Abstract

We present experimental results on the transverse modulation instability of an elliptical beam propagating in a bulk nonlinear Kerr medium, and the formation and self-organization of spatial solitons. We have observed the emergence of order, self organization and a transition to an unstable state. Order emerges through the formation of spatial solitons in a periodic array. If the initial period of the array is unstable the solitons will tend to self-organize into a larger (more stable) period. Finally the system transitions to a disordered state where most of the solitons disappear and the beam profile becomes unstable to small changes in the input energy.

© 2005 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Femtosecond laser filament array generated with step phase plate in air

Hui Gao, Wei Chu, Guoliang Yu, Bin Zeng, Jiayu Zhao, Zhi Wang, Weiwei Liu, Ya Cheng, and Zhizhan Xu
Opt. Express 21(4) 4612-4622 (2013)

A simple method for determination of nonlinear propagation regimes in gases

Selcuk Akturk, Ciro D’Amico, Michel Franco, Arnaud Couairon, and Andre Mysyrowicz
Opt. Express 15(23) 15260-15267 (2007)

Direct phase and amplitude characterization of femtosecond laser pulses undergoing filamentation in air

Johanan Odhner and Robert J. Levis
Opt. Lett. 37(10) 1775-1777 (2012)

References

  • View by:
  • |
  • |
  • |

  1. Y. Kivshar and D. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331, 118–195 (2000).
    [Crossref]
  2. V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Sov. Phys. JETP 38, 494–500 (1974).
  3. M. Saffman, G. McCarthy, and W. Krolikowski, “Two-dimensional modulational instability in photorefractive media,” J. Opt. Soc. Am. B. 6, 387–403 (2004).
  4. H. Maillotte, J. Monneret, A. Barthelemy, and C. Froehly, “Laser beam self-splitting into solitons by optical Kerr nonlinearity,” Opt. Commun. 109, 265–271 (1994)
    [Crossref]
  5. R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997);
    [Crossref]
  6. D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
    [Crossref] [PubMed]
  7. B. Crosignani and P. Di Porto, “Nonlinear propagation in Kerr media of beams with unequal transverse widths,” Opt. Lett. 18, 1394–1396 (1993);
    [Crossref] [PubMed]
  8. A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Break-up of two-dimensional bright spatial solitons due to transverse modulation instability,” Europhys. Lett. 35, 25–30 (1996);
    [Crossref]
  9. G. Fibich and B. Ilan, “Self-focusing of elliptic beams: an example of the failure of the aberrationless approximation,” J. Opt. Soc. Am. B 17, 1749–1758 (2000);
    [Crossref]
  10. A. Dubietis, G. Tamogauskas, G. Fibich G, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity”, Opt. Lett. 29, 1126–1128 (2004);
    [Crossref] [PubMed]
  11. R. Malendevich, L. Jankovic, G. Stegeman, and J. S. Aitchison, “Spatial modulation instability in a Kerr slab waveguide,” Opt. Lett. 26, 1879–1881 (2001);
    [Crossref]
  12. C. Cambournac, H. Maillotte, E. Lantz, J. M. Dudley, and M. Chauvet, “Spatiotemporal behavior of periodic arrays of spatial solitons in a planar waveguide with relaxing Kerr nonlinearity,” J. Opt. Soc. Am. B 19, 574–585 (2002);
    [Crossref]
  13. E. Lantz, C. Cambournac, and H. Maillotte, “Spatiotemporal dynamics of soliton arrays generated from spatial noise in a planar waveguide with relaxing Kerr nonlinearity,” Opt. Express 10, 942–948 (2002);
    [PubMed]
  14. C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85, 4888–4891 (2000);
    [Crossref] [PubMed]
  15. G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: Universality and diversity,” Science 286, 1518–1523 (1999).
    [Crossref] [PubMed]
  16. A. Barthelemy, S. Maneuf, and C. Froehly, “Soliton Propagation and Self-Confinement of Laser-Beams by Kerr Optical Non-Linearity,” , Opt. Commun. 55, 201–206 (1985).
    [Crossref]
  17. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial Solitons in Photorefractive Media,” Phys. Rev. Lett. 68, 923–926 (1992).
    [Crossref] [PubMed]
  18. W. E. Torruelas, Z. Wang, D. J. Hagan, E. W. Vanstryl, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-Dimensional Spatial Solitary Waves in a Quadratic Medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
    [Crossref]
  19. A. J. Campillo, S. L. Shapiro, and B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628–630 (1973).
    [Crossref]
  20. J. P. Gordon, “Interaction Forces among Solitons in Optical Fibers,” Opt. Lett. 8, 596–598 (1983).
    [Crossref] [PubMed]
  21. M. Shalaby, F. Reynaud, and A. Barthelemy, “Experimental observation of spatial soliton interactions with a pi/2 relative phase difference,” Opt. Lett. 17, 778–780 (1992).
    [Crossref] [PubMed]
  22. M. Petrovi, D. Träger, A. Strinic, M. Belic, J. Schroder, and C. Denz, “Solitonic lattices in photorefractive crystals,” Phys. Rev. E 68, 055601 (2003)
    [Crossref]
  23. R. Mcleod, K. Wagner, and S. Blair, “(3+1)-Dimensional Optical Soliton Dragging Logic,” Phys. Rev. A 52, 3254–3278 (1995).
    [Crossref] [PubMed]
  24. M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in liquid crystals,” Nature 432, 733 (2004).
    [Crossref] [PubMed]
  25. M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically Turbulent Femtosecond Light Guide in Air,” Phys. Rev. Lett. 83, 2938–2941 (1999).
    [Crossref]
  26. L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of Terrawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
    [Crossref] [PubMed]
  27. H. Schroeder and S. L. Chin, “Visualization of the evolution of multiple filaments in methanol,” Opt. Commun. 234, 399–406 (2004).
    [Crossref]
  28. R Boyd, Nonlinear Optics, Academic Press, 2003.
  29. R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
    [Crossref]
  30. M. Fujimoto, S. Aoshima, M. Hosoda, and Y. Tsuchiya, “Femtosecond time-resolved optical polarigraphy: imaging of the propagation dynamics of intense light in a medium,” Opt. Lett. 24, 850–852 (1999).
    [Crossref]
  31. G. G. Luther, A. C. Newell, J. V. Moloney, and E. M. Wright, “Short-Pulse Conical Emission and Spectral Broadening in Normally Dispersive Media,” Opt. Lett. 19, 789–791 (1994).
    [Crossref] [PubMed]
  32. E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, “Conical emission from self-guided femtosecond pulses in air,” Opt. Lett. 21, 62–64 (1996).
    [Crossref] [PubMed]
  33. M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium,” Phys. Rev. A 71063811 (2005).
    [Crossref]
  34. J. M. Halbout and C. L. Tang, “Femtosecond interferometry for nonlinear optics,” Appl. Phys. Lett. 40, 765–767 (1982)
    [Crossref]
  35. D. McMorrow, W. T. Lotshaw, and G. A. Kenneywallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443–454 (1988)).
    [Crossref]
  36. A. Piekara, “On self-trapping of a laser beam,” IEEE J. Quantum Electron. QE-2, 249–250 (1966).
    [Crossref]
  37. A. Vinçotte and L. Berge, “Ç(5) susceptibility stabilizes the propagation of ultrashort laser pulses in air,” Phys. Rev. A 70, 061802 (2004)
    [Crossref]
  38. M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B. 69, 133–136 (1999).
    [Crossref]
  39. R.A. Ganeev, A.I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun. 231, 431–436 (2004).
    [Crossref]

2005 (1)

M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium,” Phys. Rev. A 71063811 (2005).
[Crossref]

2004 (8)

L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of Terrawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref] [PubMed]

H. Schroeder and S. L. Chin, “Visualization of the evolution of multiple filaments in methanol,” Opt. Commun. 234, 399–406 (2004).
[Crossref]

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[Crossref]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in liquid crystals,” Nature 432, 733 (2004).
[Crossref] [PubMed]

M. Saffman, G. McCarthy, and W. Krolikowski, “Two-dimensional modulational instability in photorefractive media,” J. Opt. Soc. Am. B. 6, 387–403 (2004).

A. Dubietis, G. Tamogauskas, G. Fibich G, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity”, Opt. Lett. 29, 1126–1128 (2004);
[Crossref] [PubMed]

A. Vinçotte and L. Berge, “Ç(5) susceptibility stabilizes the propagation of ultrashort laser pulses in air,” Phys. Rev. A 70, 061802 (2004)
[Crossref]

R.A. Ganeev, A.I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun. 231, 431–436 (2004).
[Crossref]

2003 (1)

M. Petrovi, D. Träger, A. Strinic, M. Belic, J. Schroder, and C. Denz, “Solitonic lattices in photorefractive crystals,” Phys. Rev. E 68, 055601 (2003)
[Crossref]

2002 (2)

2001 (1)

2000 (4)

G. Fibich and B. Ilan, “Self-focusing of elliptic beams: an example of the failure of the aberrationless approximation,” J. Opt. Soc. Am. B 17, 1749–1758 (2000);
[Crossref]

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85, 4888–4891 (2000);
[Crossref] [PubMed]

Y. Kivshar and D. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331, 118–195 (2000).
[Crossref]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

1999 (4)

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: Universality and diversity,” Science 286, 1518–1523 (1999).
[Crossref] [PubMed]

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically Turbulent Femtosecond Light Guide in Air,” Phys. Rev. Lett. 83, 2938–2941 (1999).
[Crossref]

M. Fujimoto, S. Aoshima, M. Hosoda, and Y. Tsuchiya, “Femtosecond time-resolved optical polarigraphy: imaging of the propagation dynamics of intense light in a medium,” Opt. Lett. 24, 850–852 (1999).
[Crossref]

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B. 69, 133–136 (1999).
[Crossref]

1997 (1)

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997);
[Crossref]

1996 (2)

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Break-up of two-dimensional bright spatial solitons due to transverse modulation instability,” Europhys. Lett. 35, 25–30 (1996);
[Crossref]

E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, “Conical emission from self-guided femtosecond pulses in air,” Opt. Lett. 21, 62–64 (1996).
[Crossref] [PubMed]

1995 (2)

R. Mcleod, K. Wagner, and S. Blair, “(3+1)-Dimensional Optical Soliton Dragging Logic,” Phys. Rev. A 52, 3254–3278 (1995).
[Crossref] [PubMed]

W. E. Torruelas, Z. Wang, D. J. Hagan, E. W. Vanstryl, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-Dimensional Spatial Solitary Waves in a Quadratic Medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[Crossref]

1994 (2)

G. G. Luther, A. C. Newell, J. V. Moloney, and E. M. Wright, “Short-Pulse Conical Emission and Spectral Broadening in Normally Dispersive Media,” Opt. Lett. 19, 789–791 (1994).
[Crossref] [PubMed]

H. Maillotte, J. Monneret, A. Barthelemy, and C. Froehly, “Laser beam self-splitting into solitons by optical Kerr nonlinearity,” Opt. Commun. 109, 265–271 (1994)
[Crossref]

1993 (1)

1992 (2)

1988 (1)

D. McMorrow, W. T. Lotshaw, and G. A. Kenneywallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443–454 (1988)).
[Crossref]

1985 (1)

A. Barthelemy, S. Maneuf, and C. Froehly, “Soliton Propagation and Self-Confinement of Laser-Beams by Kerr Optical Non-Linearity,” , Opt. Commun. 55, 201–206 (1985).
[Crossref]

1983 (1)

1982 (1)

J. M. Halbout and C. L. Tang, “Femtosecond interferometry for nonlinear optics,” Appl. Phys. Lett. 40, 765–767 (1982)
[Crossref]

1974 (1)

V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Sov. Phys. JETP 38, 494–500 (1974).

1973 (1)

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628–630 (1973).
[Crossref]

1966 (1)

A. Piekara, “On self-trapping of a laser beam,” IEEE J. Quantum Electron. QE-2, 249–250 (1966).
[Crossref]

Aitchison, J. S.

Anastassiou, C.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85, 4888–4891 (2000);
[Crossref] [PubMed]

Aoshima, S.

Assanto, G.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in liquid crystals,” Nature 432, 733 (2004).
[Crossref] [PubMed]

Baba, M.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[Crossref]

R.A. Ganeev, A.I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun. 231, 431–436 (2004).
[Crossref]

Baboiu, D. M.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997);
[Crossref]

Barthelemy, A.

H. Maillotte, J. Monneret, A. Barthelemy, and C. Froehly, “Laser beam self-splitting into solitons by optical Kerr nonlinearity,” Opt. Commun. 109, 265–271 (1994)
[Crossref]

M. Shalaby, F. Reynaud, and A. Barthelemy, “Experimental observation of spatial soliton interactions with a pi/2 relative phase difference,” Opt. Lett. 17, 778–780 (1992).
[Crossref] [PubMed]

A. Barthelemy, S. Maneuf, and C. Froehly, “Soliton Propagation and Self-Confinement of Laser-Beams by Kerr Optical Non-Linearity,” , Opt. Commun. 55, 201–206 (1985).
[Crossref]

Belic, M.

M. Petrovi, D. Träger, A. Strinic, M. Belic, J. Schroder, and C. Denz, “Solitonic lattices in photorefractive crystals,” Phys. Rev. E 68, 055601 (2003)
[Crossref]

Berge, L.

L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of Terrawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref] [PubMed]

A. Vinçotte and L. Berge, “Ç(5) susceptibility stabilizes the propagation of ultrashort laser pulses in air,” Phys. Rev. A 70, 061802 (2004)
[Crossref]

Blair, S.

R. Mcleod, K. Wagner, and S. Blair, “(3+1)-Dimensional Optical Soliton Dragging Logic,” Phys. Rev. A 52, 3254–3278 (1995).
[Crossref] [PubMed]

Bourayou, R.

L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of Terrawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref] [PubMed]

Boyd, R

R Boyd, Nonlinear Optics, Academic Press, 2003.

Cambournac, C.

Campillo, A. J.

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628–630 (1973).
[Crossref]

Centurion, M.

M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium,” Phys. Rev. A 71063811 (2005).
[Crossref]

Chauvet, M.

Chin, S. L.

H. Schroeder and S. L. Chin, “Visualization of the evolution of multiple filaments in methanol,” Opt. Commun. 234, 399–406 (2004).
[Crossref]

Christodoulides, D. N.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85, 4888–4891 (2000);
[Crossref] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

Conti, C.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in liquid crystals,” Nature 432, 733 (2004).
[Crossref] [PubMed]

Crosignani, B.

B. Crosignani and P. Di Porto, “Nonlinear propagation in Kerr media of beams with unequal transverse widths,” Opt. Lett. 18, 1394–1396 (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]

Curley, P. F.

Denz, C.

M. Petrovi, D. Träger, A. Strinic, M. Belic, J. Schroder, and C. Denz, “Solitonic lattices in photorefractive crystals,” Phys. Rev. E 68, 055601 (2003)
[Crossref]

Dubietis, A.

Dudley, J. M.

Eugenieva, E.

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

Eugenieva, E. D.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85, 4888–4891 (2000);
[Crossref] [PubMed]

Falconieri, M.

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B. 69, 133–136 (1999).
[Crossref]

Fibich, G.

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]

Franco, M. A.

Froehly, C.

H. Maillotte, J. Monneret, A. Barthelemy, and C. Froehly, “Laser beam self-splitting into solitons by optical Kerr nonlinearity,” Opt. Commun. 109, 265–271 (1994)
[Crossref]

A. Barthelemy, S. Maneuf, and C. Froehly, “Soliton Propagation and Self-Confinement of Laser-Beams by Kerr Optical Non-Linearity,” , Opt. Commun. 55, 201–206 (1985).
[Crossref]

Fuerst, R. A.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997);
[Crossref]

Fujimoto, M.

G, G. Fibich

Ganeev, R. A.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[Crossref]

Ganeev, R.A.

R.A. Ganeev, A.I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun. 231, 431–436 (2004).
[Crossref]

Gordon, J. P.

Grillon, G.

Hagan, D. J.

W. E. Torruelas, Z. Wang, D. J. Hagan, E. W. Vanstryl, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-Dimensional Spatial Solitary Waves in a Quadratic Medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[Crossref]

Halbout, J. M.

J. M. Halbout and C. L. Tang, “Femtosecond interferometry for nonlinear optics,” Appl. Phys. Lett. 40, 765–767 (1982)
[Crossref]

Hosoda, M.

Ilan, B.

Ishizawa, N.

R.A. Ganeev, A.I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun. 231, 431–436 (2004).
[Crossref]

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[Crossref]

Jankovic, L.

Kasparian, J.

L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of Terrawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref] [PubMed]

Kenneywallace, G. A.

D. McMorrow, W. T. Lotshaw, and G. A. Kenneywallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443–454 (1988)).
[Crossref]

Kip, D.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85, 4888–4891 (2000);
[Crossref] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

Kivshar, Y.

Y. Kivshar and D. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331, 118–195 (2000).
[Crossref]

Kolesik, M.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically Turbulent Femtosecond Light Guide in Air,” Phys. Rev. Lett. 83, 2938–2941 (1999).
[Crossref]

Krolikowski, W.

M. Saffman, G. McCarthy, and W. Krolikowski, “Two-dimensional modulational instability in photorefractive media,” J. Opt. Soc. Am. B. 6, 387–403 (2004).

Kuroda, H.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[Crossref]

R.A. Ganeev, A.I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun. 231, 431–436 (2004).
[Crossref]

Lantz, E.

Lawrence, B.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997);
[Crossref]

Lederer, F.

L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of Terrawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref] [PubMed]

Lotshaw, W. T.

D. McMorrow, W. T. Lotshaw, and G. A. Kenneywallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443–454 (1988)).
[Crossref]

Luca, A. De

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in liquid crystals,” Nature 432, 733 (2004).
[Crossref] [PubMed]

Luther, G. G.

Maillotte, H.

Malendevich, R.

Mamaev, A. V.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Break-up of two-dimensional bright spatial solitons due to transverse modulation instability,” Europhys. Lett. 35, 25–30 (1996);
[Crossref]

Maneuf, S.

A. Barthelemy, S. Maneuf, and C. Froehly, “Soliton Propagation and Self-Confinement of Laser-Beams by Kerr Optical Non-Linearity,” , Opt. Commun. 55, 201–206 (1985).
[Crossref]

McCarthy, G.

M. Saffman, G. McCarthy, and W. Krolikowski, “Two-dimensional modulational instability in photorefractive media,” J. Opt. Soc. Am. B. 6, 387–403 (2004).

Mcleod, R.

R. Mcleod, K. Wagner, and S. Blair, “(3+1)-Dimensional Optical Soliton Dragging Logic,” Phys. Rev. A 52, 3254–3278 (1995).
[Crossref] [PubMed]

McMorrow, D.

D. McMorrow, W. T. Lotshaw, and G. A. Kenneywallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443–454 (1988)).
[Crossref]

Mejean, G.

L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of Terrawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref] [PubMed]

Menyuk, C. R.

W. E. Torruelas, Z. Wang, D. J. Hagan, E. W. Vanstryl, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-Dimensional Spatial Solitary Waves in a Quadratic Medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[Crossref]

Mlejnek, M.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically Turbulent Femtosecond Light Guide in Air,” Phys. Rev. Lett. 83, 2938–2941 (1999).
[Crossref]

Moloney, J. V.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically Turbulent Femtosecond Light Guide in Air,” Phys. Rev. Lett. 83, 2938–2941 (1999).
[Crossref]

G. G. Luther, A. C. Newell, J. V. Moloney, and E. M. Wright, “Short-Pulse Conical Emission and Spectral Broadening in Normally Dispersive Media,” Opt. Lett. 19, 789–791 (1994).
[Crossref] [PubMed]

Monneret, J.

H. Maillotte, J. Monneret, A. Barthelemy, and C. Froehly, “Laser beam self-splitting into solitons by optical Kerr nonlinearity,” Opt. Commun. 109, 265–271 (1994)
[Crossref]

Musslimani, Z. H.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85, 4888–4891 (2000);
[Crossref] [PubMed]

Mysyrowicz, A.

Newell, A. C.

Nibbering, E. T. J.

Peccianti, M.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in liquid crystals,” Nature 432, 733 (2004).
[Crossref] [PubMed]

Pelinovsky, D.

Y. Kivshar and D. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331, 118–195 (2000).
[Crossref]

Petrovi, M.

M. Petrovi, D. Träger, A. Strinic, M. Belic, J. Schroder, and C. Denz, “Solitonic lattices in photorefractive crystals,” Phys. Rev. E 68, 055601 (2003)
[Crossref]

Piekara, A.

A. Piekara, “On self-trapping of a laser beam,” IEEE J. Quantum Electron. QE-2, 249–250 (1966).
[Crossref]

Porto, P. Di

Prade, B. S.

Psaltis, D.

M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium,” Phys. Rev. A 71063811 (2005).
[Crossref]

Pu, Y.

M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium,” Phys. Rev. A 71063811 (2005).
[Crossref]

Reynaud, F.

Rodriguez, M.

L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of Terrawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref] [PubMed]

Rubenchik, A. M.

V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Sov. Phys. JETP 38, 494–500 (1974).

Ryasnyansky, A. I.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[Crossref]

Ryasnyansky, A.I.

R.A. Ganeev, A.I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun. 231, 431–436 (2004).
[Crossref]

Saffman, M.

M. Saffman, G. McCarthy, and W. Krolikowski, “Two-dimensional modulational instability in photorefractive media,” J. Opt. Soc. Am. B. 6, 387–403 (2004).

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Break-up of two-dimensional bright spatial solitons due to transverse modulation instability,” Europhys. Lett. 35, 25–30 (1996);
[Crossref]

Sakakibara, S.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[Crossref]

R.A. Ganeev, A.I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun. 231, 431–436 (2004).
[Crossref]

Salin, F.

Salmon, E.

L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of Terrawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref] [PubMed]

Salvetti, G.

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B. 69, 133–136 (1999).
[Crossref]

Sauerbrey, R.

L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of Terrawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref] [PubMed]

Schroder, J.

M. Petrovi, D. Träger, A. Strinic, M. Belic, J. Schroder, and C. Denz, “Solitonic lattices in photorefractive crystals,” Phys. Rev. E 68, 055601 (2003)
[Crossref]

Schroeder, H.

H. Schroeder and S. L. Chin, “Visualization of the evolution of multiple filaments in methanol,” Opt. Commun. 234, 399–406 (2004).
[Crossref]

Segev, M.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85, 4888–4891 (2000);
[Crossref] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: Universality and diversity,” Science 286, 1518–1523 (1999).
[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]

Shalaby, M.

Shapiro, S. L.

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628–630 (1973).
[Crossref]

Skupin, S.

L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of Terrawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref] [PubMed]

Soljacic, M.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85, 4888–4891 (2000);
[Crossref] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

Stegeman, G.

Stegeman, G. I.

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: Universality and diversity,” Science 286, 1518–1523 (1999).
[Crossref] [PubMed]

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997);
[Crossref]

W. E. Torruelas, Z. Wang, D. J. Hagan, E. W. Vanstryl, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-Dimensional Spatial Solitary Waves in a Quadratic Medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[Crossref]

Strinic, A.

M. Petrovi, D. Träger, A. Strinic, M. Belic, J. Schroder, and C. Denz, “Solitonic lattices in photorefractive crystals,” Phys. Rev. E 68, 055601 (2003)
[Crossref]

Suydam, B. R.

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628–630 (1973).
[Crossref]

Suzuki, M.

R.A. Ganeev, A.I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun. 231, 431–436 (2004).
[Crossref]

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[Crossref]

Tamogauskas, G.

Tang, C. L.

J. M. Halbout and C. L. Tang, “Femtosecond interferometry for nonlinear optics,” Appl. Phys. Lett. 40, 765–767 (1982)
[Crossref]

Torner, L.

W. E. Torruelas, Z. Wang, D. J. Hagan, E. W. Vanstryl, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-Dimensional Spatial Solitary Waves in a Quadratic Medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[Crossref]

Torres, J. P.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85, 4888–4891 (2000);
[Crossref] [PubMed]

Torruelas, W. E.

W. E. Torruelas, Z. Wang, D. J. Hagan, E. W. Vanstryl, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-Dimensional Spatial Solitary Waves in a Quadratic Medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[Crossref]

Torruellas, W. E.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997);
[Crossref]

Träger, D.

M. Petrovi, D. Träger, A. Strinic, M. Belic, J. Schroder, and C. Denz, “Solitonic lattices in photorefractive crystals,” Phys. Rev. E 68, 055601 (2003)
[Crossref]

Trillo, S.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997);
[Crossref]

Tsang, M.

M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium,” Phys. Rev. A 71063811 (2005).
[Crossref]

Tsuchiya, Y.

Turu, M.

R.A. Ganeev, A.I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun. 231, 431–436 (2004).
[Crossref]

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[Crossref]

Umeton, C.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in liquid crystals,” Nature 432, 733 (2004).
[Crossref] [PubMed]

Vanstryl, E. W.

W. E. Torruelas, Z. Wang, D. J. Hagan, E. W. Vanstryl, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-Dimensional Spatial Solitary Waves in a Quadratic Medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[Crossref]

Vinçotte, A.

A. Vinçotte and L. Berge, “Ç(5) susceptibility stabilizes the propagation of ultrashort laser pulses in air,” Phys. Rev. A 70, 061802 (2004)
[Crossref]

Wabnitz, S.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997);
[Crossref]

Wagner, K.

R. Mcleod, K. Wagner, and S. Blair, “(3+1)-Dimensional Optical Soliton Dragging Logic,” Phys. Rev. A 52, 3254–3278 (1995).
[Crossref] [PubMed]

Wang, Z.

W. E. Torruelas, Z. Wang, D. J. Hagan, E. W. Vanstryl, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-Dimensional Spatial Solitary Waves in a Quadratic Medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[Crossref]

Wolf, J. P.

L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of Terrawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref] [PubMed]

Woste, L.

L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of Terrawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref] [PubMed]

Wright, E. M.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically Turbulent Femtosecond Light Guide in Air,” Phys. Rev. Lett. 83, 2938–2941 (1999).
[Crossref]

G. G. Luther, A. C. Newell, J. V. Moloney, and E. M. Wright, “Short-Pulse Conical Emission and Spectral Broadening in Normally Dispersive Media,” Opt. Lett. 19, 789–791 (1994).
[Crossref] [PubMed]

Yariv, A.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial Solitons in Photorefractive Media,” Phys. Rev. Lett. 68, 923–926 (1992).
[Crossref] [PubMed]

Yu, J.

L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of Terrawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref] [PubMed]

Zakharov, V. E.

V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Sov. Phys. JETP 38, 494–500 (1974).

Zozulya, A. A.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Break-up of two-dimensional bright spatial solitons due to transverse modulation instability,” Europhys. Lett. 35, 25–30 (1996);
[Crossref]

Appl. Phys. B (1)

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[Crossref]

Appl. Phys. B. (1)

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B. 69, 133–136 (1999).
[Crossref]

Appl. Phys. Lett. (2)

J. M. Halbout and C. L. Tang, “Femtosecond interferometry for nonlinear optics,” Appl. Phys. Lett. 40, 765–767 (1982)
[Crossref]

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628–630 (1973).
[Crossref]

Europhys. Lett. (1)

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Break-up of two-dimensional bright spatial solitons due to transverse modulation instability,” Europhys. Lett. 35, 25–30 (1996);
[Crossref]

IEEE J. Quantum Electron. (2)

D. McMorrow, W. T. Lotshaw, and G. A. Kenneywallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443–454 (1988)).
[Crossref]

A. Piekara, “On self-trapping of a laser beam,” IEEE J. Quantum Electron. QE-2, 249–250 (1966).
[Crossref]

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

J. Opt. Soc. Am. B. (1)

M. Saffman, G. McCarthy, and W. Krolikowski, “Two-dimensional modulational instability in photorefractive media,” J. Opt. Soc. Am. B. 6, 387–403 (2004).

Nature (1)

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Routing of anisotropic spatial solitons and modulational instability in liquid crystals,” Nature 432, 733 (2004).
[Crossref] [PubMed]

Opt. Commun. (4)

H. Maillotte, J. Monneret, A. Barthelemy, and C. Froehly, “Laser beam self-splitting into solitons by optical Kerr nonlinearity,” Opt. Commun. 109, 265–271 (1994)
[Crossref]

A. Barthelemy, S. Maneuf, and C. Froehly, “Soliton Propagation and Self-Confinement of Laser-Beams by Kerr Optical Non-Linearity,” , Opt. Commun. 55, 201–206 (1985).
[Crossref]

R.A. Ganeev, A.I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun. 231, 431–436 (2004).
[Crossref]

H. Schroeder and S. L. Chin, “Visualization of the evolution of multiple filaments in methanol,” Opt. Commun. 234, 399–406 (2004).
[Crossref]

Opt. Express (1)

Opt. Lett. (8)

Phys. Rep. (1)

Y. Kivshar and D. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331, 118–195 (2000).
[Crossref]

Phys. Rev. A (3)

M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium,” Phys. Rev. A 71063811 (2005).
[Crossref]

A. Vinçotte and L. Berge, “Ç(5) susceptibility stabilizes the propagation of ultrashort laser pulses in air,” Phys. Rev. A 70, 061802 (2004)
[Crossref]

R. Mcleod, K. Wagner, and S. Blair, “(3+1)-Dimensional Optical Soliton Dragging Logic,” Phys. Rev. A 52, 3254–3278 (1995).
[Crossref] [PubMed]

Phys. Rev. E (1)

M. Petrovi, D. Träger, A. Strinic, M. Belic, J. Schroder, and C. Denz, “Solitonic lattices in photorefractive crystals,” Phys. Rev. E 68, 055601 (2003)
[Crossref]

Phys. Rev. Lett. (6)

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically Turbulent Femtosecond Light Guide in Air,” Phys. Rev. Lett. 83, 2938–2941 (1999).
[Crossref]

L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of Terrawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[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]

W. E. Torruelas, Z. Wang, D. J. Hagan, E. W. Vanstryl, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of 2-Dimensional Spatial Solitary Waves in a Quadratic Medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[Crossref]

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85, 4888–4891 (2000);
[Crossref] [PubMed]

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997);
[Crossref]

Science (2)

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).
[Crossref] [PubMed]

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: Universality and diversity,” Science 286, 1518–1523 (1999).
[Crossref] [PubMed]

Sov. Phys. JETP (1)

V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Sov. Phys. JETP 38, 494–500 (1974).

Other (1)

R Boyd, Nonlinear Optics, Academic Press, 2003.

Supplementary Material (3)

» Media 1: AVI (79 KB)     
» Media 2: AVI (113 KB)     
» Media 3: AVI (259 KB)     

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 (8)

Fig. 1.
Fig. 1.

FTOP Setup. The pump pulse is focused in the material with a cylindrical lens to generate a single column of filaments. The beam profile at the output is imaged on CCD 1. The probe pulse goes through a variable delay line, a polarizer and analyzer and is imaged on CCD.

Fig. 2.
Fig. 2.

Beam profile of the pump pulse at the output of the CS2 cell. The power increases form left to right: a) P = 12Pcr , b) 40Pcr , c) 80Pcr , d) 170Pcr , e) 250Pcr , f) 390Pcr , g) 530Pcr , h) 1200Pcr .

Fig. 3.
Fig. 3.

Video clip of changes in the beam profile as a result of fluctuations in the pulse energy for P = 170 Pcr (78.5 KB). The image area is 0.36 mm (h) × 0.89 mm (v).

Fig. 4.
Fig. 4.

Video clip of changes in the beam profile as a result of fluctuations in the pulse energy for P = 390 Pcr (113 KB). The image area is 0.36 mm (h) × 0.89 mm (v).

Fig. 5.
Fig. 5.

Video clip of pulse propagation inside CS2 from 2 mm to 4 mm from the cell entrance for a pulse power of 390 Pcr. An initially uniform beam breaks up into stable filaments (258 KB). The image size is 2.4 mm (h) × 1.6 mm (v).

Fig. 6.
Fig. 6.

Pulse trajectories and 1-D Fourier transforms. (a,c): The trajectory of the pulse is reconstructed by digitally adding up the FTOP frames for different positions of the pulse. Each separate image corresponds to frames taken for a fixed position of CCD camera. The camera was moved laterally to capture the beam profile further along inside the cell. The pulse power is 390Pcr in (a) and 1200Pcr in (c). (b,d) Show the 1-D Fourier transforms of the filamentation patterns in (a) and (c), respectively. The central component is blocked to visualize higher frequencies.

Fig. 7.
Fig. 7.

Interactions between filaments from 3.5 mm to 4.2 mm from the cell entrance for an input pulse power of 1200Pcr . Some filaments propagate undisturbed (a-c). We have observed fusion of two filaments (b), divergence of a filament (d) and the generation of a new filament (e).

Fig. 8.
Fig. 8.

1-D Fourier transforms for numerically calculated beam propagation. The beam propagation is numerically calculated for four different power levels a) P = 250 Pcr , b) 390 Pcr , c) 530 Pcr , d) 1200 Pcr . A 1-D Fourier transform on the side view of the beam profile is calculated for each along the propagation direction. The total distance is 10 mm. The central peak (DC component) in the Fourier transform is blocked to improve the contrast in the image.

Equations (2)

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

P cr = π ( 0.61 ) 2 λ 2 8 n 0 n 2 .
dA dz = i 2 k n 0 ( 2 x 2 + 2 y 2 ) A + ik ( n 2 A 2 ) A ik ( n 4 A 4 ) A β A 2 A

Metrics