Nonspecular Total Internal Reflection of Spatial Solitons at the Interface between Highly Birefringent Media

We investigate total internal reflection of nonlocal spatial optical solitons at the interface between two differently oriented regions of a highly birefringent nematic liquid crystal. The solitons survive the interaction with an induced index mismatch and undergo nonspecular reflection, with an emerging angle differing appreciably from the incidence angle.

Figure 1

(a) Sketch of the NLC cell. Tailored contacts on the top cover enable the application of distinct voltages $V_1$ and $V_2$ with respect to the ground plane and the definition of two regions (1 and 2) separated by plane $xp$. (b) Angles $\xi$ and $\rho$ of director $\widehat{n}$ in the coordinate system $xtp$. (c) Photograph of the interface $||p$ in a cell containing E7 and biased with $V_1=1.5\mathrm{V}$ and $V_2=0\mathrm{V}$.

Figure 2

(a) ISWN for the permitted wave vector $k_R$ upon TIR at the interface between regions 1 and 2 for ${\rho }_0=0.28\pi$ and ${\xi }_1>{\xi }_2$, i.e. $V_1>V_2$. Solid and dashed lines are the intersection of ISWN with the propagation plane $tp$ for $e$ waves in media 1 and 2, respectively; (b) No permitted wavevector $k_R$ exist for $o$ waves. (c) 2D contour map of reflection asymmetry $\Delta \Phi ={\Phi }_I-{\Phi }_R$ versus ${\xi }_1$ and ${\Phi }_I$. The dashed line indicates the critical angle ${\Phi }_c({\xi }_1)$ and identifies the parameter interval (on its right) where TIR occurs (${\Phi }_I>{\Phi }_c({\xi }_1)$).

Figure 3

Role of anisotropy in nonspecular reflection. (a) Angles ${\Phi }_{\mathrm{IS}}$ and ${\Phi }_{\mathrm{RS}}$ of the (observable) incident and reflected Poynting vectors $S_I$ and $S_R$ differ from ${\Phi }_I$ and ${\Phi }_R$ by the apparent walk-offs ${\delta }_{{\mathrm{tp}}_{-}I}$ and ${\delta }_{{\mathrm{tp}}_{-}R}$, respectively. (b) Contour map of the calculated observable nonspecularity $\Delta {\Phi }_s={\Phi }_{\mathrm{RS}}-{\Phi }_{\mathrm{IS}}$ versus ${\xi }_1$ and ${\Phi }_I$ for ${\rho }_0=0.28\pi$: for ${\Phi }_I>{\Phi }_c({\xi }_1)$ then ${\Phi }_{\mathrm{RS}}>{\Phi }_{\mathrm{IS}}$, with $|\Delta {\Phi }_s|<|\Delta \Phi |$. As in Fig. 2, TIR takes place on the right of the dashed line defining the critical angle.

Figure 4

(a) Photograph of a diffracting $o$ beam launched in region 1 with $V_1=1.5\mathrm{V}$ and propagating into region 2 with $V_2=0\mathrm{V}$; (b) photograph of a nematicon propagating straight from region 1 to region 2 for $V_1=V_2=1.5\mathrm{V}$; (c) photograph of a nematicon undergoing reflection when $V_1=1.5\mathrm{V}$ and $V_2=0\mathrm{V}$. (d) The observable trajectories $S_I$ and $S_R$ of incident and reflected solitons (dashed and solid lines, respectively), allow us to evaluate ${\Phi }_{\mathrm{IS}}$ and ${\Phi }_{\mathrm{RS}}$. The horizontal dashed line indicates the interface $||p$.