Abstract

We show that the saturation of defocusing nonlinearities leads to qualitative changes in the onset of wave breaking, determining double shock formation whose regularization occurs in terms of antidark solitons. In a given material, the crossover between different regimes can be controlled by changing the input intensity.

© 2012 Optical Society of America

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  1. A. V. Gurevich and L. P. Pitaevskii, Sov. Phys. JETP 38, 291 (1974) [Zh. Eksp. Teor. Fiz. 65, 590 (1973), in Russian].
  2. A. V. Gurevich and A. L. Krylov, Sov. Phys. JETP 65, 944 (1973) [Zh. Eksp. Teor. Fiz.. 92, 1684 (1987), in Russian].
  3. B. A. Dubrovin and S. P. Novikov, Russ. Math. Surv. 44, 35 (1989) [Usp. Mat. Nauk. 44, 29 (1989), in Russian].
  4. A. M. Kamchatnov, Phys. Rep. 286, 199 (1997).
    [CrossRef]
  5. M. Hoefer and M. Ablowitz, Scholarpedia 4, 5562 (2009).
  6. J. E. Rothenberg and D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
    [CrossRef]
  7. Y. Kodama and S. Wabnitz, Opt. Lett. 20, 2291 (1995).
    [CrossRef]
  8. S. Trillo and A. Valiani, Opt. Lett. 35, 3967 (2010).
    [CrossRef]
  9. W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2007).
    [CrossRef]
  10. N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 99, 043903 (2007).
    [CrossRef]
  11. S. Jia, W. Wan, and J. W. Fleischer, Phys. Rev. Lett. 99, 223901 (2007).
    [CrossRef]
  12. C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
    [CrossRef]
  13. G. A. El, A. Gammal, E. G. Khamis, R. A. Kraenkel, and A. M. Kamchatnov, Phys. Rev. A 76, 053813 (2007).
    [CrossRef]
  14. Y.-F. Chen, K. Beckwitt, F. Wise, B. G. Aitken, J. S. Sanghera, and I. D. Aggarwal, J. Opt. Soc. Am. B 23, 347(2006).
    [CrossRef]
  15. Z. Q. Zhang, W. Q. He, C. M. Gu, W. Z. Shen, H. Ogawa, and Q. X. Guo, Appl. Phys. Lett. 91, 221902 (2007).
    [CrossRef]
  16. G. I. Stegeman and R. H. Stolen, J. Opt. Soc. Am. B 6, 652 (1989).
    [CrossRef]
  17. G. B. Whitham, Linear and Nonlinear Waves (Wiley, 1974).
  18. M. Crosta, A. Fratalocchi, and S. Trillo, Phys. Rev. A 84, 063809 (2011).
    [CrossRef]

2011

M. Crosta, A. Fratalocchi, and S. Trillo, Phys. Rev. A 84, 063809 (2011).
[CrossRef]

2010

2009

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

M. Hoefer and M. Ablowitz, Scholarpedia 4, 5562 (2009).

2007

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2007).
[CrossRef]

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

S. Jia, W. Wan, and J. W. Fleischer, Phys. Rev. Lett. 99, 223901 (2007).
[CrossRef]

G. A. El, A. Gammal, E. G. Khamis, R. A. Kraenkel, and A. M. Kamchatnov, Phys. Rev. A 76, 053813 (2007).
[CrossRef]

Z. Q. Zhang, W. Q. He, C. M. Gu, W. Z. Shen, H. Ogawa, and Q. X. Guo, Appl. Phys. Lett. 91, 221902 (2007).
[CrossRef]

2006

1997

A. M. Kamchatnov, Phys. Rep. 286, 199 (1997).
[CrossRef]

1995

1989

G. I. Stegeman and R. H. Stolen, J. Opt. Soc. Am. B 6, 652 (1989).
[CrossRef]

B. A. Dubrovin and S. P. Novikov, Russ. Math. Surv. 44, 35 (1989) [Usp. Mat. Nauk. 44, 29 (1989), in Russian].

J. E. Rothenberg and D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
[CrossRef]

1974

A. V. Gurevich and L. P. Pitaevskii, Sov. Phys. JETP 38, 291 (1974) [Zh. Eksp. Teor. Fiz. 65, 590 (1973), in Russian].

1973

A. V. Gurevich and A. L. Krylov, Sov. Phys. JETP 65, 944 (1973) [Zh. Eksp. Teor. Fiz.. 92, 1684 (1987), in Russian].

Ablowitz, M.

M. Hoefer and M. Ablowitz, Scholarpedia 4, 5562 (2009).

Aggarwal, I. D.

Aitken, B. G.

Beckwitt, K.

Chen, Y.-F.

Conti, C.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

Crosta, M.

M. Crosta, A. Fratalocchi, and S. Trillo, Phys. Rev. A 84, 063809 (2011).
[CrossRef]

Dubrovin, B. A.

B. A. Dubrovin and S. P. Novikov, Russ. Math. Surv. 44, 35 (1989) [Usp. Mat. Nauk. 44, 29 (1989), in Russian].

El, G. A.

G. A. El, A. Gammal, E. G. Khamis, R. A. Kraenkel, and A. M. Kamchatnov, Phys. Rev. A 76, 053813 (2007).
[CrossRef]

Fleischer, J. W.

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2007).
[CrossRef]

S. Jia, W. Wan, and J. W. Fleischer, Phys. Rev. Lett. 99, 223901 (2007).
[CrossRef]

Fratalocchi, A.

M. Crosta, A. Fratalocchi, and S. Trillo, Phys. Rev. A 84, 063809 (2011).
[CrossRef]

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

Gammal, A.

G. A. El, A. Gammal, E. G. Khamis, R. A. Kraenkel, and A. M. Kamchatnov, Phys. Rev. A 76, 053813 (2007).
[CrossRef]

Ghofraniha, N.

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

Grischkowsky, D.

J. E. Rothenberg and D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
[CrossRef]

Gu, C. M.

Z. Q. Zhang, W. Q. He, C. M. Gu, W. Z. Shen, H. Ogawa, and Q. X. Guo, Appl. Phys. Lett. 91, 221902 (2007).
[CrossRef]

Guo, Q. X.

Z. Q. Zhang, W. Q. He, C. M. Gu, W. Z. Shen, H. Ogawa, and Q. X. Guo, Appl. Phys. Lett. 91, 221902 (2007).
[CrossRef]

Gurevich, A. V.

A. V. Gurevich and L. P. Pitaevskii, Sov. Phys. JETP 38, 291 (1974) [Zh. Eksp. Teor. Fiz. 65, 590 (1973), in Russian].

A. V. Gurevich and A. L. Krylov, Sov. Phys. JETP 65, 944 (1973) [Zh. Eksp. Teor. Fiz.. 92, 1684 (1987), in Russian].

He, W. Q.

Z. Q. Zhang, W. Q. He, C. M. Gu, W. Z. Shen, H. Ogawa, and Q. X. Guo, Appl. Phys. Lett. 91, 221902 (2007).
[CrossRef]

Hoefer, M.

M. Hoefer and M. Ablowitz, Scholarpedia 4, 5562 (2009).

Jia, S.

S. Jia, W. Wan, and J. W. Fleischer, Phys. Rev. Lett. 99, 223901 (2007).
[CrossRef]

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2007).
[CrossRef]

Kamchatnov, A. M.

G. A. El, A. Gammal, E. G. Khamis, R. A. Kraenkel, and A. M. Kamchatnov, Phys. Rev. A 76, 053813 (2007).
[CrossRef]

A. M. Kamchatnov, Phys. Rep. 286, 199 (1997).
[CrossRef]

Khamis, E. G.

G. A. El, A. Gammal, E. G. Khamis, R. A. Kraenkel, and A. M. Kamchatnov, Phys. Rev. A 76, 053813 (2007).
[CrossRef]

Kodama, Y.

Kraenkel, R. A.

G. A. El, A. Gammal, E. G. Khamis, R. A. Kraenkel, and A. M. Kamchatnov, Phys. Rev. A 76, 053813 (2007).
[CrossRef]

Krylov, A. L.

A. V. Gurevich and A. L. Krylov, Sov. Phys. JETP 65, 944 (1973) [Zh. Eksp. Teor. Fiz.. 92, 1684 (1987), in Russian].

Novikov, S. P.

B. A. Dubrovin and S. P. Novikov, Russ. Math. Surv. 44, 35 (1989) [Usp. Mat. Nauk. 44, 29 (1989), in Russian].

Ogawa, H.

Z. Q. Zhang, W. Q. He, C. M. Gu, W. Z. Shen, H. Ogawa, and Q. X. Guo, Appl. Phys. Lett. 91, 221902 (2007).
[CrossRef]

Peccianti, M.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

Pitaevskii, L. P.

A. V. Gurevich and L. P. Pitaevskii, Sov. Phys. JETP 38, 291 (1974) [Zh. Eksp. Teor. Fiz. 65, 590 (1973), in Russian].

Rothenberg, J. E.

J. E. Rothenberg and D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
[CrossRef]

Ruocco, G.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

Sanghera, J. S.

Shen, W. Z.

Z. Q. Zhang, W. Q. He, C. M. Gu, W. Z. Shen, H. Ogawa, and Q. X. Guo, Appl. Phys. Lett. 91, 221902 (2007).
[CrossRef]

Stegeman, G. I.

Stolen, R. H.

Trillo, S.

M. Crosta, A. Fratalocchi, and S. Trillo, Phys. Rev. A 84, 063809 (2011).
[CrossRef]

S. Trillo and A. Valiani, Opt. Lett. 35, 3967 (2010).
[CrossRef]

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

Valiani, A.

Wabnitz, S.

Wan, W.

S. Jia, W. Wan, and J. W. Fleischer, Phys. Rev. Lett. 99, 223901 (2007).
[CrossRef]

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2007).
[CrossRef]

Whitham, G. B.

G. B. Whitham, Linear and Nonlinear Waves (Wiley, 1974).

Wise, F.

Zhang, Z. Q.

Z. Q. Zhang, W. Q. He, C. M. Gu, W. Z. Shen, H. Ogawa, and Q. X. Guo, Appl. Phys. Lett. 91, 221902 (2007).
[CrossRef]

Appl. Phys. Lett.

Z. Q. Zhang, W. Q. He, C. M. Gu, W. Z. Shen, H. Ogawa, and Q. X. Guo, Appl. Phys. Lett. 91, 221902 (2007).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Phys.

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2007).
[CrossRef]

Opt. Lett.

Phys. Rep.

A. M. Kamchatnov, Phys. Rep. 286, 199 (1997).
[CrossRef]

Phys. Rev. A

G. A. El, A. Gammal, E. G. Khamis, R. A. Kraenkel, and A. M. Kamchatnov, Phys. Rev. A 76, 053813 (2007).
[CrossRef]

M. Crosta, A. Fratalocchi, and S. Trillo, Phys. Rev. A 84, 063809 (2011).
[CrossRef]

Phys. Rev. Lett.

J. E. Rothenberg and D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
[CrossRef]

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

S. Jia, W. Wan, and J. W. Fleischer, Phys. Rev. Lett. 99, 223901 (2007).
[CrossRef]

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

Russ. Math. Surv.

B. A. Dubrovin and S. P. Novikov, Russ. Math. Surv. 44, 35 (1989) [Usp. Mat. Nauk. 44, 29 (1989), in Russian].

Scholarpedia

M. Hoefer and M. Ablowitz, Scholarpedia 4, 5562 (2009).

Sov. Phys. JETP

A. V. Gurevich and L. P. Pitaevskii, Sov. Phys. JETP 38, 291 (1974) [Zh. Eksp. Teor. Fiz. 65, 590 (1973), in Russian].

A. V. Gurevich and A. L. Krylov, Sov. Phys. JETP 65, 944 (1973) [Zh. Eksp. Teor. Fiz.. 92, 1684 (1987), in Russian].

Other

G. B. Whitham, Linear and Nonlinear Waves (Wiley, 1974).

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Figures (3)

Fig. 1.
Fig. 1.

Snapshots (z=1) of intensity profiles ρ(x) from Eqs. (6)–(9), for ρ0=0.5 and (a) α=0.1, single shock; (b) α=0.45, double shock.

Fig. 2.
Fig. 2.

(a) Snapshots of the dynamics ruled by Eq. (2): (a) intensity versus x. The insets show a zoom of the nonstationary DSW at (b) z=24 and (c) z=35. Here ε=0.01, α=0.1, and the input is a super-Gaussian [red dashed curve in (a)] with pedestal ρ0=2/3.

Fig. 3.
Fig. 3.

(a) Snapshots of double shock evolution from Eq. (2) with ε=0.01, α=0.46 (>αc): (a) intensity versus x at z=24 (black) and z=35 (blue), compared with the input (dashed red). The insets show a zoom of the DSWs composed by a train of (b) antidark solitons and (c) dark solitons at z=35.

Equations (9)

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iUZ+12k2UX2γ2|U|2U+γ4|U|4U=0,
iϵψz+ϵ222ψx2|ψ|2ψ+α|ψ|4ψ=0,
zρ+x(uρ)=0,zu+uxuxn=0,
R(ρ)=ρ(12αρ)+cos1(14αρ)22α,
λ±z+V±λ±x=0,
ξ=R(ρ=1)R(ρ)ρ(12αρ),
ξ=R(ρ)R(ρ0)+ρ(12αρ).
xi±=[R(ρ=1)R(ρi)±ρi(12αρi)]z.
xe=12αz;xe+=ρ0(12αρ0)z.

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