. M. Shih, M. Segev, and G. Salamo, “Three-dimensional spiraling of interacting spatial solitons,” Phys. Rev. Lett. 78, 2551–2554 (1997).
    [CrossRef]
  33. W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
    [CrossRef]
  34. A. Stepken, F. Kaiser, M. R. Belić, and W. Krolikowski, “Interaction of incoherent two-dimensional photorefractive solitons,” Phys. Rev. E 58, R4112–R4115 (1998).
    [CrossRef]
  35. A. V. Buryak, Y. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82, 81–84 (1999).
    [CrossRef]
  36. 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]
  37. C. M. Gomez Sarabia, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, and V. Vysloukh, “Dynamics of photoinduced lens formation in photorefractive Bi12TiO20 crystal under external DC electric field,” J. Opt. Soc. Am. B 13, 2767–2774 (1996).
    [CrossRef]
  38. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
    [CrossRef]
  39. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1995).
  40. M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals,” Opt. Commun. 120, 311–315 (1995).
    [CrossRef]
  41. M. Lax, G. P. Agrawal, M. R. Belić, B. J. Coffey, and W. L. Louisell, “Electromagnetic-field distribution in loaded unstable resonators,” J. Opt. Soc. Am. A 2, 731–742 (1985).
    [CrossRef]
  42. M. R. Belić, J. Leonardy, D. Timotijević, and F. Kaiser, “Spatiotemporal effects in double phase conjugation,” J. Opt. Soc. Am. B 12, 1602–1616 (1995).
    [CrossRef]
  43. A. Stepken, M. R. Belić, F. Kaiser, W. Krolikowski, and B. Luther-Davies, “Three dimensional trajectories of interacting incoherent photorefractive solitons,” Phys. Rev. Lett. 82, 540–543 (1999).
    [CrossRef]
  44. M. R. Belić, A. Stepken, and F. Kaiser, “Spiraling behavior of photorefractive screening solitons,” Phys. Rev. Lett. 82, 544–547 (1999).
    [CrossRef]

1999

A. V. Buryak, Y. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82, 81–84 (1999).
[CrossRef]

A. Stepken, M. R. Belić, F. Kaiser, W. Krolikowski, and B. Luther-Davies, “Three dimensional trajectories of interacting incoherent photorefractive solitons,” Phys. Rev. Lett. 82, 540–543 (1999).
[CrossRef]

M. R. Belić, A. Stepken, and F. Kaiser, “Spiraling behavior of photorefractive screening solitons,” Phys. Rev. Lett. 82, 544–547 (1999).
[CrossRef]

A. V. Buryak and V. V. Steblina, “Soliton collisions in bulk quadratic media: analytical and numerical study,” J. Opt. Soc. Am. B 16, 245–255 (1999).
[CrossRef]

1998

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
[CrossRef]

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

A. Stepken, F. Kaiser, M. R. Belić, and W. Krolikowski, “Interaction of incoherent two-dimensional photorefractive solitons,” Phys. Rev. E 58, R4112–R4115 (1998).
[CrossRef]

1997

1996

M. Segev, M. Shih, and G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13, 706–718 (1996).
[CrossRef]

C. M. Gomez Sarabia, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, and V. Vysloukh, “Dynamics of photoinduced lens formation in photorefractive Bi12TiO20 crystal under external DC electric field,” J. Opt. Soc. Am. B 13, 2767–2774 (1996).
[CrossRef]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

W. Krolikowski and S. A. Holstrom, “Fusion and birth of spatial solitons upon collision,” Opt. Lett. 22, 369–371 (1996).
[CrossRef]

M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).
[CrossRef] [PubMed]

M. Shih, M. Segev, and G. Salamo, “Circular waveguides induced by two-dimensional bright steady-state photorefractive spatial screening solitons,” Opt. Lett. 21, 931–933 (1996).
[CrossRef] [PubMed]

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Observation of incoherently coupled photorefractive spatial soliton pairs,” Opt. Lett. 21, 1436–1438 (1996).
[CrossRef] [PubMed]

M. Shih and M. Segev, “Incoherent collisions between two-dimensional bright steady-state photorefractive spatial screening solitons,” Opt. Lett. 21, 1538–1540 (1996).
[CrossRef] [PubMed]

1995

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, 3095–3100 (1995).
[CrossRef] [PubMed]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

M. Morin, G. Duree, G. Salamo, and M. Segev, “Waveguides formed by quasi-steady-state photorefractive spatial solitons,” Opt. Lett. 20, 2066–2068 (1995).
[CrossRef] [PubMed]

M. R. Belić, J. Leonardy, D. Timotijević, and F. Kaiser, “Spatiotemporal effects in double phase conjugation,” J. Opt. Soc. Am. B 12, 1602–1616 (1995).
[CrossRef]

D. N. Christodoulides and M. J. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12, 1628–1633 (1995).
[CrossRef]

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]

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals,” Opt. Commun. 120, 311–315 (1995).
[CrossRef]

1994

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi20TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, 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

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

N. N. Akhmediev and A. Ankiewicz, “Spatial soliton X-junctions and couplers,” Opt. Commun. 100, 186–192 (1993).
[CrossRef]

1992

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

S. Gatz and J. Herrmann, “Soliton collision and soliton fusion in dispersive materials with a linear and quadratic intensity depending refraction index change,” IEEE J. Quantum Electron. 28, 1732–1738 (1992).
[CrossRef]

B. Luther-Davies and X. Yang, “Waveguides and Y junctions formed in bulk media by using dark spatial solitons,” Opt. Lett. 17, 496–498 (1992).
[CrossRef] [PubMed]

1991

B. A. Malomed, “Polarization dynamics and interactions of solitons in a birefringent optical fiber,” Phys. Rev. A 43, 410–423 (1991).
[CrossRef] [PubMed]

1990

D. J. Kaup, “Perturbation theory for solitons in optical fibers,” Phys. Rev. A 42, 5689–5694 (1990).
[CrossRef] [PubMed]

1985

1981

K. A. Gorshkov and L. A. Ostrovsky, “Interaction of solitons in nonintegrable systems: direct perturbation method and applications,” Physica D 2, 428–438 (1981).
[CrossRef]

1979

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

1972

V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971); “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972).

Agrawal, G. P.

Akhmediev, N. N.

N. N. Akhmediev and A. Ankiewicz, “Spatial soliton X-junctions and couplers,” Opt. Commun. 100, 186–192 (1993).
[CrossRef]

Anderson, D. Z.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
[CrossRef]

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]

Ankiewicz, A.

N. N. Akhmediev and A. Ankiewicz, “Spatial soliton X-junctions and couplers,” Opt. Commun. 100, 186–192 (1993).
[CrossRef]

Bashaw, M.

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, 3095–3100 (1995).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

Bashaw, M. C.

Belic, M. R.

A. Stepken, M. R. Belić, F. Kaiser, W. Krolikowski, and B. Luther-Davies, “Three dimensional trajectories of interacting incoherent photorefractive solitons,” Phys. Rev. Lett. 82, 540–543 (1999).
[CrossRef]

M. R. Belić, A. Stepken, and F. Kaiser, “Spiraling behavior of photorefractive screening solitons,” Phys. Rev. Lett. 82, 544–547 (1999).
[CrossRef]

A. Stepken, F. Kaiser, M. R. Belić, and W. Krolikowski, “Interaction of incoherent two-dimensional photorefractive solitons,” Phys. Rev. E 58, R4112–R4115 (1998).
[CrossRef]

M. R. Belić, J. Leonardy, D. Timotijević, and F. Kaiser, “Spatiotemporal effects in double phase conjugation,” J. Opt. Soc. Am. B 12, 1602–1616 (1995).
[CrossRef]

M. Lax, G. P. Agrawal, M. R. Belić, B. J. Coffey, and W. L. Louisell, “Electromagnetic-field distribution in loaded unstable resonators,” J. Opt. Soc. Am. A 2, 731–742 (1985).
[CrossRef]

Buryak, A. V.

A. V. Buryak, Y. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82, 81–84 (1999).
[CrossRef]

A. V. Buryak and V. V. Steblina, “Soliton collisions in bulk quadratic media: analytical and numerical study,” J. Opt. Soc. Am. B 16, 245–255 (1999).
[CrossRef]

Carvalho, M. I.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals,” Opt. Commun. 120, 311–315 (1995).
[CrossRef]

Carvalho, M. J.

Chen, Z.

Christodoulides, D. N.

Coffey, B. J.

Coskun, T. H.

Crosignani, B.

B. Crosignani, P. DiPorto, A. Degasperis, M. Segev, and S. Trillo, “Three-dimensional optical beam propagation and solitons in photorefractive crystals,” J. Opt. Soc. Am. B 14, 3078–3090 (1997).
[CrossRef]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, 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. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and 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. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

Degasperis, A.

Denz, C.

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

DiPorto, P.

B. Crosignani, P. DiPorto, A. Degasperis, M. Segev, and S. Trillo, “Three-dimensional optical beam propagation and solitons in photorefractive crystals,” J. Opt. Soc. Am. B 14, 3078–3090 (1997).
[CrossRef]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

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

Duree, G.

M. Morin, G. Duree, G. Salamo, and M. Segev, “Waveguides formed by quasi-steady-state photorefractive spatial solitons,” Opt. Lett. 20, 2066–2068 (1995).
[CrossRef] [PubMed]

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

Feigelson, S.

Fejer, M. M.

M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B 14, 1772–1781 (1997).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, 3095–3100 (1995).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

Garrett, M. H.

Gatz, S.

S. Gatz and J. Herrmann, “The propagation of optical beams and the properties of two-dimensional spatial solitons in media with a local saturable nonlinear refractive index,” J. Opt. Soc. Am. B 14, 1795–1806 (1997).
[CrossRef]

S. Gatz and J. Herrmann, “Soliton collision and soliton fusion in dispersive materials with a linear and quadratic intensity depending refraction index change,” IEEE J. Quantum Electron. 28, 1732–1738 (1992).
[CrossRef]

Gomez Sarabia, C. M.

Gorshkov, K. A.

K. A. Gorshkov and L. A. Ostrovsky, “Interaction of solitons in nonintegrable systems: direct perturbation method and applications,” Physica D 2, 428–438 (1981).
[CrossRef]

Herrmann, J.

S. Gatz and J. Herrmann, “The propagation of optical beams and the properties of two-dimensional spatial solitons in media with a local saturable nonlinear refractive index,” J. Opt. Soc. Am. B 14, 1795–1806 (1997).
[CrossRef]

S. Gatz and J. Herrmann, “Soliton collision and soliton fusion in dispersive materials with a linear and quadratic intensity depending refraction index change,” IEEE J. Quantum Electron. 28, 1732–1738 (1992).
[CrossRef]

Holstrom, S. A.

Iturbe-Castillo, M. D.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi20TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[CrossRef]

Kaiser, F.

M. R. Belić, A. Stepken, and F. Kaiser, “Spiraling behavior of photorefractive screening solitons,” Phys. Rev. Lett. 82, 544–547 (1999).
[CrossRef]

A. Stepken, M. R. Belić, F. Kaiser, W. Krolikowski, and B. Luther-Davies, “Three dimensional trajectories of interacting incoherent photorefractive solitons,” Phys. Rev. Lett. 82, 540–543 (1999).
[CrossRef]

A. Stepken, F. Kaiser, M. R. Belić, and W. Krolikowski, “Interaction of incoherent two-dimensional photorefractive solitons,” Phys. Rev. E 58, R4112–R4115 (1998).
[CrossRef]

M. R. Belić, J. Leonardy, D. Timotijević, and F. Kaiser, “Spatiotemporal effects in double phase conjugation,” J. Opt. Soc. Am. B 12, 1602–1616 (1995).
[CrossRef]

Kaup, D. J.

D. J. Kaup, “Perturbation theory for solitons in optical fibers,” Phys. Rev. A 42, 5689–5694 (1990).
[CrossRef] [PubMed]

Kivshar, Y.

Kivshar, Y. S.

A. V. Buryak, Y. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82, 81–84 (1999).
[CrossRef]

A. W. Snyder and Y. S. Kivshar, “Bright spatial solitons in non-Kerr media: stationary beams and dynamical evolution,” J. Opt. Soc. Am. B 14, 3025–3031 (1997).
[CrossRef]

Krolikowski, W.

A. Stepken, M. R. Belić, F. Kaiser, W. Krolikowski, and B. Luther-Davies, “Three dimensional trajectories of interacting incoherent photorefractive solitons,” Phys. Rev. Lett. 82, 540–543 (1999).
[CrossRef]

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

A. Stepken, F. Kaiser, M. R. Belić, and W. Krolikowski, “Interaction of incoherent two-dimensional photorefractive solitons,” Phys. Rev. E 58, R4112–R4115 (1998).
[CrossRef]

W. Krolikowski and S. A. Holstrom, “Fusion and birth of spatial solitons upon collision,” Opt. Lett. 22, 369–371 (1996).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Lax, M.

Leach, P.

Lee, H.

Leonardy, J.

Louisell, W. L.

Luther-Davies, B.

A. Stepken, M. R. Belić, F. Kaiser, W. Krolikowski, and B. Luther-Davies, “Three dimensional trajectories of interacting incoherent photorefractive solitons,” Phys. Rev. Lett. 82, 540–543 (1999).
[CrossRef]

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

B. Luther-Davies and X. Yang, “Waveguides and Y junctions formed in bulk media by using dark spatial solitons,” Opt. Lett. 17, 496–498 (1992).
[CrossRef] [PubMed]

Malomed, B. A.

B. A. Malomed, “Polarization dynamics and interactions of solitons in a birefringent optical fiber,” Phys. Rev. A 43, 410–423 (1991).
[CrossRef] [PubMed]

Mamaev, A. V.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Marquez Aguilar, P. A.

Marquez-Aguilar, P. A.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi20TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[CrossRef]

Mitchell, M.

Morin, M.

Neurgaonkar, R.

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

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Ostrovsky, L. A.

K. A. Gorshkov and L. A. Ostrovsky, “Interaction of solitons in nonintegrable systems: direct perturbation method and applications,” Physica D 2, 428–438 (1981).
[CrossRef]

Saffman, M.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
[CrossRef]

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

Salamo, G.

M. Shih, M. Segev, and G. Salamo, “Three-dimensional spiraling of interacting spatial solitons,” Phys. Rev. Lett. 78, 2551–2554 (1997).
[CrossRef]

M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).
[CrossRef] [PubMed]

M. Shih, M. Segev, and G. Salamo, “Circular waveguides induced by two-dimensional bright steady-state photorefractive spatial screening solitons,” Opt. Lett. 21, 931–933 (1996).
[CrossRef] [PubMed]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

M. Morin, G. Duree, G. Salamo, and M. Segev, “Waveguides formed by quasi-steady-state photorefractive spatial solitons,” Opt. Lett. 20, 2066–2068 (1995).
[CrossRef] [PubMed]

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

Sanchez Mondragon, J. J.

Sanchez-Mondragon, J. J.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi20TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[CrossRef]

Segev, M.

A. V. Buryak, Y. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82, 81–84 (1999).
[CrossRef]

B. Crosignani, P. DiPorto, A. Degasperis, M. Segev, and S. Trillo, “Three-dimensional optical beam propagation and solitons in photorefractive crystals,” J. Opt. Soc. Am. B 14, 3078–3090 (1997).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, and Y. Kivshar, “Coupled photorefractive spatial soliton pairs,” J. Opt. Soc. Am. B 14, 3066–3077 (1997).
[CrossRef]

M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B 14, 1772–1781 (1997).
[CrossRef]

M. Shih, M. Segev, and G. Salamo, “Three-dimensional spiraling of interacting spatial solitons,” Phys. Rev. Lett. 78, 2551–2554 (1997).
[CrossRef]

M. Shih, Z. Chen, M. Mitchell, M. Segev, H. Lee, S. Feigelson, and J. P. Wilde, “Waveguides induced by photorefractive screening solitons,” J. Opt. Soc. Am. B 14, 3091–3101 (1997).
[CrossRef]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

M. Shih and M. Segev, “Incoherent collisions between two-dimensional bright steady-state photorefractive spatial screening solitons,” Opt. Lett. 21, 1538–1540 (1996).
[CrossRef] [PubMed]

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Observation of incoherently coupled photorefractive spatial soliton pairs,” Opt. Lett. 21, 1436–1438 (1996).
[CrossRef] [PubMed]

M. Segev, M. Shih, and G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13, 706–718 (1996).
[CrossRef]

M. Shih, M. Segev, and G. Salamo, “Circular waveguides induced by two-dimensional bright steady-state photorefractive spatial screening solitons,” Opt. Lett. 21, 931–933 (1996).
[CrossRef] [PubMed]

M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).
[CrossRef] [PubMed]

M. Morin, G. Duree, G. Salamo, and M. Segev, “Waveguides formed by quasi-steady-state photorefractive spatial solitons,” Opt. Lett. 20, 2066–2068 (1995).
[CrossRef] [PubMed]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, 3095–3100 (1995).
[CrossRef] [PubMed]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, 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. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and 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. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971); “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972).

Sharp, E.

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

Shih, M.

Shultz, J. L.

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

Singh, S. R.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals,” Opt. Commun. 120, 311–315 (1995).
[CrossRef]

Snyder, A. W.

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Steblina, V. V.

Stepanov, S.

C. M. Gomez Sarabia, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, and V. Vysloukh, “Dynamics of photoinduced lens formation in photorefractive Bi12TiO20 crystal under external DC electric field,” J. Opt. Soc. Am. B 13, 2767–2774 (1996).
[CrossRef]

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi20TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[CrossRef]

Stepken, A.

M. R. Belić, A. Stepken, and F. Kaiser, “Spiraling behavior of photorefractive screening solitons,” Phys. Rev. Lett. 82, 544–547 (1999).
[CrossRef]

A. Stepken, M. R. Belić, F. Kaiser, W. Krolikowski, and B. Luther-Davies, “Three dimensional trajectories of interacting incoherent photorefractive solitons,” Phys. Rev. Lett. 82, 540–543 (1999).
[CrossRef]

A. Stepken, F. Kaiser, M. R. Belić, and W. Krolikowski, “Interaction of incoherent two-dimensional photorefractive solitons,” Phys. Rev. E 58, R4112–R4115 (1998).
[CrossRef]

Taya, M.

M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B 14, 1772–1781 (1997).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, 3095–3100 (1995).
[CrossRef] [PubMed]

Timotijevic, D.

Trillo, S.

Valley, G. C.

M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B 14, 1772–1781 (1997).
[CrossRef]

M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).
[CrossRef] [PubMed]

M. Segev, M. Shih, and G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13, 706–718 (1996).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, 3095–3100 (1995).
[CrossRef] [PubMed]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, 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. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Vysloukh, V.

C. M. Gomez Sarabia, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, and V. Vysloukh, “Dynamics of photoinduced lens formation in photorefractive Bi12TiO20 crystal under external DC electric field,” J. Opt. Soc. Am. B 13, 2767–2774 (1996).
[CrossRef]

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi20TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[CrossRef]

Wilde, J. P.

Yang, X.

Yariv, A.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, 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. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and 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. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971); “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972).

Zozulya, A. A.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
[CrossRef]

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. Phys. Lett.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi20TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[CrossRef]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

Electron. Lett.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

Ferroelectrics

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

IEEE J. Quantum Electron.

S. Gatz and J. Herrmann, “Soliton collision and soliton fusion in dispersive materials with a linear and quadratic intensity depending refraction index change,” IEEE J. Quantum Electron. 28, 1732–1738 (1992).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B 14, 1772–1781 (1997).
[CrossRef]

S. Gatz and J. Herrmann, “The propagation of optical beams and the properties of two-dimensional spatial solitons in media with a local saturable nonlinear refractive index,” J. Opt. Soc. Am. B 14, 1795–1806 (1997).
[CrossRef]

A. W. Snyder and Y. S. Kivshar, “Bright spatial solitons in non-Kerr media: stationary beams and dynamical evolution,” J. Opt. Soc. Am. B 14, 3025–3031 (1997).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, and Y. Kivshar, “Coupled photorefractive spatial soliton pairs,” J. Opt. Soc. Am. B 14, 3066–3077 (1997).
[CrossRef]

B. Crosignani, P. DiPorto, A. Degasperis, M. Segev, and S. Trillo, “Three-dimensional optical beam propagation and solitons in photorefractive crystals,” J. Opt. Soc. Am. B 14, 3078–3090 (1997).
[CrossRef]

M. Shih, Z. Chen, M. Mitchell, M. Segev, H. Lee, S. Feigelson, and J. P. Wilde, “Waveguides induced by photorefractive screening solitons,” J. Opt. Soc. Am. B 14, 3091–3101 (1997).
[CrossRef]

A. V. Buryak and V. V. Steblina, “Soliton collisions in bulk quadratic media: analytical and numerical study,” J. Opt. Soc. Am. B 16, 245–255 (1999).
[CrossRef]

M. R. Belić, J. Leonardy, D. Timotijević, and F. Kaiser, “Spatiotemporal effects in double phase conjugation,” J. Opt. Soc. Am. B 12, 1602–1616 (1995).
[CrossRef]

D. N. Christodoulides and M. J. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12, 1628–1633 (1995).
[CrossRef]

M. Segev, M. Shih, and G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13, 706–718 (1996).
[CrossRef]

C. M. Gomez Sarabia, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, and V. Vysloukh, “Dynamics of photoinduced lens formation in photorefractive Bi12TiO20 crystal under external DC electric field,” J. Opt. Soc. Am. B 13, 2767–2774 (1996).
[CrossRef]

Opt. Commun.

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals,” Opt. Commun. 120, 311–315 (1995).
[CrossRef]

N. N. Akhmediev and A. Ankiewicz, “Spatial soliton X-junctions and couplers,” Opt. Commun. 100, 186–192 (1993).
[CrossRef]

Opt. Lett.

Phys. Rev. A

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, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
[CrossRef]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, 3095–3100 (1995).
[CrossRef] [PubMed]

D. J. Kaup, “Perturbation theory for solitons in optical fibers,” Phys. Rev. A 42, 5689–5694 (1990).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Phys. Rev. E

A. Stepken, F. Kaiser, M. R. Belić, and W. Krolikowski, “Interaction of incoherent two-dimensional photorefractive solitons,” Phys. Rev. E 58, R4112–R4115 (1998).
[CrossRef]

Phys. Rev. Lett.

A. V. Buryak, Y. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82, 81–84 (1999).
[CrossRef]

M. Shih, M. Segev, and G. Salamo, “Three-dimensional spiraling of interacting spatial solitons,” Phys. Rev. Lett. 78, 2551–2554 (1997).
[CrossRef]

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef]

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[CrossRef]

Sov. Phys. JETP

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Other

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Figures (5)

Fig. 1
Fig. 1

Interaction of incoherent beams launched on the x axis. The normalized propagation distance is 2. The initial separations are (a) 0.9, (b) 1.0, (c) 0.966, and (d) 0.967. The normalized input intensity is 1.5.

Fig. 2
Fig. 2

Interacting incoherent beams for three different launching intensities and three different initial separations. The normalized intensity increases from 1.5 in the upper row, to 3.5 in the middle, to 5.5 in the bottom row. The normalized separation is 0.4 (left column), 0.7 (middle column), and 1.0 (right column). The beams propagate for two diffraction lengths.

Fig. 3
Fig. 3

Intensity distributions for two interacting incoherent beams, launched separated along the y axis. The normalized separations are (a) 1.6, (b) 2.4, and (c) 3.2. The normalized input intensity is 1.5.

Fig. 4
Fig. 4

Interaction of tilted incoherent beams. The trajectories of the beams in the plane (x, z) are shown. The beams propagate (a) in parallel, and the beams are tilted in the x direction for (b) -0.5, and (c) -0.75. The tilt along the y direction is zero. The normalized input intensity is 1.5.

Fig. 5
Fig. 5

Interaction of arbitrarily oriented solitons. Transverse intensity distributions at the input face of the crystal are displayed in the top row for three different pairs of solitons, initially skewed by (a) 15°, (e) 45°, and (i) 75°. The output face of the crystal is shown for three different input intensities: 1.0 in the second row, 3.0 in the third, and 5.0 in the bottom row. All pairs propagate for two diffraction lengths; their initial separation is 1.5.

Equations (16)

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2ikn0zA+2A+2ikn0(θ·)A
+k2(nˆ2A-n02A)=0,
z A-i22A+β(θ·)A=iγ2xϕA,
tND+=Si(Isat+I)(ND-ND+)-SrnND+,
e(tn-tND+)=-j,
j=μenϕ+μkBTn,
0r2ϕ=e(ND+-NA-n).
n=Si(1+I)(ND-NA)Sr NA.
0rt(2ϕ)-μen2ϕ-μenϕ-μkBT2n=0.
τt(2ϕ˜)-2ϕ˜- ln(1+I)ϕ˜
=-E0x ln(1+I)+kBTe{2 ln(1+I)+[ ln(1+I)]2},
τ=0rSrNAμeSi(1+I)(ND-NA)
zA1-i22A1+β(θ1·)A1=iγ2xϕA1,
zA2-i22A2+β(θ2·)A2=iγ2xϕA2.
A1(x, y,0)=A10 exp-(x-x1)2σx2-(y-y1)2σy2,
A2(x, y,0)=A20 exp-(x-x2)2σ˜x2-(y-y2)2σ˜y2,

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