Abstract

We are able to detect the details of spatial optical collisionless wave breaking through the high aperture imaging of a beam suffering shock in a fluorescent nonlinear nonlocal thermal medium. This allows us to directly measure how nonlocality and nonlinearity affect the point of shock formation and compare results with numerical simulations.

© 2012 Optical Society of America

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  1. G. B. Whitman, Linear and Nonlinear Waves (Wiley, 1974).
  2. A. Gurevich and L. P. Pitaevskii, Sov. Phys. JETP 38, 291 (1973) [Zh. Eksp. Teor. Fiz. 65, 590 (1973), in Russian].
  3. J. C. Bronski and D. McLaughlin, in Singular Limits of Dispersive Waves (Plenum, 1994).
  4. A. M. Kamchatnov, R. A. Kraenkel, and B. A. Umarov, Phys. Rev. E 66, 036609 (2002).
    [CrossRef]
  5. R. J. Taylor, D. R. Baker, and H. Ikezi, Phys. Rev. Lett. 24, 206 (1970).
    [CrossRef]
  6. J. E. Rothenberg and D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
    [CrossRef]
  7. C. Conti, S. Stark, P. St. J. Russell, and F. Biancalana, Phys. Rev. A 82 (2010).
    [CrossRef]
  8. W. Wan, S. Jia, and J. Fleischer, Nat. Phys. 3, 46 (2007).
    [CrossRef]
  9. M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A 74, 023623 (2006).
    [CrossRef]
  10. A. M. Deykoon and G. A. Swartzlander, J. Opt. Soc. Am. B 18, 804 (2001).
    [CrossRef]
  11. J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
    [CrossRef]
  12. C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
    [CrossRef]
  13. G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, Nat. Nanotechnol. 6, 107 (2011).
    [CrossRef]
  14. C. Conti and E. DelRe, Phys. Rev. Lett. 105, 118301 (2010).
    [CrossRef]
  15. C. Barsi, W. Wan, C. Sun, and J. W. Fleischer, Opt. Lett. 32, 2930 (2007).
    [CrossRef]
  16. N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 99, 043903 (2007).
    [CrossRef]
  17. C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
    [CrossRef]
  18. A. Minovich, D. N. Neshev, A. Dreischuh, W. Krolikowski, and Y. S. Kivshar, Opt. Lett. 32, 1599 (2007).
    [CrossRef]

2011

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, Nat. Nanotechnol. 6, 107 (2011).
[CrossRef]

2010

C. Conti and E. DelRe, Phys. Rev. Lett. 105, 118301 (2010).
[CrossRef]

C. Conti, S. Stark, P. St. J. Russell, and F. Biancalana, Phys. Rev. A 82 (2010).
[CrossRef]

2009

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

2007

A. Minovich, D. N. Neshev, A. Dreischuh, W. Krolikowski, and Y. S. Kivshar, Opt. Lett. 32, 1599 (2007).
[CrossRef]

C. Barsi, W. Wan, C. Sun, and J. W. Fleischer, Opt. Lett. 32, 2930 (2007).
[CrossRef]

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

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

2006

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

2004

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef]

2002

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
[CrossRef]

A. M. Kamchatnov, R. A. Kraenkel, and B. A. Umarov, Phys. Rev. E 66, 036609 (2002).
[CrossRef]

2001

1989

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

1973

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

1970

R. J. Taylor, D. R. Baker, and H. Ikezi, Phys. Rev. Lett. 24, 206 (1970).
[CrossRef]

Ablowitz, M. J.

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

Assanto, G.

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef]

Baker, D. R.

R. J. Taylor, D. R. Baker, and H. Ikezi, Phys. Rev. Lett. 24, 206 (1970).
[CrossRef]

Bang, O.

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
[CrossRef]

Barsi, C.

Biancalana, F.

C. Conti, S. Stark, P. St. J. Russell, and F. Biancalana, Phys. Rev. A 82 (2010).
[CrossRef]

Bronski, J. C.

J. C. Bronski and D. McLaughlin, in Singular Limits of Dispersive Waves (Plenum, 1994).

Coddington, I.

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

Conti, C.

C. Conti, S. Stark, P. St. J. Russell, and F. Biancalana, Phys. Rev. A 82 (2010).
[CrossRef]

C. Conti and E. DelRe, Phys. Rev. Lett. 105, 118301 (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]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef]

Cornell, E. A.

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

DelRe, E.

C. Conti and E. DelRe, Phys. Rev. Lett. 105, 118301 (2010).
[CrossRef]

Deykoon, A. M.

Dreischuh, A.

Engels, P.

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

Fleischer, J.

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

Fleischer, J. W.

Fratalocchi, A.

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

Ghofraniha, N.

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

Gosztola, D. J.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, Nat. Nanotechnol. 6, 107 (2011).
[CrossRef]

Grischkowsky, D.

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

Gurevich, A.

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

Hendren, W.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, Nat. Nanotechnol. 6, 107 (2011).
[CrossRef]

Hoefer, M. A.

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

Ikezi, H.

R. J. Taylor, D. R. Baker, and H. Ikezi, Phys. Rev. Lett. 24, 206 (1970).
[CrossRef]

Jia, S.

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

Kamchatnov, A. M.

A. M. Kamchatnov, R. A. Kraenkel, and B. A. Umarov, Phys. Rev. E 66, 036609 (2002).
[CrossRef]

Kivshar, Y. S.

Kraenkel, R. A.

A. M. Kamchatnov, R. A. Kraenkel, and B. A. Umarov, Phys. Rev. E 66, 036609 (2002).
[CrossRef]

Krolikowski, W.

A. Minovich, D. N. Neshev, A. Dreischuh, W. Krolikowski, and Y. S. Kivshar, Opt. Lett. 32, 1599 (2007).
[CrossRef]

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
[CrossRef]

McLaughlin, D.

J. C. Bronski and D. McLaughlin, in Singular Limits of Dispersive Waves (Plenum, 1994).

Minovich, A.

Neshev, D. N.

Peccianti, M.

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

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef]

Pitaevskii, L. P.

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

Podolskiy, V. A.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, Nat. Nanotechnol. 6, 107 (2011).
[CrossRef]

Pollard, R.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, Nat. Nanotechnol. 6, 107 (2011).
[CrossRef]

Rasmussen, J. J.

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
[CrossRef]

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]

Russell, P. St. J.

C. Conti, S. Stark, P. St. J. Russell, and F. Biancalana, Phys. Rev. A 82 (2010).
[CrossRef]

Schweikhard, V.

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

Stark, S.

C. Conti, S. Stark, P. St. J. Russell, and F. Biancalana, Phys. Rev. A 82 (2010).
[CrossRef]

Sun, C.

Swartzlander, G. A.

Taylor, R. J.

R. J. Taylor, D. R. Baker, and H. Ikezi, Phys. Rev. Lett. 24, 206 (1970).
[CrossRef]

Trillo, S.

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]

Umarov, B. A.

A. M. Kamchatnov, R. A. Kraenkel, and B. A. Umarov, Phys. Rev. E 66, 036609 (2002).
[CrossRef]

Wan, W.

Whitman, G. B.

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

Wiederrecht, G. P.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, Nat. Nanotechnol. 6, 107 (2011).
[CrossRef]

Wurtz, G. A.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, Nat. Nanotechnol. 6, 107 (2011).
[CrossRef]

Wyller, J.

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
[CrossRef]

Zayats, A. V.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, Nat. Nanotechnol. 6, 107 (2011).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Nanotechnol.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, Nat. Nanotechnol. 6, 107 (2011).
[CrossRef]

Nat. Phys.

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

Opt. Lett.

Phys. Rev. A

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

C. Conti, S. Stark, P. St. J. Russell, and F. Biancalana, Phys. Rev. A 82 (2010).
[CrossRef]

Phys. Rev. E

A. M. Kamchatnov, R. A. Kraenkel, and B. A. Umarov, Phys. Rev. E 66, 036609 (2002).
[CrossRef]

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
[CrossRef]

Phys. Rev. Lett.

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef]

C. Conti and E. DelRe, Phys. Rev. Lett. 105, 118301 (2010).
[CrossRef]

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

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

R. J. Taylor, D. R. Baker, and H. Ikezi, Phys. Rev. Lett. 24, 206 (1970).
[CrossRef]

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

Zh. Eksp. Teor. Fiz.

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

Other

J. C. Bronski and D. McLaughlin, in Singular Limits of Dispersive Waves (Plenum, 1994).

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

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Figures (4)

Fig. 1.
Fig. 1.

a–d, beam propagation a–c as observed from top fluorescence emission for three different input powers and d, calculated by numerical simulation; e–g, corresponding transmitted intensity in the experiments and h, in the simulations. Superimposed curves give the intensity x profile.

Fig. 2.
Fig. 2.

Normalized intensity profiles IN (black curve, top) along with derivative (xIN, red curve, bottom) for three different z at P=600mW: a, input, z=0; b, z=zs=273μm, shock point; c, z=850μm, postshock.

Fig. 3.
Fig. 3.

Steepness S(z) of transverse profiles as functions of z for three different powers. The point of maximum corresponds to shock distance zs.

Fig. 4.
Fig. 4.

a, shock position zs versus input power for sample B at two different beam waists: squares, 25μm; circles, 18μm; b, shock position versus input power for beam waist=25μm and different dye concentrations: squares, 0.067mM; circles, 0.1mM. Experiments are denoted by black (dark) and simulations by red (clear) symbols.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

iψζ+122ψθψ=iα2ψ,σ22θ+θ=|ψ|2,
ϕξ=k0ζn0dξK(ξξ)Iξ,

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