Experimental observation of front propagation in a negatively diffractive inhomogeneous Kerr cavity

A focusing Kerr Fabry-Pérot cavity operating in a negative diffraction regime exhibits transverse propagating fronts connecting two different nematic liquid crystal molecule average orientations. Under an inhomogeneous spatial pumping beam, these fronts stop to propagate and lead to the formation of a stable localized structure. The trajectory of the front position is derived from the mean-field model. Its hyperbolic tangent analytical expression perfectly fits the experimental data.

Figure 1

Inhomogeneous Kerr cavity with negative diffraction. (a) Experimental setup. (b) Schematic representation of the physical cavity and the equivalent cavity: OI is the optical isolator; BS is the beam splitter; LC is the liquid crystal slice; $\text{D}{}_1$ and $\text{D}{}_2$ are photodetectors; $\text{L}{}_1$ and $\text{L}{}_2$ are lenses of focal length $f$; $p$ and $s$ are the polarized components of the pump (solid line) and probe (dashed line) beams, respectively; and $\text{M}{}_1$ and $\text{M}{}_2$ are the real cavity mirrors but the optical Fabry-Pérot cavity is delimited by $\text{M}{}_1$ and ${\text{M}}^{\prime }{}_2$ mirrors and its length is $d$.

Figure 2

Front propagation in the negative diffractive inhomogeneous Kerr cavity. (a) and (b) Transverse cross section of the initial (final) average localized structure shown by the dashed black (solid gray) line. (c) and (d) Spatiotemporal response to a step function of the input intensity from the lower to the upper branch of the bistable cycle. (e) and (f) Experimental and numerical cross section of the localized state. Light region account for high intensity of the light. (a), (c), and (e) Experiments with $I_0=433W{\text{cm}}^{-2}$, $d=-5\text{mm}$, $\phi =-0.6$ rad, $w_x=1400\mu \text{m}$, $w_y=100\mu \text{m}$, $R_1=81.8\%$, and $R_2=81.4\%$. (b) and (d) Numerical simulation of the LL model with $E_0=1.9$, $\Delta =3.0$, $\alpha =0.001$, $w_x=1400\mu \text{m}$, $w_y=100\mu \text{m}$, and $\varepsilon =0.4$.

Figure 3

Temporal evolution of the front position $x_0\left(t\right)$ corresponding to the spatiotemporal diagrams of Fig. 2. (a) Experiment and (b) numerical simulations of the LL model (1) using the same parameters considered in Fig. 2. Diamonds represent the location values extracted from the smoothed spatiotemporal diagrams. Dashed curves are the best fit using expression (5). The experimental fit parameters are $a=308\mu \text{m}$, $b=0.069$, and $t_0=35.2\text{s}$; the numerical fit parameters are $a=306\mu \text{m}$, $b=0.017$, and $t_0=107.7$.