Experimental focusing shocklike dynamics in a nonlocal optical stochastic Kerr medium

We experimentally study the propagating of an optical intensity jump discontinuity in a nonlocal stochastic Kerr focusing nematic liquid crystal cell. We show both theoretically and experimentally that nonlocality opens a route towards beam steering in our system. Indeed, the discontinuity trajectory follows a curve that bends with the injected power. Despite the stochastic nature of the medium and the constant presence of transverse instabilities, the development of a focusing shocklike dynamics is shown to survive. The distance $Z_s$ for the focusing shock to occur follows a power law with the beam power $P$ according to $Z_s\propto P^{\chi }$, with $\chi =-4/3$, as for shock dynamics in self-defocusing media.

Figure 1

Experimental setup: CYL - cylindrical lens with $f=75\text{-mm}$ focal length, C - light cutter, L - plano-concave lenses with $f=100\text{-mm}$ focal length, BS1,BS2 - beam splitters. IS1 - imaging system composed of a 10X, NA = 0.25 microscope objective (Olympus) and a camera (Thorlabs CMOS camera, 10bit). BS2 - an imaging system composed of a 5X, NA = 0.1 microscope objective (Mitutoyo) mounted on a lens tube with $f=200\text{mm}$ focal length and a camera (Thorlabs).

Figure 2

(a) Steplike Gaussian intensity profile injected in the LC cell. Spatiotemporal evolution of the beam transverse profile after $z=1.2\text{-mm}$ propagation for (b) the local ($K_2=0$) and (c) nonlocal ($K_2=6.57\times {10}^{-12}\text{N}$) cases. Both profiles are normalized to their maximum values. (b) A = 5000 and (c) A = 31 250. $\epsilon =0$, $\beta =0$, $n_{\parallel }=1.7589$, $n_{\perp }=1.5269$, ${\lambda }_0=532\times {10}^{-9}\text{m,}$ and ${\omega }_y\approx 960\mu \text{m}$.

Figure 3

Spatial evolution of the initial intensity jump discontinuity vs propagating distance $z$ for increasing laser power measured before the sample entrance, namely, (a) $P=17.5\text{mW}$, (b) $P=73.8\text{mW}$, and (c) $P=193.5\text{mW}$. The intensity profiles are normalized to their maximum values. (d) Transverse intensity profiles at $z=354\mu \text{m}$ propagating distance [dotted lines on (a), (b), and (c)] for the three power values of diagrams (a), (b), and (c). Black circles on (d) locate the scattered light intensity discontinuity $Y_S$ (see text for definition). (e) Evolution of the intensity profile at $z=1200\mu \text{m}$ vs the injected light power $P$; the transverse profiles collected for each value of $P$ are normalized to 1 in order the render the image readable. All data are averaged over 20 s of dynamics.

Figure 4

(a) Typical experimental maximum transverse steepening $S_{{max}_z}\left(z\right)$ (see text for definition) evolution with increasing power, $P=137.18\text{mW}$ (black), $193.5\text{mW}$ (blue), and $279.7\text{mW}$ (red); the dot indicates the location $Z_S$ and refers to the maximum of $S_{{max}_z}\left(z\right)$. (b) Numerical maximum transverse steepening $S_{{max}_z}\left(z\right)$ evolution with increasing intensity values ${\left|A\right|}^2=5.64\times {10}^6$ (black), ${\left|A\right|}^2=7.98\times {10}^6$ (blue), and ${\left|A\right|}^2=9.76\times {10}^6{\text{V}}^2/{\text{m}}^2$ (red), respectively. (c) Experimental evolution of the focusing shocklike distance $Z_s$ (see text for definition) vs injected power $P$ in logarithmic scales showing a power law $Z_s\propto P^{\chi }$, with $\chi =-4/3$ coefficient. (d) Experimental evolution of the transverse position $Y_s$ of the intensity discontinuity (see text for definition) at $z=1.2\text{mm}$ vs injected power $P$ in logarithmic scales showing a power law $Y_s\propto P^{\chi }$, with $\chi =1/25$ coefficient. All experimental values are averaged over 20 s of dynamics.