Abstract

The transverse snake instability of the bright soliton solution of the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation is experimentally studied. We observed this instability in the spatial ditribution of the temporal spectrum of spatially extended femtosecond pulses propagating in normally dispersive self-defocusing planar semiconductor waveguide.

© 2006 Optical Society of America

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  1. V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  2. V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).
  3. J. R. Myra and C. S. Liu, Phys. Fluids 23, 2258 (1980).
    [CrossRef]
  4. K. Rypdal and J. J. Rasmussen, Phys. Scr. 40, 192 (1989).
    [CrossRef]
  5. Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
    [CrossRef]
  6. D. E. Pelinovsky, Math. Comput. Simul. 55, 585 (2001).
    [CrossRef]
  7. E. A. Kuznetsov and S. K. Turitsyn, Sov. Phys. JETP 67, 1583 (1988).
  8. A. V. Mamaev, M. Saffman, and A. A. Zozulia, Europhys. Lett. 35, 25 (1996).
    [CrossRef]
  9. V. Tikhonenko, J. Christou, B. Luther-Davies, and Y. S. Kivshar, Opt. Lett. 21, 1129 (1996).
    [CrossRef] [PubMed]
  10. S.-P. Gorza, N. Roig, Ph. Emplit, and M. Haelterman, Phys. Rev. Lett. 92, 084101 (2004).
    [CrossRef] [PubMed]
  11. E. D. Brown, S. B. Buchsbaum, R. E. Hall, J. P. Penhune, K. F. Schmitt, K. M. Watson, and D. C. Wyatt, J. Fluid Mech. 204, 263 (1989).
    [CrossRef]
  12. M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
    [CrossRef]
  13. S. Adachi, Phys. Rev. B 38, 12345 (1988).
    [CrossRef]
  14. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
  15. A. M. Weiner, J. P. Heritage, and M. Kirschner, J. Opt. Soc. Am. B 5, 1563 (1988).
    [CrossRef]

2004 (1)

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

2001 (2)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

D. E. Pelinovsky, Math. Comput. Simul. 55, 585 (2001).
[CrossRef]

2000 (1)

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

1996 (2)

1991 (1)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef]

1989 (2)

E. D. Brown, S. B. Buchsbaum, R. E. Hall, J. P. Penhune, K. F. Schmitt, K. M. Watson, and D. C. Wyatt, J. Fluid Mech. 204, 263 (1989).
[CrossRef]

K. Rypdal and J. J. Rasmussen, Phys. Scr. 40, 192 (1989).
[CrossRef]

1988 (3)

E. A. Kuznetsov and S. K. Turitsyn, Sov. Phys. JETP 67, 1583 (1988).

S. Adachi, Phys. Rev. B 38, 12345 (1988).
[CrossRef]

A. M. Weiner, J. P. Heritage, and M. Kirschner, J. Opt. Soc. Am. B 5, 1563 (1988).
[CrossRef]

1980 (1)

J. R. Myra and C. S. Liu, Phys. Fluids 23, 2258 (1980).
[CrossRef]

1974 (1)

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

1972 (1)

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Adachi, S.

S. Adachi, Phys. Rev. B 38, 12345 (1988).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

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, J. Fluid Mech. 204, 263 (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, J. Fluid Mech. 204, 263 (1989).
[CrossRef]

Christou, J.

Emplit, Ph.

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

Gorza, S.-P.

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

Haelterman, M.

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

Hagan, D. J.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (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, J. Fluid Mech. 204, 263 (1989).
[CrossRef]

Heritage, J. P.

Hutchings, D. C.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef]

Kirschner, M.

Kivshar, Y. S.

Kuznetsov, E. A.

E. A. Kuznetsov and S. K. Turitsyn, Sov. Phys. JETP 67, 1583 (1988).

Liu, C. S.

J. R. Myra and C. S. Liu, Phys. Fluids 23, 2258 (1980).
[CrossRef]

Luther-Davies, B.

Mamaev, A. V.

A. V. Mamaev, M. Saffman, and A. A. Zozulia, Europhys. Lett. 35, 25 (1996).
[CrossRef]

Myra, J. R.

J. R. Myra and C. S. Liu, Phys. Fluids 23, 2258 (1980).
[CrossRef]

Pelinovsky, D. E.

D. E. Pelinovsky, Math. Comput. Simul. 55, 585 (2001).
[CrossRef]

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

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, J. Fluid Mech. 204, 263 (1989).
[CrossRef]

Rasmussen, J. J.

K. Rypdal and J. J. Rasmussen, Phys. Scr. 40, 192 (1989).
[CrossRef]

Roig, N.

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

Rubenchik, A. M.

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

Rypdal, K.

K. Rypdal and J. J. Rasmussen, Phys. Scr. 40, 192 (1989).
[CrossRef]

Saffman, M.

A. V. Mamaev, M. Saffman, and A. A. Zozulia, Europhys. Lett. 35, 25 (1996).
[CrossRef]

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, J. Fluid Mech. 204, 263 (1989).
[CrossRef]

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Sheik-Bahae, M.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef]

Tikhonenko, V.

Turitsyn, S. K.

E. A. Kuznetsov and S. K. Turitsyn, Sov. Phys. JETP 67, 1583 (1988).

Van Stryland, E. W.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (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, J. Fluid Mech. 204, 263 (1989).
[CrossRef]

Weiner, A. M.

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, J. Fluid Mech. 204, 263 (1989).
[CrossRef]

Zakharov, V. E.

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

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Zozulia, A. A.

A. V. Mamaev, M. Saffman, and A. A. Zozulia, Europhys. Lett. 35, 25 (1996).
[CrossRef]

Europhys. Lett. (1)

A. V. Mamaev, M. Saffman, and A. A. Zozulia, Europhys. Lett. 35, 25 (1996).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (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, J. Fluid Mech. 204, 263 (1989).
[CrossRef]

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

Math. Comput. Simul. (1)

D. E. Pelinovsky, Math. Comput. Simul. 55, 585 (2001).
[CrossRef]

Opt. Lett. (1)

Phys. Fluids (1)

J. R. Myra and C. S. Liu, Phys. Fluids 23, 2258 (1980).
[CrossRef]

Phys. Rep. (1)

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

Phys. Rev. B (1)

S. Adachi, Phys. Rev. B 38, 12345 (1988).
[CrossRef]

Phys. Rev. Lett. (1)

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

Phys. Scr. (1)

K. Rypdal and J. J. Rasmussen, Phys. Scr. 40, 192 (1989).
[CrossRef]

Sov. Phys. JETP (3)

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

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

E. A. Kuznetsov and S. K. Turitsyn, Sov. Phys. JETP 67, 1583 (1988).

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

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Figures (3)

Fig. 1
Fig. 1

Density plots of the spatiotemporal field distribution obtained by numerical simulation: (a) z = 0 , (b) z = 5 mm . (c) Time-averaged spatial spectrum corresponding to (a) (dashed curve) and (b) (solid curve).

Fig. 2
Fig. 2

Time-averaged spatial spectra recorded at the output of the 5 mm long sample (a) in the linear regime and (b) at twice the soliton power (the dashed curve corresponds to the propagation of the seed beam alone).

Fig. 3
Fig. 3

Density plots of the spatially resolved temporal spectrum. (a)–(d) Experimental results recorded at the output of the 5 mm long planar waveguide. The average power is, respectively, 8.25, 20, 27.5, and 36 mW . (e)–(h) Numerical simulations with the same parameters.

Equations (1)

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i E z + 1 2 β E x x β 2 2 E t t + γ ( 1 + i κ ) E 2 E = 0 ,

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