Laser Trapping of Small Colloidal Particles in a Nematic Liquid Crystal: Clouds and Ghosts

We show that, contrary to intuition, small $(\le 1\mu \mathrm{m})$ transparent particles can be trapped and manipulated in a nematic liquid crystal using an intense laser beam, although their index of refraction is lower than both refractive indices of the surrounding birefringent fluid. Two mechanisms are identified that are responsible for this anomalous trapping: (i) surface-induced distortion of the birefringent media around the particle, creating a high-index “cloud” around the colloid, and (ii) laser-induced distortion or (partial) melting of a nematic, creating a ghost colloid.

Figure 1

(a) Sequence of micrograph images under crossed polarizers, showing a trapping event at large laser power ($64\mathrm{m}\mathrm{W}$) in E12. Note the apparent size of a $0.97\mu \mathrm{m}$ colloid, and the bright spot ghost. The bright spot is due to the local birefringent area, created by the laser light-induced distortion of the director field. (b) The trapping event observed under crossed polarizers in 5CB at large laser power ($64\mathrm{m}\mathrm{W}$). Note the black spot ghost. It appears black, as the 5CB is locally molten into the isotropic phase. (c) The Brownian trajectory of a $0.97\mu \mathrm{m}$ silica particle in a homeotropic nematic cell filled with E12, in another experiment, laser power ($32\mathrm{m}\mathrm{W}$). The zero position is at the optical trap. The light is switched off at $A$ and switched on at $B$. (d) The particle-trap separation as a function of time for the trajectory shown in (c). Note the range of attraction.

Figure 2

(a) The positions of 5000 points out of 15 000 recorded during the Brownian motion of a $0.97\mu \mathrm{m}$ silica particle in an optical trap in homeotropic E12. (b) The corresponding histograms for each coordinate. (c) The probability density $p(r)$ for the Brownian cloud at two power levels. The solid lines are the best fits to Eq. (1). (d) The reconstructed profile of the optical potential. The parabolic fit yields spring constants of the trap $k_{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{p}}=9.2(1\pm 0.05)\mathrm{p}\mathrm{N}/\mu \mathrm{m}$ for $32\mathrm{m}\mathrm{W}$ laser power and $k_{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{p}}=2.0(1\pm 0.05)\mathrm{p}\mathrm{N}/\mu \mathrm{m}$ for $8\mathrm{m}\mathrm{W}$.