Shock Waves in Disordered Media

We experimentally investigate the interplay between spatial shock waves and the degree of disorder during nonlinear optical propagation in a thermal defocusing medium. We characterize the way the shock point is affected by the amount of disorder and scales with wave amplitude. Evidence for the existence of a phase diagram in terms of nonlinearity and amount of randomness is reported. The results are in quantitative agreement with a theoretical approach based on the hydrodynamic approximation.

Figure 1

Images of transmitted intensity for different input power $P$ and particle concentration $c$: (a) $P=5\mathrm{mW}$, $c=0$, (b) $P=400\mathrm{mW}$, $c=0$, (c) $P=5\mathrm{mW}$, $c=0.017\mathrm{w}/\mathrm{w}$, (d) $P=400\mathrm{mW}$, $c=0.017\mathrm{w}/\mathrm{w}$ (e) $P=5\mathrm{mW}$, $c=0.030\mathrm{w}/\mathrm{w}$, (f) $P=400\mathrm{mW}$, $c=0.030\mathrm{w}/\mathrm{w}$. Superimposed curves show the measured section of the intensity profiles.

Figure 2

Beam propagation as observed from top fluorescence emission for different input power $P$ and particle concentration $c$: (a) $P=8\mathrm{mW}$, $c=0$, (b) $P=450\mathrm{mW}$, $c=0$, (c) $P=8\mathrm{mW}$, $c=0.017\mathrm{w}/\mathrm{w}$, (d) $P=450\mathrm{mW}$, $c=0.017\mathrm{w}/\mathrm{w}$ (e) $P=8\mathrm{mW}$, $c=0.030\mathrm{w}/\mathrm{w}$, (f) $P=450\mathrm{mW}$, $c=0.030\mathrm{w}/\mathrm{w}$.

Figure 3

(a) Measured shock point $Z_{\mathrm{S}}$ vs $P$ for various $c$; (b) disorder-power phase diagram with shock and nonshock regimes obtained from the data in panel (a): the dots correspond to the threshold powers, the dashed line and the dot-dashed line are the boundaries as estimated by the theory.

Figure 4

Trajectories of colliding particles forming shock vs $z$: (a) without disorder ($\eta =0$) and (b) for $\eta =0.1$; (c) shock profile in the phase space for $\eta =0$ and (d) for $\eta =0.1$ ($z$ varies in the range [0, 3]).

Figure 5

Theoretical histograms of particle positions for $\eta =0$ (ordered case, panel a) and for $\eta =0.2$ (panel b); (c) theoretical normalized shock position $z_s$ vs amount of disorder $\eta$ (black continuous line) and comparison with the measured $z_s$ vs concentration $c$ (red squares).