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

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Appl. Phys. B

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

M. Falconieri, 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.

J. M. Halbout, 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.

A. V. Mamaev, M. Saffman, 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.

D. McMorrow, W. T. Lotshaw, 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.

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

J. Opt. Soc. Am. B

J. Opt. Soc. Am. B.

G. Fibich, 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);

Nature

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

Opt. Commun.

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

H. Maillotte, J. Monneret, A. Barthelemy, C. Froehly, �??�??Laser beam self-splitting into solitons by optical Kerr nonlinearity,�??�?? Opt. Commun. 109, 265-271 (1994)
[CrossRef]

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, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, H. Kuroda, �??�??Two- and three-photon absorption in CS2,�??�?? Opt. Commun. 231, 431-436 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rep.

Y. Kivshar, D. Pelinovsky, �??Self-focusing and transverse instabilities of solitary waves,�?? Phys. Rep. 331, 118-195 (2000).

Phys. Rev. A

M. Centurion, Y. Pu, M. Tsang, D. Psaltis, �??Dynamics of filament formation in a Kerr medium,�?? Phys. Rev. A 71 063811 (2005).
[CrossRef]

A. Vinçotte, L. Berge, �??�?(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]

Phys. Rev. E

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

Phys. Rev. Lett.

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, R. Sauerbrey, �??Multiple filamentation of Terrawatt laser pulses in air,�?? Phys. Rev. Lett. 92, 225002 (2004).
[CrossRef]

M. Segev, B. Crosignani, A. Yariv and B. Fischer, �??Spatial Solitons in Photorefractive Media,�?? Phys. Rev. Lett. 68, 923-926 (1992).
[CrossRef]

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

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

Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, J. P. Torres, �??�??Eliminating the transverse instabilities of Kerr solitons,�??�?? Phys. Rev. Lett. 85, 4888�??4891 (2000);
[CrossRef]

Science

G. I. Stegeman, M. Segev, �??Optical spatial solitons and their interactions: Universality and diversity,�?? Science 286, 1518-1523 (1999).
[CrossRef]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, D. N. Christodoulides, �??Modulation instability and pattern formation in spatially incoherent light beams,�?? Science 290, 495-498 (2000).
[CrossRef]

Sov. Phys. JETP

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

Other

R Boyd, Nonlinear Optics, Academic Press, 2003.

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