Abstract

The neck instability of bright solitons of the hyperbolic nonlinear Shrödinger equation is investigated. It is shown that this instability originates from a four-wave mixing interaction that links on-axis to off-axis radiation at opposite frequency bands. Our experiment supports this interpretation.

© 2012 Optical Society of America

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References

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  1. A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996).
    [CrossRef]
  2. Z. Dutton, M. Budde, C. Slowe, and L. V. Hau, Science 293, 663 (2001).
    [CrossRef]
  3. N. R. Pereira, A. Sen, and A. Bers, Phys. Fluids 21, 117 (1978).
    [CrossRef]
  4. S.-P. Gorza, N. Roig, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 92, 084101 (2004).
    [CrossRef]
  5. X. Liu, K. Beckwitt, and F. Wise, Phys. Rev. Lett. 85, 1871 (2000).
    [CrossRef]
  6. V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).
  7. Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
    [CrossRef]
  8. B. Deconinck, D. E. Pelinovsky, and J. D. Carter, Proc. R. Soc. A 462, 2039 (2006).
    [CrossRef]
  9. S.-P. Gorza, P. Kockaert, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 102, 134101 (2009).
    [CrossRef]
  10. K. Germaschewski, R. Grauer, L. Bergé, V. K. Mezentsev, and J. J. Rasmussen, Physica D 151, 175 (2001).
    [CrossRef]
  11. A. V. Yulin, D. V. Skryabin, and A. G. Vladimirov, Opt. Express 14, 12347 (2006).
    [CrossRef]
  12. D. V. Skryabin, Phys. Rev. E 60, 7511 (1999).
    [CrossRef]
  13. M. A. Porras, A. Parola, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. A 76, 011803 (2007).
    [CrossRef]
  14. S.-P. Gorza, B. Deconinck, P. Emplit, T. Trogdon, and M. Haelterman, Phys. Rev. Lett. 106, 094101 (2011).
    [CrossRef]

2011 (1)

S.-P. Gorza, B. Deconinck, P. Emplit, T. Trogdon, and M. Haelterman, Phys. Rev. Lett. 106, 094101 (2011).
[CrossRef]

2009 (1)

S.-P. Gorza, P. Kockaert, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 102, 134101 (2009).
[CrossRef]

2007 (1)

M. A. Porras, A. Parola, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. A 76, 011803 (2007).
[CrossRef]

2006 (2)

B. Deconinck, D. E. Pelinovsky, and J. D. Carter, Proc. R. Soc. A 462, 2039 (2006).
[CrossRef]

A. V. Yulin, D. V. Skryabin, and A. G. Vladimirov, Opt. Express 14, 12347 (2006).
[CrossRef]

2004 (1)

S.-P. Gorza, N. Roig, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 92, 084101 (2004).
[CrossRef]

2001 (2)

Z. Dutton, M. Budde, C. Slowe, and L. V. Hau, Science 293, 663 (2001).
[CrossRef]

K. Germaschewski, R. Grauer, L. Bergé, V. K. Mezentsev, and J. J. Rasmussen, Physica D 151, 175 (2001).
[CrossRef]

2000 (2)

Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
[CrossRef]

X. Liu, K. Beckwitt, and F. Wise, Phys. Rev. Lett. 85, 1871 (2000).
[CrossRef]

1999 (1)

D. V. Skryabin, Phys. Rev. E 60, 7511 (1999).
[CrossRef]

1996 (1)

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996).
[CrossRef]

1978 (1)

N. R. Pereira, A. Sen, and A. Bers, Phys. Fluids 21, 117 (1978).
[CrossRef]

1974 (1)

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

Anderson, D. Z.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996).
[CrossRef]

Beckwitt, K.

X. Liu, K. Beckwitt, and F. Wise, Phys. Rev. Lett. 85, 1871 (2000).
[CrossRef]

Bergé, L.

K. Germaschewski, R. Grauer, L. Bergé, V. K. Mezentsev, and J. J. Rasmussen, Physica D 151, 175 (2001).
[CrossRef]

Bers, A.

N. R. Pereira, A. Sen, and A. Bers, Phys. Fluids 21, 117 (1978).
[CrossRef]

Budde, M.

Z. Dutton, M. Budde, C. Slowe, and L. V. Hau, Science 293, 663 (2001).
[CrossRef]

Carter, J. D.

B. Deconinck, D. E. Pelinovsky, and J. D. Carter, Proc. R. Soc. A 462, 2039 (2006).
[CrossRef]

Couairon, A.

M. A. Porras, A. Parola, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. A 76, 011803 (2007).
[CrossRef]

Deconinck, B.

S.-P. Gorza, B. Deconinck, P. Emplit, T. Trogdon, and M. Haelterman, Phys. Rev. Lett. 106, 094101 (2011).
[CrossRef]

B. Deconinck, D. E. Pelinovsky, and J. D. Carter, Proc. R. Soc. A 462, 2039 (2006).
[CrossRef]

Di Trapani, P.

M. A. Porras, A. Parola, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. A 76, 011803 (2007).
[CrossRef]

Dutton, Z.

Z. Dutton, M. Budde, C. Slowe, and L. V. Hau, Science 293, 663 (2001).
[CrossRef]

Emplit, P.

S.-P. Gorza, B. Deconinck, P. Emplit, T. Trogdon, and M. Haelterman, Phys. Rev. Lett. 106, 094101 (2011).
[CrossRef]

S.-P. Gorza, P. Kockaert, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 102, 134101 (2009).
[CrossRef]

S.-P. Gorza, N. Roig, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 92, 084101 (2004).
[CrossRef]

Faccio, D.

M. A. Porras, A. Parola, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. A 76, 011803 (2007).
[CrossRef]

Germaschewski, K.

K. Germaschewski, R. Grauer, L. Bergé, V. K. Mezentsev, and J. J. Rasmussen, Physica D 151, 175 (2001).
[CrossRef]

Gorza, S.-P.

S.-P. Gorza, B. Deconinck, P. Emplit, T. Trogdon, and M. Haelterman, Phys. Rev. Lett. 106, 094101 (2011).
[CrossRef]

S.-P. Gorza, P. Kockaert, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 102, 134101 (2009).
[CrossRef]

S.-P. Gorza, N. Roig, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 92, 084101 (2004).
[CrossRef]

Grauer, R.

K. Germaschewski, R. Grauer, L. Bergé, V. K. Mezentsev, and J. J. Rasmussen, Physica D 151, 175 (2001).
[CrossRef]

Haelterman, M.

S.-P. Gorza, B. Deconinck, P. Emplit, T. Trogdon, and M. Haelterman, Phys. Rev. Lett. 106, 094101 (2011).
[CrossRef]

S.-P. Gorza, P. Kockaert, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 102, 134101 (2009).
[CrossRef]

S.-P. Gorza, N. Roig, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 92, 084101 (2004).
[CrossRef]

Hau, L. V.

Z. Dutton, M. Budde, C. Slowe, and L. V. Hau, Science 293, 663 (2001).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
[CrossRef]

Kockaert, P.

S.-P. Gorza, P. Kockaert, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 102, 134101 (2009).
[CrossRef]

Liu, X.

X. Liu, K. Beckwitt, and F. Wise, Phys. Rev. Lett. 85, 1871 (2000).
[CrossRef]

Mamaev, A. V.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996).
[CrossRef]

Mezentsev, V. K.

K. Germaschewski, R. Grauer, L. Bergé, V. K. Mezentsev, and J. J. Rasmussen, Physica D 151, 175 (2001).
[CrossRef]

Parola, A.

M. A. Porras, A. Parola, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. A 76, 011803 (2007).
[CrossRef]

Pelinovsky, D. E.

B. Deconinck, D. E. Pelinovsky, and J. D. Carter, Proc. R. Soc. A 462, 2039 (2006).
[CrossRef]

Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
[CrossRef]

Pereira, N. R.

N. R. Pereira, A. Sen, and A. Bers, Phys. Fluids 21, 117 (1978).
[CrossRef]

Porras, M. A.

M. A. Porras, A. Parola, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. A 76, 011803 (2007).
[CrossRef]

Rasmussen, J. J.

K. Germaschewski, R. Grauer, L. Bergé, V. K. Mezentsev, and J. J. Rasmussen, Physica D 151, 175 (2001).
[CrossRef]

Roig, N.

S.-P. Gorza, N. Roig, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 92, 084101 (2004).
[CrossRef]

Rubenchik, A. M.

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

Saffman, M.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996).
[CrossRef]

Sen, A.

N. R. Pereira, A. Sen, and A. Bers, Phys. Fluids 21, 117 (1978).
[CrossRef]

Skryabin, D. V.

Slowe, C.

Z. Dutton, M. Budde, C. Slowe, and L. V. Hau, Science 293, 663 (2001).
[CrossRef]

Trogdon, T.

S.-P. Gorza, B. Deconinck, P. Emplit, T. Trogdon, and M. Haelterman, Phys. Rev. Lett. 106, 094101 (2011).
[CrossRef]

Vladimirov, A. G.

Wise, F.

X. Liu, K. Beckwitt, and F. Wise, Phys. Rev. Lett. 85, 1871 (2000).
[CrossRef]

Yulin, A. V.

Zakharov, V. E.

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

Zozulya, A. A.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996).
[CrossRef]

Opt. Express (1)

Phys. Fluids (1)

N. R. Pereira, A. Sen, and A. Bers, Phys. Fluids 21, 117 (1978).
[CrossRef]

Phys. Rep. (1)

Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
[CrossRef]

Phys. Rev. A (2)

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996).
[CrossRef]

M. A. Porras, A. Parola, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. A 76, 011803 (2007).
[CrossRef]

Phys. Rev. E (1)

D. V. Skryabin, Phys. Rev. E 60, 7511 (1999).
[CrossRef]

Phys. Rev. Lett. (4)

S.-P. Gorza, P. Kockaert, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 102, 134101 (2009).
[CrossRef]

S.-P. Gorza, B. Deconinck, P. Emplit, T. Trogdon, and M. Haelterman, Phys. Rev. Lett. 106, 094101 (2011).
[CrossRef]

S.-P. Gorza, N. Roig, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 92, 084101 (2004).
[CrossRef]

X. Liu, K. Beckwitt, and F. Wise, Phys. Rev. Lett. 85, 1871 (2000).
[CrossRef]

Physica D (1)

K. Germaschewski, R. Grauer, L. Bergé, V. K. Mezentsev, and J. J. Rasmussen, Physica D 151, 175 (2001).
[CrossRef]

Proc. R. Soc. A (1)

B. Deconinck, D. E. Pelinovsky, and J. D. Carter, Proc. R. Soc. A 462, 2039 (2006).
[CrossRef]

Science (1)

Z. Dutton, M. Budde, C. Slowe, and L. V. Hau, Science 293, 663 (2001).
[CrossRef]

Sov. Phys. JETP (1)

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Neck (solid curve) and snake (dashed curve) instability gain. (b) Density plot of |pΓ| as a function of the frequency detuning Ω. The amplitude has been normalized so that the energy |pΓ|2dKx is independent of Ω in each sideband. The dashed lines show the relation Kx=±2Ω for Ω>0.

Fig. 2.
Fig. 2.

Measured spatiotemporal spectrum at the output of a 5 mm long waveguide when a soliton beam (center panels) is launched together with a seed beam with a negative frequency detuning close (top) and far (bottom) from the threshold. The peak powers at the waveguide input are 1, 3 kW and 140mW, respectively. The intensity has been normalized to one in each panel for revealing the structure of the spectrum in the sidebands. The white dotted curve shows the theoretical dominant transverse frequency of pΓ.

Fig. 3.
Fig. 3.

Transverse wavenumber of the peaks in the idler sideband as a function of Ω. The theoretical red curve shows the dominant transverse frequency of pΓ. The length of the horizontal and vertical bars correspond to the spectral width of the seed beam (6 nm) and to the camera resolution, respectively.

Equations (2)

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iψZ+122ψX2122ψT2+|ψ|2ψ=0.
pΓ(X;Ω)=ϵ0(u+iv)exp(iZ/2),

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