Abstract

The propagation of a self-trapped laser beam in a planar waveguide that exhibits a Kerr nonlinearity and a normal chromatic dispersion is considered. We demonstrate experimentally for the first time to our knowledge that such a beam undergoes an undulation responsible for ultrafast transverse oscillations of its axis. This phenomenon, called “snake instability”, was predicted theoretically in 1973 by Zakharov and Rubenchik on the basis of a study of the soliton solutions of the hyperbolic nonlinear Schrödinger equation. The signature of this instability is observed in the spatially resolved temporal spectrum.

© 2008 Optical Society of America

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  1. S. Trillo and W. Torruellas, Spatial solitons (Springer, Berlin, 2001).
  2. P. M. Kelley, "Self-focusing of optical beams," Phys. Rev. Lett. 15, 1005-1007 (1965).
    [CrossRef]
  3. V. E. Zakharov and A. M. Rubenchik, "Instablity of waveguides and solitons in nonlinear media," Sov. Phys. JETP 38, 494-500 (1974).
  4. K. Germaschewski, R. Grauer, L. Bergé, V. K. Mezentsev, and J. J. Rasmussen, "Splittings, coalescence, bunch and snake patterns in the 3D nonlinear Schrödinger equation with anisotropic dispersion," Physica D 151, 175-198 (2001).
  5. A. De Rossi, S. Trillo, A. V. Buryak, and Y. S. Kivshar, "Snake instability of one-dimensional parametric spatial solitons," Opt. Lett. 22, 868-870 (1997).
    [CrossRef] [PubMed]
  6. A. V. Mamaev, M. Saffman, and A.A. Zozulia, "Break-up of two-dimensional bright spatial solitons due to transverse modulation instability," Europhys. Lett. 35, 25-30 (1996).
    [CrossRef]
  7. V. Tikhonenko, J. Christou, B. Luther-Davies, and Y. S. Kivshar, "Observation of vortex solitons created by the instability of dark soliton stripes," Opt. Lett. 21, 1129-1131 (1996).
    [CrossRef] [PubMed]
  8. S.-P. Gorza, N. Roig, Ph. Emplit, and M. Haelterman, "Snake Instability of a Spatiotemporal Bright Soliton Stripe," Phys. Rev. Lett. 92, 084101 (2004).
    [CrossRef] [PubMed]
  9. S.-P. Gorza, Ph. Emplit, and M. Haelterman, "Observation of the snake instability of a spatially extended temporal bright soliton," Opt. Lett. 31, 1280-1282 (2006).
    [CrossRef] [PubMed]
  10. X. Liu, K. Beckwitt, and F. Wise, "Transverse Instability of Optical Spatiotemporal Solitons in QuadraticMedia," Phys. Rev. Lett. 85, 1871-1874 (2000).
    [CrossRef] [PubMed]
  11. S. D. Jenkins, D. Salerno, S. Minardi, S. Tamo�?sauskas, T. A. B. Kennedy, and P. Di Trapani, "Quantum-noise initiated symmetry breaking of spatial solitons," Phys. Rev. Lett. 95, 203902 (2005).
    [CrossRef] [PubMed]
  12. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, "Ultrashort filaments of light in weakly ionized, optically transparent media," Rep. Prog. Phys. 70, 1633-1713 (2007).
    [CrossRef]
  13. B. P. Anderson et al. "Watching dark soliton decay into vortex rings in a Bose-Einstein condensate," Phys. Rev. Lett. 86, 2926-2929 (2001).
    [CrossRef] [PubMed]
  14. Z. Dutton, M. Budde, C. Slowe, and L. V. Hau, "Observation of quatum shock waves created with ultracompressed slow light pulses in a Bose-Einstein condenstate," Science 293, 663-668 (2001).
    [CrossRef] [PubMed]
  15. E. D. Brown, S. B. Buchsbaum, R. E. Hall, J. P. Penhune, K. F. Schmitt, K. M. Watson, and D. C. Wyatt, "Observation of a nonlinear solitary wave packet in the Kelvin wake of a ship," J. Fluid Mech. 204, 263-293 (1989).
    [CrossRef]
  16. B. Deconink, D. E. Pelinovsky, and J. D. Carter, "Transverse instabilities of deep-water solitary waves," Proc. Roy. Soc. A 462, 2039-2061 (2005).
  17. M. Sheik-Bahae, D. C. Hutching, D. J. Hagan, and E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solid," IEEE J. Quantum Electron. 27, 1296-1309 (1991).
    [CrossRef]
  18. S. Adachi, "Optical properties of AlxGa1�??xAs alloys," Phys. Rev. B 38, 12345-12352 (1988).
    [CrossRef]
  19. G. P. Agrawal, Nonlinear fiber optics (Academic Press, San-Diego, 2001).
  20. H. C. Yuen and B. M. Lake, Non-linear dynamics of deep-water gravity waves (Accademic Press, New York, 1982).
  21. J. R. Myra and C. S. Liu, "Self-modulation of ion Berstein waves," Phys. Fluids 23, 2258-2264 (1980).
    [CrossRef]
  22. N. R. Pereira, A. Sen, and A. Bers, "Nonlinear development of lower hybrid cones," Phys. Fluids 21, 117-120 (1978).
    [CrossRef]

2007 (1)

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, "Ultrashort filaments of light in weakly ionized, optically transparent media," Rep. Prog. Phys. 70, 1633-1713 (2007).
[CrossRef]

2006 (1)

2005 (2)

S. D. Jenkins, D. Salerno, S. Minardi, S. Tamo�?sauskas, T. A. B. Kennedy, and P. Di Trapani, "Quantum-noise initiated symmetry breaking of spatial solitons," Phys. Rev. Lett. 95, 203902 (2005).
[CrossRef] [PubMed]

B. Deconink, D. E. Pelinovsky, and J. D. Carter, "Transverse instabilities of deep-water solitary waves," Proc. Roy. Soc. A 462, 2039-2061 (2005).

2004 (1)

S.-P. Gorza, N. Roig, Ph. Emplit, and M. Haelterman, "Snake Instability of a Spatiotemporal Bright Soliton Stripe," Phys. Rev. Lett. 92, 084101 (2004).
[CrossRef] [PubMed]

2001 (3)

B. P. Anderson et al. "Watching dark soliton decay into vortex rings in a Bose-Einstein condensate," Phys. Rev. Lett. 86, 2926-2929 (2001).
[CrossRef] [PubMed]

Z. Dutton, M. Budde, C. Slowe, and L. V. Hau, "Observation of quatum shock waves created with ultracompressed slow light pulses in a Bose-Einstein condenstate," Science 293, 663-668 (2001).
[CrossRef] [PubMed]

K. Germaschewski, R. Grauer, L. Bergé, V. K. Mezentsev, and J. J. Rasmussen, "Splittings, coalescence, bunch and snake patterns in the 3D nonlinear Schrödinger equation with anisotropic dispersion," Physica D 151, 175-198 (2001).

2000 (1)

X. Liu, K. Beckwitt, and F. Wise, "Transverse Instability of Optical Spatiotemporal Solitons in QuadraticMedia," Phys. Rev. Lett. 85, 1871-1874 (2000).
[CrossRef] [PubMed]

1997 (1)

1996 (2)

V. Tikhonenko, J. Christou, B. Luther-Davies, and Y. S. Kivshar, "Observation of vortex solitons created by the instability of dark soliton stripes," Opt. Lett. 21, 1129-1131 (1996).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, and A.A. Zozulia, "Break-up of two-dimensional bright spatial solitons due to transverse modulation instability," Europhys. Lett. 35, 25-30 (1996).
[CrossRef]

1991 (1)

M. Sheik-Bahae, D. C. Hutching, D. J. Hagan, and E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solid," IEEE J. Quantum Electron. 27, 1296-1309 (1991).
[CrossRef]

1989 (1)

E. D. Brown, S. B. Buchsbaum, R. E. Hall, J. P. Penhune, K. F. Schmitt, K. M. Watson, and D. C. Wyatt, "Observation of a nonlinear solitary wave packet in the Kelvin wake of a ship," J. Fluid Mech. 204, 263-293 (1989).
[CrossRef]

1988 (1)

S. Adachi, "Optical properties of AlxGa1�??xAs alloys," Phys. Rev. B 38, 12345-12352 (1988).
[CrossRef]

1980 (1)

J. R. Myra and C. S. Liu, "Self-modulation of ion Berstein waves," Phys. Fluids 23, 2258-2264 (1980).
[CrossRef]

1978 (1)

N. R. Pereira, A. Sen, and A. Bers, "Nonlinear development of lower hybrid cones," Phys. Fluids 21, 117-120 (1978).
[CrossRef]

1974 (1)

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

1965 (1)

P. M. Kelley, "Self-focusing of optical beams," Phys. Rev. Lett. 15, 1005-1007 (1965).
[CrossRef]

Adachi, S.

S. Adachi, "Optical properties of AlxGa1�??xAs alloys," Phys. Rev. B 38, 12345-12352 (1988).
[CrossRef]

Anderson, B. P.

B. P. Anderson et al. "Watching dark soliton decay into vortex rings in a Bose-Einstein condensate," Phys. Rev. Lett. 86, 2926-2929 (2001).
[CrossRef] [PubMed]

Beckwitt, K.

X. Liu, K. Beckwitt, and F. Wise, "Transverse Instability of Optical Spatiotemporal Solitons in QuadraticMedia," Phys. Rev. Lett. 85, 1871-1874 (2000).
[CrossRef] [PubMed]

Bergé, L.

K. Germaschewski, R. Grauer, L. Bergé, V. K. Mezentsev, and J. J. Rasmussen, "Splittings, coalescence, bunch and snake patterns in the 3D nonlinear Schrödinger equation with anisotropic dispersion," Physica D 151, 175-198 (2001).

Bers, A.

N. R. Pereira, A. Sen, and A. Bers, "Nonlinear development of lower hybrid cones," Phys. Fluids 21, 117-120 (1978).
[CrossRef]

Brown, E. D.

E. D. Brown, S. B. Buchsbaum, R. E. Hall, J. P. Penhune, K. F. Schmitt, K. M. Watson, and D. C. Wyatt, "Observation of a nonlinear solitary wave packet in the Kelvin wake of a ship," J. Fluid Mech. 204, 263-293 (1989).
[CrossRef]

Buchsbaum, S. B.

E. D. Brown, S. B. Buchsbaum, R. E. Hall, J. P. Penhune, K. F. Schmitt, K. M. Watson, and D. C. Wyatt, "Observation of a nonlinear solitary wave packet in the Kelvin wake of a ship," J. Fluid Mech. 204, 263-293 (1989).
[CrossRef]

Budde, M.

Z. Dutton, M. Budde, C. Slowe, and L. V. Hau, "Observation of quatum shock waves created with ultracompressed slow light pulses in a Bose-Einstein condenstate," Science 293, 663-668 (2001).
[CrossRef] [PubMed]

Buryak, A. V.

Carter, J. D.

B. Deconink, D. E. Pelinovsky, and J. D. Carter, "Transverse instabilities of deep-water solitary waves," Proc. Roy. Soc. A 462, 2039-2061 (2005).

Christou, J.

De Rossi, A.

Deconink, B.

B. Deconink, D. E. Pelinovsky, and J. D. Carter, "Transverse instabilities of deep-water solitary waves," Proc. Roy. Soc. A 462, 2039-2061 (2005).

Di Trapani, P.

S. D. Jenkins, D. Salerno, S. Minardi, S. Tamo�?sauskas, T. A. B. Kennedy, and P. Di Trapani, "Quantum-noise initiated symmetry breaking of spatial solitons," Phys. Rev. Lett. 95, 203902 (2005).
[CrossRef] [PubMed]

Dutton, Z.

Z. Dutton, M. Budde, C. Slowe, and L. V. Hau, "Observation of quatum shock waves created with ultracompressed slow light pulses in a Bose-Einstein condenstate," Science 293, 663-668 (2001).
[CrossRef] [PubMed]

Emplit, Ph.

S.-P. Gorza, Ph. Emplit, and M. Haelterman, "Observation of the snake instability of a spatially extended temporal bright soliton," Opt. Lett. 31, 1280-1282 (2006).
[CrossRef] [PubMed]

S.-P. Gorza, N. Roig, Ph. Emplit, and M. Haelterman, "Snake Instability of a Spatiotemporal Bright Soliton Stripe," Phys. Rev. Lett. 92, 084101 (2004).
[CrossRef] [PubMed]

Germaschewski, K.

K. Germaschewski, R. Grauer, L. Bergé, V. K. Mezentsev, and J. J. Rasmussen, "Splittings, coalescence, bunch and snake patterns in the 3D nonlinear Schrödinger equation with anisotropic dispersion," Physica D 151, 175-198 (2001).

Gorza, S.-P.

S.-P. Gorza, Ph. Emplit, and M. Haelterman, "Observation of the snake instability of a spatially extended temporal bright soliton," Opt. Lett. 31, 1280-1282 (2006).
[CrossRef] [PubMed]

S.-P. Gorza, N. Roig, Ph. Emplit, and M. Haelterman, "Snake Instability of a Spatiotemporal Bright Soliton Stripe," Phys. Rev. Lett. 92, 084101 (2004).
[CrossRef] [PubMed]

Grauer, R.

K. Germaschewski, R. Grauer, L. Bergé, V. K. Mezentsev, and J. J. Rasmussen, "Splittings, coalescence, bunch and snake patterns in the 3D nonlinear Schrödinger equation with anisotropic dispersion," Physica D 151, 175-198 (2001).

Haelterman, M.

S.-P. Gorza, Ph. Emplit, and M. Haelterman, "Observation of the snake instability of a spatially extended temporal bright soliton," Opt. Lett. 31, 1280-1282 (2006).
[CrossRef] [PubMed]

S.-P. Gorza, N. Roig, Ph. Emplit, and M. Haelterman, "Snake Instability of a Spatiotemporal Bright Soliton Stripe," Phys. Rev. Lett. 92, 084101 (2004).
[CrossRef] [PubMed]

Hagan, D. J.

M. Sheik-Bahae, D. C. Hutching, D. J. Hagan, and E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solid," IEEE J. Quantum Electron. 27, 1296-1309 (1991).
[CrossRef]

Hall, R. E.

E. D. Brown, S. B. Buchsbaum, R. E. Hall, J. P. Penhune, K. F. Schmitt, K. M. Watson, and D. C. Wyatt, "Observation of a nonlinear solitary wave packet in the Kelvin wake of a ship," J. Fluid Mech. 204, 263-293 (1989).
[CrossRef]

Hau, L. V.

Z. Dutton, M. Budde, C. Slowe, and L. V. Hau, "Observation of quatum shock waves created with ultracompressed slow light pulses in a Bose-Einstein condenstate," Science 293, 663-668 (2001).
[CrossRef] [PubMed]

Hutching, D. C.

M. Sheik-Bahae, D. C. Hutching, D. J. Hagan, and E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solid," IEEE J. Quantum Electron. 27, 1296-1309 (1991).
[CrossRef]

Jenkins, S. D.

S. D. Jenkins, D. Salerno, S. Minardi, S. Tamo�?sauskas, T. A. B. Kennedy, and P. Di Trapani, "Quantum-noise initiated symmetry breaking of spatial solitons," Phys. Rev. Lett. 95, 203902 (2005).
[CrossRef] [PubMed]

Kasparian, J.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, "Ultrashort filaments of light in weakly ionized, optically transparent media," Rep. Prog. Phys. 70, 1633-1713 (2007).
[CrossRef]

Kelley, P. M.

P. M. Kelley, "Self-focusing of optical beams," Phys. Rev. Lett. 15, 1005-1007 (1965).
[CrossRef]

Kennedy, T. A. B.

S. D. Jenkins, D. Salerno, S. Minardi, S. Tamo�?sauskas, T. A. B. Kennedy, and P. Di Trapani, "Quantum-noise initiated symmetry breaking of spatial solitons," Phys. Rev. Lett. 95, 203902 (2005).
[CrossRef] [PubMed]

Kivshar, Y. S.

Liu, C. S.

J. R. Myra and C. S. Liu, "Self-modulation of ion Berstein waves," Phys. Fluids 23, 2258-2264 (1980).
[CrossRef]

Liu, X.

X. Liu, K. Beckwitt, and F. Wise, "Transverse Instability of Optical Spatiotemporal Solitons in QuadraticMedia," Phys. Rev. Lett. 85, 1871-1874 (2000).
[CrossRef] [PubMed]

Luther-Davies, B.

Mamaev, A. V.

A. V. Mamaev, M. Saffman, and A.A. Zozulia, "Break-up of two-dimensional bright spatial solitons due to transverse modulation instability," Europhys. Lett. 35, 25-30 (1996).
[CrossRef]

Mezentsev, V. K.

K. Germaschewski, R. Grauer, L. Bergé, V. K. Mezentsev, and J. J. Rasmussen, "Splittings, coalescence, bunch and snake patterns in the 3D nonlinear Schrödinger equation with anisotropic dispersion," Physica D 151, 175-198 (2001).

Minardi, S.

S. D. Jenkins, D. Salerno, S. Minardi, S. Tamo�?sauskas, T. A. B. Kennedy, and P. Di Trapani, "Quantum-noise initiated symmetry breaking of spatial solitons," Phys. Rev. Lett. 95, 203902 (2005).
[CrossRef] [PubMed]

Myra, J. R.

J. R. Myra and C. S. Liu, "Self-modulation of ion Berstein waves," Phys. Fluids 23, 2258-2264 (1980).
[CrossRef]

Nuter, R.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, "Ultrashort filaments of light in weakly ionized, optically transparent media," Rep. Prog. Phys. 70, 1633-1713 (2007).
[CrossRef]

Pelinovsky, D. E.

B. Deconink, D. E. Pelinovsky, and J. D. Carter, "Transverse instabilities of deep-water solitary waves," Proc. Roy. Soc. A 462, 2039-2061 (2005).

Penhune, J. P.

E. D. Brown, S. B. Buchsbaum, R. E. Hall, J. P. Penhune, K. F. Schmitt, K. M. Watson, and D. C. Wyatt, "Observation of a nonlinear solitary wave packet in the Kelvin wake of a ship," J. Fluid Mech. 204, 263-293 (1989).
[CrossRef]

Pereira, N. R.

N. R. Pereira, A. Sen, and A. Bers, "Nonlinear development of lower hybrid cones," Phys. Fluids 21, 117-120 (1978).
[CrossRef]

Rasmussen, J. J.

K. Germaschewski, R. Grauer, L. Bergé, V. K. Mezentsev, and J. J. Rasmussen, "Splittings, coalescence, bunch and snake patterns in the 3D nonlinear Schrödinger equation with anisotropic dispersion," Physica D 151, 175-198 (2001).

Roig, N.

S.-P. Gorza, N. Roig, Ph. Emplit, and M. Haelterman, "Snake Instability of a Spatiotemporal Bright Soliton Stripe," Phys. Rev. Lett. 92, 084101 (2004).
[CrossRef] [PubMed]

Rubenchik, A. M.

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

Saffman, M.

A. V. Mamaev, M. Saffman, and A.A. Zozulia, "Break-up of two-dimensional bright spatial solitons due to transverse modulation instability," Europhys. Lett. 35, 25-30 (1996).
[CrossRef]

Salerno, D.

S. D. Jenkins, D. Salerno, S. Minardi, S. Tamo�?sauskas, T. A. B. Kennedy, and P. Di Trapani, "Quantum-noise initiated symmetry breaking of spatial solitons," Phys. Rev. Lett. 95, 203902 (2005).
[CrossRef] [PubMed]

Schmitt, K. F.

E. D. Brown, S. B. Buchsbaum, R. E. Hall, J. P. Penhune, K. F. Schmitt, K. M. Watson, and D. C. Wyatt, "Observation of a nonlinear solitary wave packet in the Kelvin wake of a ship," J. Fluid Mech. 204, 263-293 (1989).
[CrossRef]

Sen, A.

N. R. Pereira, A. Sen, and A. Bers, "Nonlinear development of lower hybrid cones," Phys. Fluids 21, 117-120 (1978).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, D. C. Hutching, D. J. Hagan, and E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solid," IEEE J. Quantum Electron. 27, 1296-1309 (1991).
[CrossRef]

Skupin, S.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, "Ultrashort filaments of light in weakly ionized, optically transparent media," Rep. Prog. Phys. 70, 1633-1713 (2007).
[CrossRef]

Slowe, C.

Z. Dutton, M. Budde, C. Slowe, and L. V. Hau, "Observation of quatum shock waves created with ultracompressed slow light pulses in a Bose-Einstein condenstate," Science 293, 663-668 (2001).
[CrossRef] [PubMed]

Tamo??sauskas, S.

S. D. Jenkins, D. Salerno, S. Minardi, S. Tamo�?sauskas, T. A. B. Kennedy, and P. Di Trapani, "Quantum-noise initiated symmetry breaking of spatial solitons," Phys. Rev. Lett. 95, 203902 (2005).
[CrossRef] [PubMed]

Tikhonenko, V.

Trillo, S.

Van Stryland, E. W.

M. Sheik-Bahae, D. C. Hutching, D. J. Hagan, and E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solid," IEEE J. Quantum Electron. 27, 1296-1309 (1991).
[CrossRef]

Watson, K. M.

E. D. Brown, S. B. Buchsbaum, R. E. Hall, J. P. Penhune, K. F. Schmitt, K. M. Watson, and D. C. Wyatt, "Observation of a nonlinear solitary wave packet in the Kelvin wake of a ship," J. Fluid Mech. 204, 263-293 (1989).
[CrossRef]

Wise, F.

X. Liu, K. Beckwitt, and F. Wise, "Transverse Instability of Optical Spatiotemporal Solitons in QuadraticMedia," Phys. Rev. Lett. 85, 1871-1874 (2000).
[CrossRef] [PubMed]

Wolf, J.-P.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, "Ultrashort filaments of light in weakly ionized, optically transparent media," Rep. Prog. Phys. 70, 1633-1713 (2007).
[CrossRef]

Wyatt, D. C.

E. D. Brown, S. B. Buchsbaum, R. E. Hall, J. P. Penhune, K. F. Schmitt, K. M. Watson, and D. C. Wyatt, "Observation of a nonlinear solitary wave packet in the Kelvin wake of a ship," J. Fluid Mech. 204, 263-293 (1989).
[CrossRef]

Zakharov, V. E.

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

Zozulia, A.A.

A. V. Mamaev, M. Saffman, and A.A. Zozulia, "Break-up of two-dimensional bright spatial solitons due to transverse modulation instability," Europhys. Lett. 35, 25-30 (1996).
[CrossRef]

Europhys. Lett. (1)

A. V. Mamaev, M. Saffman, and A.A. Zozulia, "Break-up of two-dimensional bright spatial solitons due to transverse modulation instability," Europhys. Lett. 35, 25-30 (1996).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, D. C. Hutching, D. J. Hagan, and E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solid," IEEE J. Quantum Electron. 27, 1296-1309 (1991).
[CrossRef]

J. Fluid Mech. (1)

E. D. Brown, S. B. Buchsbaum, R. E. Hall, J. P. Penhune, K. F. Schmitt, K. M. Watson, and D. C. Wyatt, "Observation of a nonlinear solitary wave packet in the Kelvin wake of a ship," J. Fluid Mech. 204, 263-293 (1989).
[CrossRef]

Opt. Lett. (3)

Phys. Fluids (2)

J. R. Myra and C. S. Liu, "Self-modulation of ion Berstein waves," Phys. Fluids 23, 2258-2264 (1980).
[CrossRef]

N. R. Pereira, A. Sen, and A. Bers, "Nonlinear development of lower hybrid cones," Phys. Fluids 21, 117-120 (1978).
[CrossRef]

Phys. Rev. B (1)

S. Adachi, "Optical properties of AlxGa1�??xAs alloys," Phys. Rev. B 38, 12345-12352 (1988).
[CrossRef]

Phys. Rev. Lett. (5)

S.-P. Gorza, N. Roig, Ph. Emplit, and M. Haelterman, "Snake Instability of a Spatiotemporal Bright Soliton Stripe," Phys. Rev. Lett. 92, 084101 (2004).
[CrossRef] [PubMed]

B. P. Anderson et al. "Watching dark soliton decay into vortex rings in a Bose-Einstein condensate," Phys. Rev. Lett. 86, 2926-2929 (2001).
[CrossRef] [PubMed]

X. Liu, K. Beckwitt, and F. Wise, "Transverse Instability of Optical Spatiotemporal Solitons in QuadraticMedia," Phys. Rev. Lett. 85, 1871-1874 (2000).
[CrossRef] [PubMed]

S. D. Jenkins, D. Salerno, S. Minardi, S. Tamo�?sauskas, T. A. B. Kennedy, and P. Di Trapani, "Quantum-noise initiated symmetry breaking of spatial solitons," Phys. Rev. Lett. 95, 203902 (2005).
[CrossRef] [PubMed]

P. M. Kelley, "Self-focusing of optical beams," Phys. Rev. Lett. 15, 1005-1007 (1965).
[CrossRef]

Physica D (1)

K. Germaschewski, R. Grauer, L. Bergé, V. K. Mezentsev, and J. J. Rasmussen, "Splittings, coalescence, bunch and snake patterns in the 3D nonlinear Schrödinger equation with anisotropic dispersion," Physica D 151, 175-198 (2001).

Proc. Roy. Soc. A (1)

B. Deconink, D. E. Pelinovsky, and J. D. Carter, "Transverse instabilities of deep-water solitary waves," Proc. Roy. Soc. A 462, 2039-2061 (2005).

Rep. Prog. Phys. (1)

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, "Ultrashort filaments of light in weakly ionized, optically transparent media," Rep. Prog. Phys. 70, 1633-1713 (2007).
[CrossRef]

Science (1)

Z. Dutton, M. Budde, C. Slowe, and L. V. Hau, "Observation of quatum shock waves created with ultracompressed slow light pulses in a Bose-Einstein condenstate," Science 293, 663-668 (2001).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

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

Other (3)

S. Trillo and W. Torruellas, Spatial solitons (Springer, Berlin, 2001).

G. P. Agrawal, Nonlinear fiber optics (Academic Press, San-Diego, 2001).

H. C. Yuen and B. M. Lake, Non-linear dynamics of deep-water gravity waves (Accademic Press, New York, 1982).

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Figures (6)

Fig. 1.
Fig. 1.

Snake instability of laser beams. The interplay between normal dispersion, diffraction and Kerr nonlinearity leads to transverse undulations of self-trapped beams. The schematic on the right hand side explains that the periodic lateral beam shift results from the amplification of an antisymmetric unstable mode.

Fig. 2.
Fig. 2.

Experimental setup. λ/2: half-waveplate, iso: isolator, Lc : cylindrical lens, L: lens.

Fig. 3.
Fig. 3.

Laser beam profile at the output of the guiding structure. In the linear propagation regime, the beam broadens due to diffraction (top). At high power, the optical Kerr non-linearity balances the diffraction and a spatial soliton is formed (bottom).

Fig. 4.
Fig. 4.

Input and output spectra of the laser beam. Nonlinear effects within the laser source are responsible for the presence of small sidebands in the spectrum. When a soliton is formed, these sidebands are amplified and higher harmonics appear because of the instability process.

Fig. 5.
Fig. 5.

Spatially resolved output spectrum of the self-trapped beam. Left: spectrum in logarithmic scale. Right: Density plot in linear scale of the area marked by the white square on the left. As a lateral beam displacement is associated with the presence of an antisymmetric mode (see Fig.1), the dip in the center of the spectral sidebands is the signature of the soliton beam undulations, i.e., of the snake instability.

Fig. 6.
Fig. 6.

Wavelength dependent output profiles. Spatial profiles of the sideband at 1512 nm (red curve) and of the main peak at 1530 nm (dark curve). The dip is exactly located at the beam center as expected from theory (blue curve [16]). The discrepancy between theory and experiment is due to the growth of both antisymmetric and symmetric unstable modes.

Equations (1)

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i A z + 1 2 k 2 A x 2 β 2 2 2 A t 2 + γ A 2 A = 0 ,

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