Abstract

We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.

© 2007 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
  2. J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
    [CrossRef]
  3. W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2007).
    [CrossRef]
  4. V. I. Karpman, Nonlinear Waves in Dispersive Media (Pergamon, 1974).
  5. A. Litvak, V. Mironov, G. Fraiman, and A. Yunakovskii, Sov. J. Plasma Phys. 1, 31 (1975).
  6. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999).
    [CrossRef]
  7. D. Suter and T. Blasberg, Phys. Rev. A 48, 4583 (1993).
    [CrossRef] [PubMed]
  8. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
    [CrossRef] [PubMed]
  9. C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
    [CrossRef] [PubMed]
  10. J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
    [CrossRef]
  11. S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
    [CrossRef]
  12. W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, Phys. Rev. E 64, 016612 (2001).
    [CrossRef]
  13. E. Madelung, Z. Phys. 40, 322 (1927).
    [CrossRef]
  14. C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
    [CrossRef] [PubMed]
  15. C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
    [CrossRef]
  16. E. A. Mclean, L. Sica, and A. J. Glass, Appl. Phys. Lett. 13, 369 (1968).
    [CrossRef]
  17. P. M. Livingston, Appl. Opt. 10, 426 (1971).
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  18. N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 99, 043903 (2007).
    [CrossRef] [PubMed]

2007 (2)

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] [PubMed]

2006 (2)

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

2005 (1)

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

2003 (1)

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

2001 (1)

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, Phys. Rev. E 64, 016612 (2001).
[CrossRef]

1999 (1)

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999).
[CrossRef]

1993 (1)

D. Suter and T. Blasberg, Phys. Rev. A 48, 4583 (1993).
[CrossRef] [PubMed]

1992 (1)

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

1975 (1)

A. Litvak, V. Mironov, G. Fraiman, and A. Yunakovskii, Sov. J. Plasma Phys. 1, 31 (1975).

1971 (1)

1968 (2)

E. A. Mclean, L. Sica, and A. J. Glass, Appl. Phys. Lett. 13, 369 (1968).
[CrossRef]

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
[CrossRef]

1965 (1)

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

1927 (1)

E. Madelung, Z. Phys. 40, 322 (1927).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

E. A. Mclean, L. Sica, and A. J. Glass, Appl. Phys. Lett. 13, 369 (1968).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, IEEE J. Quantum Electron. QE-4, 568 (1968).
[CrossRef]

J. Appl. Phys. (1)

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Nat. Phys. (2)

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

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

Phys. Rev. A (1)

D. Suter and T. Blasberg, Phys. Rev. A 48, 4583 (1993).
[CrossRef] [PubMed]

Phys. Rev. E (1)

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, Phys. Rev. E 64, 016612 (2001).
[CrossRef]

Phys. Rev. Lett. (4)

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

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

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

Rev. Mod. Phys. (2)

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999).
[CrossRef]

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Sov. J. Plasma Phys. (1)

A. Litvak, V. Mironov, G. Fraiman, and A. Yunakovskii, Sov. J. Plasma Phys. 1, 31 (1975).

Z. Phys. (1)

E. Madelung, Z. Phys. 40, 322 (1927).
[CrossRef]

Other (2)

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

V. I. Karpman, Nonlinear Waves in Dispersive Media (Pergamon, 1974).

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Figures (4)

Fig. 1
Fig. 1

Numerical simulation of dispersive shock waves as a function of nonlocal response width ( w , normalized to the width of the input Gaussian hump). The red bars on the x-axis indicate the FWHM of the initial hump, which has a 25:1 peak-to-background intensity ratio.

Fig. 2
Fig. 2

Experimental evolution of dispersive shock wave after 1 cm of propagation in an ethanol + iodine liquid cell. (a) Linear case. Inset, input profile. (b) Initial shock formation in nonlinear, nonlocal case. (c) Approximately 200 ms later, quasi-steady-state (before convection of fluid) shock profile. (d) Steady state, with asymmetry due to convection.

Fig. 3
Fig. 3

Shock length, measured horizontally from centerline to the end of oscillations, as a function of hump-to-background intensity ratio. Black dots, experimental measurements. Solid curve, best fit of D s = a s ( 1 + b s ρ ρ ) , with a s = 46 μ m and b s = 0.13 . Inset, numerical simulation, showing consistency of scaling relation as a function of nonlocal response width w .

Fig. 4
Fig. 4

Comparison of shock profiles with background (a)–(c) and without background (d)–(f). From top to bottom, the laser power is 6.1, 24.4, and 36.6 mW , respectively.

Equations (4)

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i ψ z + 1 2 k 0 2 ψ + Δ n ( ρ ) ψ = 0 ,
R ( x ) = ( π w 2 ) 1 2 exp ( x 2 w 2 ) ,
ρ z + x ( ρ v ) = 0 ,
ν z + ν ν x = x [ Δ n ( ψ 2 ) ] + 1 2 x ( 1 ρ 2 x 2 ρ ) ,

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