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Shock waves are well-known nonlinear waves, displaying an abrupt discontinuity. Observation can be made in a lot of physical fields, as in water wave, plasma and nonlinear optics. Shock waves can either break or relax through either catastrophic or regularization phenomena. In this work, we restrain our study to dispersive shock waves. This regularization phenomenon implies the emission of dispersive waves. We demonstrate experimentally and numerically the generation of spatial dispersive shock waves in a nonlocal focusing media.
The generation of dispersive shock wave in a focusing media is more problematic than in a defocusing one. Indeed, the modulational instability has to be frustrated to observe this phenomenon. In 2010, the dispersive shock wave was demonstrated experimentally in a focusing media with a partially coherent beam [1]. Another way is to use a nonlocal media [2]. The impact of nonlocality is more important than the modulational instability frustration. Here, we use nematic liquid crystals (NLC) as Kerr-like nonlocal medium. To achieve shock formation, we use the Riemann condition as initial spatial condition (edge at the beam entrance of the NLC cell).
In these experimental conditions, we generate, experimentally and numerically, shock waves that relax through the emission of dispersive waves. Associated with this phenomenon, we evidence the emergence of a localized wave that travels through the transverse beam profile. The beam steepness, which is a good indicator of the shock formation, is maximal at the shock point position. This latter follows a power law versus the injected power as in [3]. Increasing the injected power, we found multiple shock points. We have good agreements between the numerical simulations and the experimental results.
[1] W. Wan, D. V Dylov, C. Barsi, and J. W. Fleischer, Opt. Lett. 35, 2819 (2010).
[2] G. Assanto, T. R. Marchant, and N. F. Smyth, Phys. Rev. A - At. Mol. Opt. Phys. 78, 1 (2008).
[3] N. Ghofraniha, L. S. Amato, V. Folli, S. Trillo, E. DelRe, and C. Conti, Opt. Lett. 37, 2325 (2012).
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