Abstract

An investigation of the propagation of optical beams and the main properties of spatial solitons in three-dimensional media with a local saturable nonlinear refractive-index change is presented. The fundamental bright-soliton solution is calculated from a first integral that describes a two-value solution branch. Although both solution branches are stable in the framework of linear stability theory, the dynamic of beam propagation shows that slightly perturbed initial soliton beams do not evolve to a perfect solitary beam but lead to periodic oscillations of the amplitude. The dependence of the long-living oscillations and the possible azimuthal-symmetry breaking with formation of filaments on the saturation parameter γ and the initial-beam parameters are studied in detail. The results are compared with experimental observations of two-dimensional photorefractive solitons. The interaction and the collision of two spatial solitons are investigated. Beam fusion can appear for parallel propagation as well for small collision angles and small phase differences for solitary beams of both solution branches. Furthermore, solitary-beam dragging with initially overlapping beams of different directions is studied.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Sov. Phys. JETP 34, 62 (1972)].
  2. S. Maneuf, R. Desailly, and C. Froehly, “Stable self-trapping of laser beams: observation in a nonlinear planar waveguide,” Opt. Commun. 65, 193 (1988).
    [CrossRef]
  3. For a comprehensive review, see J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35 (1975).
    [CrossRef]
  4. Y. R. Shen, “Self-focusing: experimental,” Prog. Quantum Electron. 4, 1 (1975).
    [CrossRef]
  5. T. K. Gustafson, P. C. Kelley, B. Y. Chiao, and B. G. Brewer, “Self-trapping in media with saturation of nonlinear index,” Appl. Phys. Lett. 12, 165 (1968).
    [CrossRef]
  6. J. D. Reichert and W. G. Wagner, “Self-trapped optical beams in liquids,” IEEE J. Quantum Electron. QE4, 221 (1968).
    [CrossRef]
  7. J. H. Marburger, L. Huff, J. D. Reichert, and W. G. Wagner, “Stationary self-trapping of optical beams in dense media with Lorentz local-field corrections,” Phys. Rev. 184, 255 (1968).
    [CrossRef]
  8. W. G. Wagner, H. H. Haus, and J. H. Marburger, “Large-scale self-trapping of optical beam in the paraxial ray approximation,” Phys. Rev. 175, 256 (1968).
    [CrossRef]
  9. J. H. Marburger and E. L. Dawes, “Dynamic formation of a small-scale filament,” Phys. Rev. Lett. 21, 556 (1968).
    [CrossRef]
  10. E. L. Dawes and J. H. Marburger, “Computer studies in self-focusing,” Phys. Rev. 179, 862 (1969).
    [CrossRef]
  11. S. N. Vlasov, V. A. Petrishehev, and V. I. Talanov, Radiophys. Quantum Electron. 14, 1062 (1971).
    [CrossRef]
  12. B. B. Suydam, “Self-focusing of very powerful laser beams. II,” IEEE J. Quantum Electron. QE-10, 837 (1974).
    [CrossRef]
  13. J. F. Lam, B. Lippmann, and F. Tappert, “Moment theory of self-trapped laser beams with nonlinear saturation,” Opt. Commun. 15, 419 (1975).
    [CrossRef]
  14. M. Karlson, “Optical beams in saturable self-focusing media,” Phys. Rev. A 46, 2726 (1992).
    [CrossRef]
  15. V. Koono and H. Suzuki, Phys. Scr. 20, 382 (1979).
    [CrossRef]
  16. J. M. Soto-Crespo, E. M. Wright, and N. N. Akhmediev, “Recurrence and azimuthal-symmetry breaking of a cylindrical Gaussian beam in a saturable self-focusing medium,” Phys. Rev. A 45, 3168 (1992).
    [CrossRef] [PubMed]
  17. D. Grishkowsky, “Self-focusing of light in potassium vapor,” Phys. Rev. Lett. 24, 868 (1970).
  18. J. E. Bjorkholm and A. Ashkin, “Cw self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32, 129 (1974).
    [CrossRef]
  19. C. E. Max, J. Arons, and A. B. Langdon, “Self-modulation and self-focusing of electromagnetic waves in plasmas,” Phys. Rev. Lett. 33, 209 (1974).
    [CrossRef]
  20. A. B. Borisov, A. V. Borovskij, O. B. Shiryaev, V. V. Korobkin, A. M. Prokhorov, I. C. Solem, T. S. Luk, K. Boyer, and C. K. Rhodes, “Relativistic charge-displacement self-channeling of intense ultrashort laser pulses in plasmas,” Phys. Rev. A 45, 5830 (1992).
    [CrossRef] [PubMed]
  21. A. B. Borisov, A. V. Borovskij, V. V. Korobkin, A. M. Prokhorov, O. B. Shiryaev, X. M. Shi, T. S. Luk, A. McPherson, I. C. Solem, K. Boyer, and C. K. Rhodes, “Observation of relativistic and charge displacement self-channeling of intense subpicosecond UV-radiation in plasmas,” Phys. Rev. Lett. 68, 2309 (1992).
    [CrossRef] [PubMed]
  22. P. Monot, T. Auguste, P. Gibbon, F. Jakober, G. Mainfray, A. Duliev, M. Louis-Jacquet, G. Malka, and I. L. Miguel, “Experimental demonstration of relativistic self-channeling of a multiterrawatt laser pulse in an underdence plasma,” Phys. Rev. Lett. 74, 2953 (1995).
    [CrossRef] [PubMed]
  23. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20, 73 (1995).
    [CrossRef] [PubMed]
  24. S. Henz and J. Herrmann, “Two-dimensional spatial optical solitons in bulk Kerr-media stabilized by self-induced photoionization,” Phys. Rev. E 53, 4092 (1996).
    [CrossRef]
  25. K. N. Karamzin and A. P. Sukhorukov, Pisma Zh. Eksp. Teor. Fiz. 20, 774 (1974) [JETP Lett. 20, 339 (1974)].
  26. K. Hayata and M. Koshiba, “Multidimensional solitons in quadratic nonlinear medium,” Phys. Rev. Lett. 71, 3275 (1993).
    [CrossRef] [PubMed]
  27. W. Torruellas, Z. Wang, D. J. Hagan, E. W. van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
    [CrossRef] [PubMed]
  28. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923 (1992).
    [CrossRef] [PubMed]
  29. G. Duree, J. L. Shultz, G. 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]
  30. M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. I. Stepanov, and V. A. Vysloukh, “Spatial soliton in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408 (1994).
    [CrossRef]
  31. M. Segev, G. C. Valley, B. Crosignani, D. 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]
  32. M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and D. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826 (1995).
    [CrossRef]
  33. 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 (1996).
    [CrossRef] [PubMed]
  34. M. Shih, M. Segev, and G. Salamo, “Circular waveguides induced by two-dimensional bright steady-state photorefractive partial screening solitons,” Opt. Lett. 21, 1 (1996).
  35. 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 (1994).
    [CrossRef] [PubMed]
  36. 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]
  37. S. Gatz and J. Herrmann, “Soliton propagation in materials with saturable nonlinearity,” J. Opt. Soc. Am. B 8, 2296 (1991).
    [CrossRef]
  38. S. Gatz and J. Herrmann, “Propagation, collision and fusion of spatial optical solitons in three-dimensional media with saturable nonlinear refractive index change,” in Quantum Electronics and Laser Science Conference (QELS’96), Vol. 10 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 210.
  39. E. W. Wright, B. L. Lawrence, W. Torruellas, and G. Stegeman, “Stable self-trapping and ring formation in polydiacetylene para-toluene sulfonate,” Opt. Lett. 20, 2481 (1995).
    [CrossRef]
  40. A. Zozulya and D. 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 (1995).
    [CrossRef] [PubMed]
  41. G. S. Garcia Quirino, M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Interferometric measurements of the photoinduced refractive index profiles in photorefractive Bi12TiO20 crystals,” Opt. Commun. 123, 592 (1996).
    [CrossRef]
  42. N. Kuktarev, Sov. Tech. Phys. Lett. 2, 438 (1976).
  43. P. Günter and J.-P. Huignard, eds., Photorefractive Materials and their Application (Springer-Verlag, New York, 1988).
  44. S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, “Higher-order space charge field effects on the evolution of spatial solitons in biased photorefractive crystals,” Opt. Commun. 130, 288 (1996).
    [CrossRef]
  45. M. Segev, G. Valley, M. I. Carvalho, and D. N. Christodoulides, “Vector photorefractive spatial solitons,” Opt. Lett. 20, 1764 (1995).
    [CrossRef] [PubMed]
  46. N. G. Vakhitov and A. A. Kolokolov, “Stability of stationary solutions of nonlinear wave equations,” Radiophys. Quantum Electron. 16, 783 (1975).
    [CrossRef]
  47. For a comprehensive review article, see J. J. Rasmussen and K. Rypdal, “Blow up in nonlinear Schrödinger equations: a general review,” Phys. Scr. 33, 491 (1986).
    [CrossRef]
  48. J. Herrmann, “Bistable bright solitons in dispersive media with a linear and quadratic intensity-depending refraction index change,” Opt. Commun. 87, 161 (1992).
    [CrossRef]
  49. 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 (1992).
    [CrossRef]
  50. S. Gatz and J. Herrmann, “Soliton propagation and soliton collision in double-doped fibers with a non-Kerr-like nonlinear refractive-index change,” Opt. Lett. 17, 484 (1992).
    [CrossRef] [PubMed]
  51. D. M. Babiou, G. I. Stegeman, and L. Torner, “Interaction of one-dimensional bright solitary waves in quadratic media,” Opt. Lett. 20, 2282 (1995).
    [CrossRef]
  52. V. Tikhonenko, J. Christov, and B. Luther-Davies, “Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698 (1996).
    [CrossRef] [PubMed]
  53. M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salomo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons and induced waveguides,” in Quantum Electronics and Laser Science Conference (QELS’96) Vol. 10 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 209.
  54. M. N. Islam, “Ultrafast all-optical logic gates,” Opt. Lett. 14, 1257 (1989).
    [CrossRef] [PubMed]
  55. M. N. Islam, “All-optical cascadable nor gate with gain,” Opt. Lett. 15, 417 (1990).
    [CrossRef] [PubMed]
  56. M. Shalaby and A. Barthelemy, “Experimental spatial soliton trapping and switching,” Opt. Lett. 16, 1472 (1991).
    [CrossRef] [PubMed]
  57. S. Blair, K. Wagner, and R. McLeod, “Asymmetric spatial soliton dragging,” Opt. Lett. 19, 1943 (1994).
    [CrossRef] [PubMed]
  58. I. U. Kang, G. I. Stegeman, and J. C. Aitchinson, “One-dimensional spatial soliton dragging, trapping, and all-optical switching in AlGaAs waveguides,” Opt. Lett. 21, 189 (1996).
    [CrossRef] [PubMed]

1996 (7)

S. Henz and J. Herrmann, “Two-dimensional spatial optical solitons in bulk Kerr-media stabilized by self-induced photoionization,” Phys. Rev. E 53, 4092 (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 (1996).
[CrossRef] [PubMed]

M. Shih, M. Segev, and G. Salamo, “Circular waveguides induced by two-dimensional bright steady-state photorefractive partial screening solitons,” Opt. Lett. 21, 1 (1996).

G. S. Garcia Quirino, M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Interferometric measurements of the photoinduced refractive index profiles in photorefractive Bi12TiO20 crystals,” Opt. Commun. 123, 592 (1996).
[CrossRef]

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, “Higher-order space charge field effects on the evolution of spatial solitons in biased photorefractive crystals,” Opt. Commun. 130, 288 (1996).
[CrossRef]

V. Tikhonenko, J. Christov, and B. Luther-Davies, “Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

I. U. Kang, G. I. Stegeman, and J. C. Aitchinson, “One-dimensional spatial soliton dragging, trapping, and all-optical switching in AlGaAs waveguides,” Opt. Lett. 21, 189 (1996).
[CrossRef] [PubMed]

1995 (9)

D. M. Babiou, G. I. Stegeman, and L. Torner, “Interaction of one-dimensional bright solitary waves in quadratic media,” Opt. Lett. 20, 2282 (1995).
[CrossRef]

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

E. W. Wright, B. L. Lawrence, W. Torruellas, and G. Stegeman, “Stable self-trapping and ring formation in polydiacetylene para-toluene sulfonate,” Opt. Lett. 20, 2481 (1995).
[CrossRef]

A. Zozulya and D. 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 (1995).
[CrossRef] [PubMed]

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]

P. Monot, T. Auguste, P. Gibbon, F. Jakober, G. Mainfray, A. Duliev, M. Louis-Jacquet, G. Malka, and I. L. Miguel, “Experimental demonstration of relativistic self-channeling of a multiterrawatt laser pulse in an underdence plasma,” Phys. Rev. Lett. 74, 2953 (1995).
[CrossRef] [PubMed]

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20, 73 (1995).
[CrossRef] [PubMed]

W. Torruellas, Z. Wang, D. J. Hagan, E. W. van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

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

1994 (4)

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. I. Stepanov, and V. A. Vysloukh, “Spatial soliton in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

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

S. Blair, K. Wagner, and R. McLeod, “Asymmetric spatial soliton dragging,” Opt. Lett. 19, 1943 (1994).
[CrossRef] [PubMed]

1993 (2)

G. Duree, J. L. Shultz, G. 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]

K. Hayata and M. Koshiba, “Multidimensional solitons in quadratic nonlinear medium,” Phys. Rev. Lett. 71, 3275 (1993).
[CrossRef] [PubMed]

1992 (8)

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

A. B. Borisov, A. V. Borovskij, O. B. Shiryaev, V. V. Korobkin, A. M. Prokhorov, I. C. Solem, T. S. Luk, K. Boyer, and C. K. Rhodes, “Relativistic charge-displacement self-channeling of intense ultrashort laser pulses in plasmas,” Phys. Rev. A 45, 5830 (1992).
[CrossRef] [PubMed]

A. B. Borisov, A. V. Borovskij, V. V. Korobkin, A. M. Prokhorov, O. B. Shiryaev, X. M. Shi, T. S. Luk, A. McPherson, I. C. Solem, K. Boyer, and C. K. Rhodes, “Observation of relativistic and charge displacement self-channeling of intense subpicosecond UV-radiation in plasmas,” Phys. Rev. Lett. 68, 2309 (1992).
[CrossRef] [PubMed]

M. Karlson, “Optical beams in saturable self-focusing media,” Phys. Rev. A 46, 2726 (1992).
[CrossRef]

J. M. Soto-Crespo, E. M. Wright, and N. N. Akhmediev, “Recurrence and azimuthal-symmetry breaking of a cylindrical Gaussian beam in a saturable self-focusing medium,” Phys. Rev. A 45, 3168 (1992).
[CrossRef] [PubMed]

J. Herrmann, “Bistable bright solitons in dispersive media with a linear and quadratic intensity-depending refraction index change,” Opt. Commun. 87, 161 (1992).
[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 (1992).
[CrossRef]

S. Gatz and J. Herrmann, “Soliton propagation and soliton collision in double-doped fibers with a non-Kerr-like nonlinear refractive-index change,” Opt. Lett. 17, 484 (1992).
[CrossRef] [PubMed]

1991 (2)

1990 (1)

1989 (1)

1988 (1)

S. Maneuf, R. Desailly, and C. Froehly, “Stable self-trapping of laser beams: observation in a nonlinear planar waveguide,” Opt. Commun. 65, 193 (1988).
[CrossRef]

1986 (1)

For a comprehensive review article, see J. J. Rasmussen and K. Rypdal, “Blow up in nonlinear Schrödinger equations: a general review,” Phys. Scr. 33, 491 (1986).
[CrossRef]

1979 (1)

V. Koono and H. Suzuki, Phys. Scr. 20, 382 (1979).
[CrossRef]

1976 (1)

N. Kuktarev, Sov. Tech. Phys. Lett. 2, 438 (1976).

1975 (4)

N. G. Vakhitov and A. A. Kolokolov, “Stability of stationary solutions of nonlinear wave equations,” Radiophys. Quantum Electron. 16, 783 (1975).
[CrossRef]

For a comprehensive review, see J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Y. R. Shen, “Self-focusing: experimental,” Prog. Quantum Electron. 4, 1 (1975).
[CrossRef]

J. F. Lam, B. Lippmann, and F. Tappert, “Moment theory of self-trapped laser beams with nonlinear saturation,” Opt. Commun. 15, 419 (1975).
[CrossRef]

1974 (4)

J. E. Bjorkholm and A. Ashkin, “Cw self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32, 129 (1974).
[CrossRef]

C. E. Max, J. Arons, and A. B. Langdon, “Self-modulation and self-focusing of electromagnetic waves in plasmas,” Phys. Rev. Lett. 33, 209 (1974).
[CrossRef]

K. N. Karamzin and A. P. Sukhorukov, Pisma Zh. Eksp. Teor. Fiz. 20, 774 (1974) [JETP Lett. 20, 339 (1974)].

B. B. Suydam, “Self-focusing of very powerful laser beams. II,” IEEE J. Quantum Electron. QE-10, 837 (1974).
[CrossRef]

1971 (2)

S. N. Vlasov, V. A. Petrishehev, and V. I. Talanov, Radiophys. Quantum Electron. 14, 1062 (1971).
[CrossRef]

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

1970 (1)

D. Grishkowsky, “Self-focusing of light in potassium vapor,” Phys. Rev. Lett. 24, 868 (1970).

1969 (1)

E. L. Dawes and J. H. Marburger, “Computer studies in self-focusing,” Phys. Rev. 179, 862 (1969).
[CrossRef]

1968 (5)

T. K. Gustafson, P. C. Kelley, B. Y. Chiao, and B. G. Brewer, “Self-trapping in media with saturation of nonlinear index,” Appl. Phys. Lett. 12, 165 (1968).
[CrossRef]

J. D. Reichert and W. G. Wagner, “Self-trapped optical beams in liquids,” IEEE J. Quantum Electron. QE4, 221 (1968).
[CrossRef]

J. H. Marburger, L. Huff, J. D. Reichert, and W. G. Wagner, “Stationary self-trapping of optical beams in dense media with Lorentz local-field corrections,” Phys. Rev. 184, 255 (1968).
[CrossRef]

W. G. Wagner, H. H. Haus, and J. H. Marburger, “Large-scale self-trapping of optical beam in the paraxial ray approximation,” Phys. Rev. 175, 256 (1968).
[CrossRef]

J. H. Marburger and E. L. Dawes, “Dynamic formation of a small-scale filament,” Phys. Rev. Lett. 21, 556 (1968).
[CrossRef]

Aitchinson, J. C.

Akhmediev, N. N.

J. M. Soto-Crespo, E. M. Wright, and N. N. Akhmediev, “Recurrence and azimuthal-symmetry breaking of a cylindrical Gaussian beam in a saturable self-focusing medium,” Phys. Rev. A 45, 3168 (1992).
[CrossRef] [PubMed]

Anderson, D.

A. Zozulya and D. 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 (1995).
[CrossRef] [PubMed]

Arons, J.

C. E. Max, J. Arons, and A. B. Langdon, “Self-modulation and self-focusing of electromagnetic waves in plasmas,” Phys. Rev. Lett. 33, 209 (1974).
[CrossRef]

Ashkin, A.

J. E. Bjorkholm and A. Ashkin, “Cw self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32, 129 (1974).
[CrossRef]

Auguste, T.

P. Monot, T. Auguste, P. Gibbon, F. Jakober, G. Mainfray, A. Duliev, M. Louis-Jacquet, G. Malka, and I. L. Miguel, “Experimental demonstration of relativistic self-channeling of a multiterrawatt laser pulse in an underdence plasma,” Phys. Rev. Lett. 74, 2953 (1995).
[CrossRef] [PubMed]

Babiou, D. M.

Barthelemy, A.

Bashaw, M.

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 (1994).
[CrossRef] [PubMed]

Bjorkholm, J. E.

J. E. Bjorkholm and A. Ashkin, “Cw self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32, 129 (1974).
[CrossRef]

Blair, S.

Borisov, A. B.

A. B. Borisov, A. V. Borovskij, O. B. Shiryaev, V. V. Korobkin, A. M. Prokhorov, I. C. Solem, T. S. Luk, K. Boyer, and C. K. Rhodes, “Relativistic charge-displacement self-channeling of intense ultrashort laser pulses in plasmas,” Phys. Rev. A 45, 5830 (1992).
[CrossRef] [PubMed]

A. B. Borisov, A. V. Borovskij, V. V. Korobkin, A. M. Prokhorov, O. B. Shiryaev, X. M. Shi, T. S. Luk, A. McPherson, I. C. Solem, K. Boyer, and C. K. Rhodes, “Observation of relativistic and charge displacement self-channeling of intense subpicosecond UV-radiation in plasmas,” Phys. Rev. Lett. 68, 2309 (1992).
[CrossRef] [PubMed]

Borovskij, A. V.

A. B. Borisov, A. V. Borovskij, V. V. Korobkin, A. M. Prokhorov, O. B. Shiryaev, X. M. Shi, T. S. Luk, A. McPherson, I. C. Solem, K. Boyer, and C. K. Rhodes, “Observation of relativistic and charge displacement self-channeling of intense subpicosecond UV-radiation in plasmas,” Phys. Rev. Lett. 68, 2309 (1992).
[CrossRef] [PubMed]

A. B. Borisov, A. V. Borovskij, O. B. Shiryaev, V. V. Korobkin, A. M. Prokhorov, I. C. Solem, T. S. Luk, K. Boyer, and C. K. Rhodes, “Relativistic charge-displacement self-channeling of intense ultrashort laser pulses in plasmas,” Phys. Rev. A 45, 5830 (1992).
[CrossRef] [PubMed]

Boyer, K.

A. B. Borisov, A. V. Borovskij, O. B. Shiryaev, V. V. Korobkin, A. M. Prokhorov, I. C. Solem, T. S. Luk, K. Boyer, and C. K. Rhodes, “Relativistic charge-displacement self-channeling of intense ultrashort laser pulses in plasmas,” Phys. Rev. A 45, 5830 (1992).
[CrossRef] [PubMed]

A. B. Borisov, A. V. Borovskij, V. V. Korobkin, A. M. Prokhorov, O. B. Shiryaev, X. M. Shi, T. S. Luk, A. McPherson, I. C. Solem, K. Boyer, and C. K. Rhodes, “Observation of relativistic and charge displacement self-channeling of intense subpicosecond UV-radiation in plasmas,” Phys. Rev. Lett. 68, 2309 (1992).
[CrossRef] [PubMed]

Braun, A.

Brewer, B. G.

T. K. Gustafson, P. C. Kelley, B. Y. Chiao, and B. G. Brewer, “Self-trapping in media with saturation of nonlinear index,” Appl. Phys. Lett. 12, 165 (1968).
[CrossRef]

Carvalho, M. I.

Chiao, B. Y.

T. K. Gustafson, P. C. Kelley, B. Y. Chiao, and B. G. Brewer, “Self-trapping in media with saturation of nonlinear index,” Appl. Phys. Lett. 12, 165 (1968).
[CrossRef]

Christodoulides, D. N.

Christov, J.

V. Tikhonenko, J. Christov, and B. Luther-Davies, “Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

Crosignani, B.

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

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

G. Duree, J. L. Shultz, G. 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]

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

Dawes, E. L.

E. L. Dawes and J. H. Marburger, “Computer studies in self-focusing,” Phys. Rev. 179, 862 (1969).
[CrossRef]

J. H. Marburger and E. L. Dawes, “Dynamic formation of a small-scale filament,” Phys. Rev. Lett. 21, 556 (1968).
[CrossRef]

Desailly, R.

S. Maneuf, R. Desailly, and C. Froehly, “Stable self-trapping of laser beams: observation in a nonlinear planar waveguide,” Opt. Commun. 65, 193 (1988).
[CrossRef]

Di Porto, D.

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

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

Di Porto, P.

G. Duree, J. L. Shultz, G. 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]

Du, D.

Duliev, A.

P. Monot, T. Auguste, P. Gibbon, F. Jakober, G. Mainfray, A. Duliev, M. Louis-Jacquet, G. Malka, and I. L. Miguel, “Experimental demonstration of relativistic self-channeling of a multiterrawatt laser pulse in an underdence plasma,” Phys. Rev. Lett. 74, 2953 (1995).
[CrossRef] [PubMed]

Duree, G.

G. Duree, J. L. Shultz, G. 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]

Fejer, M. M.

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 (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]

Froehly, C.

S. Maneuf, R. Desailly, and C. Froehly, “Stable self-trapping of laser beams: observation in a nonlinear planar waveguide,” Opt. Commun. 65, 193 (1988).
[CrossRef]

Garcia Quirino, G. S.

G. S. Garcia Quirino, M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Interferometric measurements of the photoinduced refractive index profiles in photorefractive Bi12TiO20 crystals,” Opt. Commun. 123, 592 (1996).
[CrossRef]

Garrett, M. H.

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 (1996).
[CrossRef] [PubMed]

M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salomo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons and induced waveguides,” in Quantum Electronics and Laser Science Conference (QELS’96) Vol. 10 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 209.

Gatz, S.

S. Gatz and J. Herrmann, “Soliton propagation and soliton collision in double-doped fibers with a non-Kerr-like nonlinear refractive-index change,” Opt. Lett. 17, 484 (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 (1992).
[CrossRef]

S. Gatz and J. Herrmann, “Soliton propagation in materials with saturable nonlinearity,” J. Opt. Soc. Am. B 8, 2296 (1991).
[CrossRef]

S. Gatz and J. Herrmann, “Propagation, collision and fusion of spatial optical solitons in three-dimensional media with saturable nonlinear refractive index change,” in Quantum Electronics and Laser Science Conference (QELS’96), Vol. 10 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 210.

Gibbon, P.

P. Monot, T. Auguste, P. Gibbon, F. Jakober, G. Mainfray, A. Duliev, M. Louis-Jacquet, G. Malka, and I. L. Miguel, “Experimental demonstration of relativistic self-channeling of a multiterrawatt laser pulse in an underdence plasma,” Phys. Rev. Lett. 74, 2953 (1995).
[CrossRef] [PubMed]

Grishkowsky, D.

D. Grishkowsky, “Self-focusing of light in potassium vapor,” Phys. Rev. Lett. 24, 868 (1970).

Gustafson, T. K.

T. K. Gustafson, P. C. Kelley, B. Y. Chiao, and B. G. Brewer, “Self-trapping in media with saturation of nonlinear index,” Appl. Phys. Lett. 12, 165 (1968).
[CrossRef]

Hagan, D. J.

W. Torruellas, Z. Wang, D. J. Hagan, E. W. van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Haus, H. H.

W. G. Wagner, H. H. Haus, and J. H. Marburger, “Large-scale self-trapping of optical beam in the paraxial ray approximation,” Phys. Rev. 175, 256 (1968).
[CrossRef]

Hayata, K.

K. Hayata and M. Koshiba, “Multidimensional solitons in quadratic nonlinear medium,” Phys. Rev. Lett. 71, 3275 (1993).
[CrossRef] [PubMed]

Henz, S.

S. Henz and J. Herrmann, “Two-dimensional spatial optical solitons in bulk Kerr-media stabilized by self-induced photoionization,” Phys. Rev. E 53, 4092 (1996).
[CrossRef]

Herrmann, J.

S. Henz and J. Herrmann, “Two-dimensional spatial optical solitons in bulk Kerr-media stabilized by self-induced photoionization,” Phys. Rev. E 53, 4092 (1996).
[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 (1992).
[CrossRef]

S. Gatz and J. Herrmann, “Soliton propagation and soliton collision in double-doped fibers with a non-Kerr-like nonlinear refractive-index change,” Opt. Lett. 17, 484 (1992).
[CrossRef] [PubMed]

J. Herrmann, “Bistable bright solitons in dispersive media with a linear and quadratic intensity-depending refraction index change,” Opt. Commun. 87, 161 (1992).
[CrossRef]

S. Gatz and J. Herrmann, “Soliton propagation in materials with saturable nonlinearity,” J. Opt. Soc. Am. B 8, 2296 (1991).
[CrossRef]

S. Gatz and J. Herrmann, “Propagation, collision and fusion of spatial optical solitons in three-dimensional media with saturable nonlinear refractive index change,” in Quantum Electronics and Laser Science Conference (QELS’96), Vol. 10 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 210.

Huff, L.

J. H. Marburger, L. Huff, J. D. Reichert, and W. G. Wagner, “Stationary self-trapping of optical beams in dense media with Lorentz local-field corrections,” Phys. Rev. 184, 255 (1968).
[CrossRef]

Islam, M. N.

Iturbe-Castillo, M. D.

G. S. Garcia Quirino, M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Interferometric measurements of the photoinduced refractive index profiles in photorefractive Bi12TiO20 crystals,” Opt. Commun. 123, 592 (1996).
[CrossRef]

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. I. Stepanov, and V. A. Vysloukh, “Spatial soliton in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Jakober, F.

P. Monot, T. Auguste, P. Gibbon, F. Jakober, G. Mainfray, A. Duliev, M. Louis-Jacquet, G. Malka, and I. L. Miguel, “Experimental demonstration of relativistic self-channeling of a multiterrawatt laser pulse in an underdence plasma,” Phys. Rev. Lett. 74, 2953 (1995).
[CrossRef] [PubMed]

Kang, I. U.

Karamzin, K. N.

K. N. Karamzin and A. P. Sukhorukov, Pisma Zh. Eksp. Teor. Fiz. 20, 774 (1974) [JETP Lett. 20, 339 (1974)].

Karlson, M.

M. Karlson, “Optical beams in saturable self-focusing media,” Phys. Rev. A 46, 2726 (1992).
[CrossRef]

Kelley, P. C.

T. K. Gustafson, P. C. Kelley, B. Y. Chiao, and B. G. Brewer, “Self-trapping in media with saturation of nonlinear index,” Appl. Phys. Lett. 12, 165 (1968).
[CrossRef]

Kolokolov, A. A.

N. G. Vakhitov and A. A. Kolokolov, “Stability of stationary solutions of nonlinear wave equations,” Radiophys. Quantum Electron. 16, 783 (1975).
[CrossRef]

Koono, V.

V. Koono and H. Suzuki, Phys. Scr. 20, 382 (1979).
[CrossRef]

Korn, G.

Korobkin, V. V.

A. B. Borisov, A. V. Borovskij, O. B. Shiryaev, V. V. Korobkin, A. M. Prokhorov, I. C. Solem, T. S. Luk, K. Boyer, and C. K. Rhodes, “Relativistic charge-displacement self-channeling of intense ultrashort laser pulses in plasmas,” Phys. Rev. A 45, 5830 (1992).
[CrossRef] [PubMed]

A. B. Borisov, A. V. Borovskij, V. V. Korobkin, A. M. Prokhorov, O. B. Shiryaev, X. M. Shi, T. S. Luk, A. McPherson, I. C. Solem, K. Boyer, and C. K. Rhodes, “Observation of relativistic and charge displacement self-channeling of intense subpicosecond UV-radiation in plasmas,” Phys. Rev. Lett. 68, 2309 (1992).
[CrossRef] [PubMed]

Koshiba, M.

K. Hayata and M. Koshiba, “Multidimensional solitons in quadratic nonlinear medium,” Phys. Rev. Lett. 71, 3275 (1993).
[CrossRef] [PubMed]

Kuktarev, N.

N. Kuktarev, Sov. Tech. Phys. Lett. 2, 438 (1976).

Lam, J. F.

J. F. Lam, B. Lippmann, and F. Tappert, “Moment theory of self-trapped laser beams with nonlinear saturation,” Opt. Commun. 15, 419 (1975).
[CrossRef]

Langdon, A. B.

C. E. Max, J. Arons, and A. B. Langdon, “Self-modulation and self-focusing of electromagnetic waves in plasmas,” Phys. Rev. Lett. 33, 209 (1974).
[CrossRef]

Lawrence, B. L.

Leach, P.

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 (1996).
[CrossRef] [PubMed]

M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salomo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons and induced waveguides,” in Quantum Electronics and Laser Science Conference (QELS’96) Vol. 10 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 209.

Lippmann, B.

J. F. Lam, B. Lippmann, and F. Tappert, “Moment theory of self-trapped laser beams with nonlinear saturation,” Opt. Commun. 15, 419 (1975).
[CrossRef]

Liu, X.

Louis-Jacquet, M.

P. Monot, T. Auguste, P. Gibbon, F. Jakober, G. Mainfray, A. Duliev, M. Louis-Jacquet, G. Malka, and I. L. Miguel, “Experimental demonstration of relativistic self-channeling of a multiterrawatt laser pulse in an underdence plasma,” Phys. Rev. Lett. 74, 2953 (1995).
[CrossRef] [PubMed]

Luk, T. S.

A. B. Borisov, A. V. Borovskij, O. B. Shiryaev, V. V. Korobkin, A. M. Prokhorov, I. C. Solem, T. S. Luk, K. Boyer, and C. K. Rhodes, “Relativistic charge-displacement self-channeling of intense ultrashort laser pulses in plasmas,” Phys. Rev. A 45, 5830 (1992).
[CrossRef] [PubMed]

A. B. Borisov, A. V. Borovskij, V. V. Korobkin, A. M. Prokhorov, O. B. Shiryaev, X. M. Shi, T. S. Luk, A. McPherson, I. C. Solem, K. Boyer, and C. K. Rhodes, “Observation of relativistic and charge displacement self-channeling of intense subpicosecond UV-radiation in plasmas,” Phys. Rev. Lett. 68, 2309 (1992).
[CrossRef] [PubMed]

Luther-Davies, B.

V. Tikhonenko, J. Christov, and B. Luther-Davies, “Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

Mainfray, G.

P. Monot, T. Auguste, P. Gibbon, F. Jakober, G. Mainfray, A. Duliev, M. Louis-Jacquet, G. Malka, and I. L. Miguel, “Experimental demonstration of relativistic self-channeling of a multiterrawatt laser pulse in an underdence plasma,” Phys. Rev. Lett. 74, 2953 (1995).
[CrossRef] [PubMed]

Malka, G.

P. Monot, T. Auguste, P. Gibbon, F. Jakober, G. Mainfray, A. Duliev, M. Louis-Jacquet, G. Malka, and I. L. Miguel, “Experimental demonstration of relativistic self-channeling of a multiterrawatt laser pulse in an underdence plasma,” Phys. Rev. Lett. 74, 2953 (1995).
[CrossRef] [PubMed]

Maneuf, S.

S. Maneuf, R. Desailly, and C. Froehly, “Stable self-trapping of laser beams: observation in a nonlinear planar waveguide,” Opt. Commun. 65, 193 (1988).
[CrossRef]

Marburger, J. H.

For a comprehensive review, see J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

E. L. Dawes and J. H. Marburger, “Computer studies in self-focusing,” Phys. Rev. 179, 862 (1969).
[CrossRef]

W. G. Wagner, H. H. Haus, and J. H. Marburger, “Large-scale self-trapping of optical beam in the paraxial ray approximation,” Phys. Rev. 175, 256 (1968).
[CrossRef]

J. H. Marburger and E. L. Dawes, “Dynamic formation of a small-scale filament,” Phys. Rev. Lett. 21, 556 (1968).
[CrossRef]

J. H. Marburger, L. Huff, J. D. Reichert, and W. G. Wagner, “Stationary self-trapping of optical beams in dense media with Lorentz local-field corrections,” Phys. Rev. 184, 255 (1968).
[CrossRef]

Marquez-Aguilar, P. A.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. I. Stepanov, and V. A. Vysloukh, “Spatial soliton in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Max, C. E.

C. E. Max, J. Arons, and A. B. Langdon, “Self-modulation and self-focusing of electromagnetic waves in plasmas,” Phys. Rev. Lett. 33, 209 (1974).
[CrossRef]

McLeod, R.

McPherson, A.

A. B. Borisov, A. V. Borovskij, V. V. Korobkin, A. M. Prokhorov, O. B. Shiryaev, X. M. Shi, T. S. Luk, A. McPherson, I. C. Solem, K. Boyer, and C. K. Rhodes, “Observation of relativistic and charge displacement self-channeling of intense subpicosecond UV-radiation in plasmas,” Phys. Rev. Lett. 68, 2309 (1992).
[CrossRef] [PubMed]

Menyuk, C. R.

W. Torruellas, Z. Wang, D. J. Hagan, E. W. van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Miguel, I. L.

P. Monot, T. Auguste, P. Gibbon, F. Jakober, G. Mainfray, A. Duliev, M. Louis-Jacquet, G. Malka, and I. L. Miguel, “Experimental demonstration of relativistic self-channeling of a multiterrawatt laser pulse in an underdence plasma,” Phys. Rev. Lett. 74, 2953 (1995).
[CrossRef] [PubMed]

Monot, P.

P. Monot, T. Auguste, P. Gibbon, F. Jakober, G. Mainfray, A. Duliev, M. Louis-Jacquet, G. Malka, and I. L. Miguel, “Experimental demonstration of relativistic self-channeling of a multiterrawatt laser pulse in an underdence plasma,” Phys. Rev. Lett. 74, 2953 (1995).
[CrossRef] [PubMed]

Mourou, G.

Neurgaonkar, R. R.

G. Duree, J. L. Shultz, G. 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]

Petrishehev, V. A.

S. N. Vlasov, V. A. Petrishehev, and V. I. Talanov, Radiophys. Quantum Electron. 14, 1062 (1971).
[CrossRef]

Prokhorov, A. M.

A. B. Borisov, A. V. Borovskij, V. V. Korobkin, A. M. Prokhorov, O. B. Shiryaev, X. M. Shi, T. S. Luk, A. McPherson, I. C. Solem, K. Boyer, and C. K. Rhodes, “Observation of relativistic and charge displacement self-channeling of intense subpicosecond UV-radiation in plasmas,” Phys. Rev. Lett. 68, 2309 (1992).
[CrossRef] [PubMed]

A. B. Borisov, A. V. Borovskij, O. B. Shiryaev, V. V. Korobkin, A. M. Prokhorov, I. C. Solem, T. S. Luk, K. Boyer, and C. K. Rhodes, “Relativistic charge-displacement self-channeling of intense ultrashort laser pulses in plasmas,” Phys. Rev. A 45, 5830 (1992).
[CrossRef] [PubMed]

Rasmussen, J. J.

For a comprehensive review article, see J. J. Rasmussen and K. Rypdal, “Blow up in nonlinear Schrödinger equations: a general review,” Phys. Scr. 33, 491 (1986).
[CrossRef]

Reichert, J. D.

J. D. Reichert and W. G. Wagner, “Self-trapped optical beams in liquids,” IEEE J. Quantum Electron. QE4, 221 (1968).
[CrossRef]

J. H. Marburger, L. Huff, J. D. Reichert, and W. G. Wagner, “Stationary self-trapping of optical beams in dense media with Lorentz local-field corrections,” Phys. Rev. 184, 255 (1968).
[CrossRef]

Rhodes, C. K.

A. B. Borisov, A. V. Borovskij, O. B. Shiryaev, V. V. Korobkin, A. M. Prokhorov, I. C. Solem, T. S. Luk, K. Boyer, and C. K. Rhodes, “Relativistic charge-displacement self-channeling of intense ultrashort laser pulses in plasmas,” Phys. Rev. A 45, 5830 (1992).
[CrossRef] [PubMed]

A. B. Borisov, A. V. Borovskij, V. V. Korobkin, A. M. Prokhorov, O. B. Shiryaev, X. M. Shi, T. S. Luk, A. McPherson, I. C. Solem, K. Boyer, and C. K. Rhodes, “Observation of relativistic and charge displacement self-channeling of intense subpicosecond UV-radiation in plasmas,” Phys. Rev. Lett. 68, 2309 (1992).
[CrossRef] [PubMed]

Rypdal, K.

For a comprehensive review article, see J. J. Rasmussen and K. Rypdal, “Blow up in nonlinear Schrödinger equations: a general review,” Phys. Scr. 33, 491 (1986).
[CrossRef]

Salamo, G.

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 (1996).
[CrossRef] [PubMed]

M. Shih, M. Segev, and G. Salamo, “Circular waveguides induced by two-dimensional bright steady-state photorefractive partial screening solitons,” Opt. Lett. 21, 1 (1996).

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

G. Duree, J. L. Shultz, G. 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]

Salomo, G.

M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salomo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons and induced waveguides,” in Quantum Electronics and Laser Science Conference (QELS’96) Vol. 10 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 209.

Sanchez-Mondragon, J. J.

G. S. Garcia Quirino, M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Interferometric measurements of the photoinduced refractive index profiles in photorefractive Bi12TiO20 crystals,” Opt. Commun. 123, 592 (1996).
[CrossRef]

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. I. Stepanov, and V. A. Vysloukh, “Spatial soliton in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Segev, M.

M. Shih, M. Segev, and G. Salamo, “Circular waveguides induced by two-dimensional bright steady-state photorefractive partial screening solitons,” Opt. Lett. 21, 1 (1996).

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 (1996).
[CrossRef] [PubMed]

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

M. Segev, G. Valley, 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, D. 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. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457 (1994).
[CrossRef] [PubMed]

G. Duree, J. L. Shultz, G. 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]

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

M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salomo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons and induced waveguides,” in Quantum Electronics and Laser Science Conference (QELS’96) Vol. 10 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 209.

Shabat, A. B.

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

Shalaby, M.

Sharp, E. J.

G. Duree, J. L. Shultz, G. 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]

Shen, Y. R.

Y. R. Shen, “Self-focusing: experimental,” Prog. Quantum Electron. 4, 1 (1975).
[CrossRef]

Shi, X. M.

A. B. Borisov, A. V. Borovskij, V. V. Korobkin, A. M. Prokhorov, O. B. Shiryaev, X. M. Shi, T. S. Luk, A. McPherson, I. C. Solem, K. Boyer, and C. K. Rhodes, “Observation of relativistic and charge displacement self-channeling of intense subpicosecond UV-radiation in plasmas,” Phys. Rev. Lett. 68, 2309 (1992).
[CrossRef] [PubMed]

Shih, M.

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 (1996).
[CrossRef] [PubMed]

M. Shih, M. Segev, and G. Salamo, “Circular waveguides induced by two-dimensional bright steady-state photorefractive partial screening solitons,” Opt. Lett. 21, 1 (1996).

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

M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salomo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons and induced waveguides,” in Quantum Electronics and Laser Science Conference (QELS’96) Vol. 10 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 209.

Shiryaev, O. B.

A. B. Borisov, A. V. Borovskij, V. V. Korobkin, A. M. Prokhorov, O. B. Shiryaev, X. M. Shi, T. S. Luk, A. McPherson, I. C. Solem, K. Boyer, and C. K. Rhodes, “Observation of relativistic and charge displacement self-channeling of intense subpicosecond UV-radiation in plasmas,” Phys. Rev. Lett. 68, 2309 (1992).
[CrossRef] [PubMed]

A. B. Borisov, A. V. Borovskij, O. B. Shiryaev, V. V. Korobkin, A. M. Prokhorov, I. C. Solem, T. S. Luk, K. Boyer, and C. K. Rhodes, “Relativistic charge-displacement self-channeling of intense ultrashort laser pulses in plasmas,” Phys. Rev. A 45, 5830 (1992).
[CrossRef] [PubMed]

Shultz, J. L.

G. Duree, J. L. Shultz, G. 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, M. I. Carvalho, and D. N. Christodoulides, “Higher-order space charge field effects on the evolution of spatial solitons in biased photorefractive crystals,” Opt. Commun. 130, 288 (1996).
[CrossRef]

Solem, I. C.

A. B. Borisov, A. V. Borovskij, O. B. Shiryaev, V. V. Korobkin, A. M. Prokhorov, I. C. Solem, T. S. Luk, K. Boyer, and C. K. Rhodes, “Relativistic charge-displacement self-channeling of intense ultrashort laser pulses in plasmas,” Phys. Rev. A 45, 5830 (1992).
[CrossRef] [PubMed]

A. B. Borisov, A. V. Borovskij, V. V. Korobkin, A. M. Prokhorov, O. B. Shiryaev, X. M. Shi, T. S. Luk, A. McPherson, I. C. Solem, K. Boyer, and C. K. Rhodes, “Observation of relativistic and charge displacement self-channeling of intense subpicosecond UV-radiation in plasmas,” Phys. Rev. Lett. 68, 2309 (1992).
[CrossRef] [PubMed]

Soto-Crespo, J. M.

J. M. Soto-Crespo, E. M. Wright, and N. N. Akhmediev, “Recurrence and azimuthal-symmetry breaking of a cylindrical Gaussian beam in a saturable self-focusing medium,” Phys. Rev. A 45, 3168 (1992).
[CrossRef] [PubMed]

Squier, J.

Stegeman, G.

Stegeman, G. I.

Stepanov, S.

G. S. Garcia Quirino, M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Interferometric measurements of the photoinduced refractive index profiles in photorefractive Bi12TiO20 crystals,” Opt. Commun. 123, 592 (1996).
[CrossRef]

Stepanov, S. I.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. I. Stepanov, and V. A. Vysloukh, “Spatial soliton in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Sukhorukov, A. P.

K. N. Karamzin and A. P. Sukhorukov, Pisma Zh. Eksp. Teor. Fiz. 20, 774 (1974) [JETP Lett. 20, 339 (1974)].

Suydam, B. B.

B. B. Suydam, “Self-focusing of very powerful laser beams. II,” IEEE J. Quantum Electron. QE-10, 837 (1974).
[CrossRef]

Suzuki, H.

V. Koono and H. Suzuki, Phys. Scr. 20, 382 (1979).
[CrossRef]

Talanov, V. I.

S. N. Vlasov, V. A. Petrishehev, and V. I. Talanov, Radiophys. Quantum Electron. 14, 1062 (1971).
[CrossRef]

Tappert, F.

J. F. Lam, B. Lippmann, and F. Tappert, “Moment theory of self-trapped laser beams with nonlinear saturation,” Opt. Commun. 15, 419 (1975).
[CrossRef]

Tikhonenko, V.

V. Tikhonenko, J. Christov, and B. Luther-Davies, “Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

Torner, L.

D. M. Babiou, G. I. Stegeman, and L. Torner, “Interaction of one-dimensional bright solitary waves in quadratic media,” Opt. Lett. 20, 2282 (1995).
[CrossRef]

W. Torruellas, Z. Wang, D. J. Hagan, E. W. van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Torruellas, W.

W. Torruellas, Z. Wang, D. J. Hagan, E. W. van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

E. W. Wright, B. L. Lawrence, W. Torruellas, and G. Stegeman, “Stable self-trapping and ring formation in polydiacetylene para-toluene sulfonate,” Opt. Lett. 20, 2481 (1995).
[CrossRef]

Vakhitov, N. G.

N. G. Vakhitov and A. A. Kolokolov, “Stability of stationary solutions of nonlinear wave equations,” Radiophys. Quantum Electron. 16, 783 (1975).
[CrossRef]

Valley, G.

Valley, G. C.

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 (1996).
[CrossRef] [PubMed]

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

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

M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salomo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons and induced waveguides,” in Quantum Electronics and Laser Science Conference (QELS’96) Vol. 10 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 209.

van Stryland, E. W.

W. Torruellas, Z. Wang, D. J. Hagan, E. W. van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Vlasov, S. N.

S. N. Vlasov, V. A. Petrishehev, and V. I. Talanov, Radiophys. Quantum Electron. 14, 1062 (1971).
[CrossRef]

Vysloukh, V.

G. S. Garcia Quirino, M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Interferometric measurements of the photoinduced refractive index profiles in photorefractive Bi12TiO20 crystals,” Opt. Commun. 123, 592 (1996).
[CrossRef]

Vysloukh, V. A.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. I. Stepanov, and V. A. Vysloukh, “Spatial soliton in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Wagner, K.

Wagner, W. G.

J. H. Marburger, L. Huff, J. D. Reichert, and W. G. Wagner, “Stationary self-trapping of optical beams in dense media with Lorentz local-field corrections,” Phys. Rev. 184, 255 (1968).
[CrossRef]

W. G. Wagner, H. H. Haus, and J. H. Marburger, “Large-scale self-trapping of optical beam in the paraxial ray approximation,” Phys. Rev. 175, 256 (1968).
[CrossRef]

J. D. Reichert and W. G. Wagner, “Self-trapped optical beams in liquids,” IEEE J. Quantum Electron. QE4, 221 (1968).
[CrossRef]

Wang, Z.

W. Torruellas, Z. Wang, D. J. Hagan, E. W. van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Wright, E. M.

J. M. Soto-Crespo, E. M. Wright, and N. N. Akhmediev, “Recurrence and azimuthal-symmetry breaking of a cylindrical Gaussian beam in a saturable self-focusing medium,” Phys. Rev. A 45, 3168 (1992).
[CrossRef] [PubMed]

Wright, E. W.

Yariv, A.

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 (1994).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, D. 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. Duree, J. L. Shultz, G. 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]

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

Zakharov, V. E.

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

Zozulya, A.

A. Zozulya and D. 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 (1995).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

T. K. Gustafson, P. C. Kelley, B. Y. Chiao, and B. G. Brewer, “Self-trapping in media with saturation of nonlinear index,” Appl. Phys. Lett. 12, 165 (1968).
[CrossRef]

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. I. Stepanov, and V. A. Vysloukh, “Spatial soliton 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 D. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826 (1995).
[CrossRef]

IEEE J. Quantum Electron. (3)

J. D. Reichert and W. G. Wagner, “Self-trapped optical beams in liquids,” IEEE J. Quantum Electron. QE4, 221 (1968).
[CrossRef]

B. B. Suydam, “Self-focusing of very powerful laser beams. II,” IEEE J. Quantum Electron. QE-10, 837 (1974).
[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 (1992).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (5)

J. F. Lam, B. Lippmann, and F. Tappert, “Moment theory of self-trapped laser beams with nonlinear saturation,” Opt. Commun. 15, 419 (1975).
[CrossRef]

S. Maneuf, R. Desailly, and C. Froehly, “Stable self-trapping of laser beams: observation in a nonlinear planar waveguide,” Opt. Commun. 65, 193 (1988).
[CrossRef]

G. S. Garcia Quirino, M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Interferometric measurements of the photoinduced refractive index profiles in photorefractive Bi12TiO20 crystals,” Opt. Commun. 123, 592 (1996).
[CrossRef]

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, “Higher-order space charge field effects on the evolution of spatial solitons in biased photorefractive crystals,” Opt. Commun. 130, 288 (1996).
[CrossRef]

J. Herrmann, “Bistable bright solitons in dispersive media with a linear and quadratic intensity-depending refraction index change,” Opt. Commun. 87, 161 (1992).
[CrossRef]

Opt. Lett. (12)

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

E. W. Wright, B. L. Lawrence, W. Torruellas, and G. Stegeman, “Stable self-trapping and ring formation in polydiacetylene para-toluene sulfonate,” Opt. Lett. 20, 2481 (1995).
[CrossRef]

S. Gatz and J. Herrmann, “Soliton propagation and soliton collision in double-doped fibers with a non-Kerr-like nonlinear refractive-index change,” Opt. Lett. 17, 484 (1992).
[CrossRef] [PubMed]

D. M. Babiou, G. I. Stegeman, and L. Torner, “Interaction of one-dimensional bright solitary waves in quadratic media,” Opt. Lett. 20, 2282 (1995).
[CrossRef]

M. N. Islam, “Ultrafast all-optical logic gates,” Opt. Lett. 14, 1257 (1989).
[CrossRef] [PubMed]

M. N. Islam, “All-optical cascadable nor gate with gain,” Opt. Lett. 15, 417 (1990).
[CrossRef] [PubMed]

M. Shalaby and A. Barthelemy, “Experimental spatial soliton trapping and switching,” Opt. Lett. 16, 1472 (1991).
[CrossRef] [PubMed]

S. Blair, K. Wagner, and R. McLeod, “Asymmetric spatial soliton dragging,” Opt. Lett. 19, 1943 (1994).
[CrossRef] [PubMed]

I. U. Kang, G. I. Stegeman, and J. C. Aitchinson, “One-dimensional spatial soliton dragging, trapping, and all-optical switching in AlGaAs waveguides,” Opt. Lett. 21, 189 (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 (1996).
[CrossRef] [PubMed]

M. Shih, M. Segev, and G. Salamo, “Circular waveguides induced by two-dimensional bright steady-state photorefractive partial screening solitons,” Opt. Lett. 21, 1 (1996).

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20, 73 (1995).
[CrossRef] [PubMed]

Phys. Rev. (3)

E. L. Dawes and J. H. Marburger, “Computer studies in self-focusing,” Phys. Rev. 179, 862 (1969).
[CrossRef]

J. H. Marburger, L. Huff, J. D. Reichert, and W. G. Wagner, “Stationary self-trapping of optical beams in dense media with Lorentz local-field corrections,” Phys. Rev. 184, 255 (1968).
[CrossRef]

W. G. Wagner, H. H. Haus, and J. H. Marburger, “Large-scale self-trapping of optical beam in the paraxial ray approximation,” Phys. Rev. 175, 256 (1968).
[CrossRef]

Phys. Rev. A (5)

M. Karlson, “Optical beams in saturable self-focusing media,” Phys. Rev. A 46, 2726 (1992).
[CrossRef]

J. M. Soto-Crespo, E. M. Wright, and N. N. Akhmediev, “Recurrence and azimuthal-symmetry breaking of a cylindrical Gaussian beam in a saturable self-focusing medium,” Phys. Rev. A 45, 3168 (1992).
[CrossRef] [PubMed]

A. B. Borisov, A. V. Borovskij, O. B. Shiryaev, V. V. Korobkin, A. M. Prokhorov, I. C. Solem, T. S. Luk, K. Boyer, and C. K. Rhodes, “Relativistic charge-displacement self-channeling of intense ultrashort laser pulses in plasmas,” Phys. Rev. A 45, 5830 (1992).
[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 (1994).
[CrossRef] [PubMed]

A. Zozulya and D. 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 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (1)

S. Henz and J. Herrmann, “Two-dimensional spatial optical solitons in bulk Kerr-media stabilized by self-induced photoionization,” Phys. Rev. E 53, 4092 (1996).
[CrossRef]

Phys. Rev. Lett. (12)

A. B. Borisov, A. V. Borovskij, V. V. Korobkin, A. M. Prokhorov, O. B. Shiryaev, X. M. Shi, T. S. Luk, A. McPherson, I. C. Solem, K. Boyer, and C. K. Rhodes, “Observation of relativistic and charge displacement self-channeling of intense subpicosecond UV-radiation in plasmas,” Phys. Rev. Lett. 68, 2309 (1992).
[CrossRef] [PubMed]

P. Monot, T. Auguste, P. Gibbon, F. Jakober, G. Mainfray, A. Duliev, M. Louis-Jacquet, G. Malka, and I. L. Miguel, “Experimental demonstration of relativistic self-channeling of a multiterrawatt laser pulse in an underdence plasma,” Phys. Rev. Lett. 74, 2953 (1995).
[CrossRef] [PubMed]

K. Hayata and M. Koshiba, “Multidimensional solitons in quadratic nonlinear medium,” Phys. Rev. Lett. 71, 3275 (1993).
[CrossRef] [PubMed]

W. Torruellas, Z. Wang, D. J. Hagan, E. W. van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[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. Duree, J. L. Shultz, G. 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]

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

D. Grishkowsky, “Self-focusing of light in potassium vapor,” Phys. Rev. Lett. 24, 868 (1970).

J. E. Bjorkholm and A. Ashkin, “Cw self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32, 129 (1974).
[CrossRef]

C. E. Max, J. Arons, and A. B. Langdon, “Self-modulation and self-focusing of electromagnetic waves in plasmas,” Phys. Rev. Lett. 33, 209 (1974).
[CrossRef]

J. H. Marburger and E. L. Dawes, “Dynamic formation of a small-scale filament,” Phys. Rev. Lett. 21, 556 (1968).
[CrossRef]

V. Tikhonenko, J. Christov, and B. Luther-Davies, “Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

Phys. Scr. (2)

For a comprehensive review article, see J. J. Rasmussen and K. Rypdal, “Blow up in nonlinear Schrödinger equations: a general review,” Phys. Scr. 33, 491 (1986).
[CrossRef]

V. Koono and H. Suzuki, Phys. Scr. 20, 382 (1979).
[CrossRef]

Pisma Zh. Eksp. Teor. Fiz. (1)

K. N. Karamzin and A. P. Sukhorukov, Pisma Zh. Eksp. Teor. Fiz. 20, 774 (1974) [JETP Lett. 20, 339 (1974)].

Prog. Quantum Electron. (2)

For a comprehensive review, see J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Y. R. Shen, “Self-focusing: experimental,” Prog. Quantum Electron. 4, 1 (1975).
[CrossRef]

Radiophys. Quantum Electron. (2)

S. N. Vlasov, V. A. Petrishehev, and V. I. Talanov, Radiophys. Quantum Electron. 14, 1062 (1971).
[CrossRef]

N. G. Vakhitov and A. A. Kolokolov, “Stability of stationary solutions of nonlinear wave equations,” Radiophys. Quantum Electron. 16, 783 (1975).
[CrossRef]

Sov. Tech. Phys. Lett. (1)

N. Kuktarev, Sov. Tech. Phys. Lett. 2, 438 (1976).

Zh. Eksp. Teor. Fiz. (1)

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

Other (3)

P. Günter and J.-P. Huignard, eds., Photorefractive Materials and their Application (Springer-Verlag, New York, 1988).

M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salomo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons and induced waveguides,” in Quantum Electronics and Laser Science Conference (QELS’96) Vol. 10 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 209.

S. Gatz and J. Herrmann, “Propagation, collision and fusion of spatial optical solitons in three-dimensional media with saturable nonlinear refractive index change,” in Quantum Electronics and Laser Science Conference (QELS’96), Vol. 10 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 210.

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 (14)

Fig. 1
Fig. 1

Dependence of the amplitude (dashed curve) and the normalized soliton power (solid curve) on normalized saturation parameter γ.

Fig. 2
Fig. 2

(a) Shapes of the solitons (dashed curves) of the upper and the lower solution branches for γ=0.5 and corresponding Gaussian beams with the same power (solid curves).

Fig. 3
Fig. 3

Dependence of the normalized power on phase-propagation constant β.

Fig. 4
Fig. 4

Dependence of inner energy HI on soliton power P.

Fig. 5
Fig. 5

Evolution of a Gaussian input beam with soliton power of the lower solution branch for γ=0.5.

Fig. 6
Fig. 6

Evolution of the on-axis intensities ρ(ξ) for Gaussian input beams (solid curves) or soliton input beams (dashed curves) for different powers P for γ=0.5: (a) P=12.4 (soliton power of the lower solution branch), (b) P=40.9, (c) P=79.7 (soliton power of the upper solution branch), and (d) P=291.

Fig. 7
Fig. 7

Evolution of the on-axis intensities ρ(ξ) for Gaussian input beams (solid curves) or soliton input beams (dashed lines) for different powers P for γ=0.16: (a) P=6.8 (soliton power of the lower solution branch), (b) P=454, (c) P=2.24×103 (soliton power of the upper solution branch), and (d) P=4.08 ×103.

Fig. 8
Fig. 8

Evolution of the on-axis intensities for Gaussian input beams (solid curves) or soliton input beams (dashed line) for different powers P for γ=0.01: (a) P=5.9 (soliton power of the lower solution branch) and (b) P=18.1.

Fig. 9
Fig. 9

Beam evolution of a Gaussian input beam with ρ0=25 for γ=0.01. Field intensity profiles as a function or the transverse coordinates for (a) ξ=0 (input), (b) ξ=0.375, (c) ξ=0.75, and (d) ξ=1.

Fig. 10
Fig. 10

Interaction of two parallel solitons (Θ=0) of the lower solution branch with equal phases (φ0=0) and an initial separation 2x0=10.

Fig. 11
Fig. 11

Collision of two solitons of the upper solution branch for collision angle Θ=0.1 with phases (a) φ0=0, (b) φ0=-0.1, and (c) φ0=-1.

Fig. 12
Fig. 12

Collision of two solitons of the upper solution branch for collision angle Θ=0.5 with phases (a) φ0=0 and (b) φ0=-1.

Fig. 13
Fig. 13

Collision of two solitons of the lower solution branch for collision angle Θ=0.1 with phases (a) φ0=0 and (b) φ0 =-0.1 and (c) for a collision angle Θ=0.5 with phase Θ=0.

Fig. 14
Fig. 14

Demonstration of solution dragging for parameters γ=0.5, Θ=0.5, and φ0=0. In curve 2 the evolution of the signal soliton without the pump soliton is shown.

Equations (20)

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

-iAz+12k2Ax2+2Ay2=kΔn(I)n0A,
Δn=Δn011+|A|2/Isat.
-iψξ+122ψx2+2ψy2+f(|ψ|2)ψ=0,
f(|ψ|2)=|ψ|21+γ|ψ|2,
γ=-n0k2w02Δn0,Δn0<0.
ψ˜(ξ, x, y, γ)=σψ(σ2ξ, σx, σy, γ),
Φξ+18-1ρ2ρs2+2ρ2ρs2-4Φs2+2ρsρs
+f(ρ)=0,
-ρξ+sρΦs+ρsΦs=0.
ρs2=8ρG(s)-1s20sG(s)2sds
ρ(s)=ρ(0)exp-0s8ρG(s)-1s20sG(s)2sds1/2ds.
β=0F[ρ(s)]sds0ρ(s)sds=0ργ-ln(1+γρ)γ2sds0ρ(s)sds.
wmin=1.3k-n0Δn01/2.
Θx=-ρΦxdxdy,Θx=-ρΦxdxdy.
H=-[ψx2+ψy2-2F(|ψ|2)]dxdy
HI=-14ρρx2+ρy2-2F(ρ)dxdy,
Hkin=- ρΦx2+Φy2dxdy.
ψ(ξ=0, s)=[1+R(x, y)]ρ0 exp(-s2 ln 2),
ψ(ξ=0, x, y)=ψs(x-x0, y)exp[i(Θx-φ0)]
+ψs(x+x0, y)×exp[-i(Θx-φ0)],

Metrics