Optical Vortices from Liquid Crystal Droplets

We report on the generation of mono- and polychromatic optical phase singularities from micron-sized birefringent droplets. This is done experimentally by using liquid crystal droplets whose three dimensional architecture of the optical axis is controlled within the bulk by surfactant agents. Because of its microscopic size these optical vortex generators are optically trapped and manipulated at will, thus realizing a robust self-aligned micro-optical device for orbital angular momentum conversion. Experimental observations are supported by a simple model of optical spin-orbit coupling in uniaxial dielectrics that emphasizes the prominent role of the transverse optical anisotropy with respect to the beam propagation direction.

Figure 1

Optical vortex generation from a radial nematic liquid crystal droplet. An incident light with circular polarization ${\mathbf{c}}_{\pm }$ having a smooth wave front profile ($\ell =0$) is partly converted into the orthogonal polarization state ${\mathbf{c}}_{\mp }$ that bears a phase singularity ($\ell \ne 0$). Insets: (a) crossed polarizers image identifying a cylindrically symmetric director distribution and (b) radial structure of the director.

Figure 2

Twin droplets interferences. Insets: table-top double-slit Young experiment using a Gaussian beam (a) and a charge two optical vortex [(b) and (c)]. Scale bar is $5\mu \mathrm{m}$.

Figure 3

Experimental spatially resolved Stokes polarimetry analysis of a single tweezed radial droplet with diameter $\simeq 7\mu \mathrm{m}$ for quasimonochromatic condenser illumination. (a) $s_1$, (b) $s_2$, (c) $s_3$.

Figure 4

(a) Experimental azimuthal phase $\Phi (\theta )$ revealing a phase singularity with charge two ($\ell =2$). Markers are experimental data and red curve is the theoretical prediction $\Phi (\theta )=2\theta$. Inset: bright field droplet image, scale bar is $5\mu \mathrm{m}$. (b) Polychromatic vortex intensity distribution (panel 1) and its RGB components (panels 1, 2, and 3).

Figure 5

Optical vortex generation for the trapping beam. (a) Fraction of converted, $P_{-}/P_0$ (open symbols), and unconverted, $P_{+}/P_0$ (filled symbols), photons vs the trapping power $P_0$ for different droplet sizes. Circles, squares, triangles and diamonds refer to droplet diameter $d=1.5$, 2.1, 2.4, and $3.2\mu \mathrm{m}$, respectively. (b) Crossed polarized images of the progressively twisted trapped droplet with $d=2.4\mu \mathrm{m}$ vs power. (c) Power conversion vs $d$ for the vortex (black color) and nonvortex (red color). Markers : experimental data; curves: theoretical prediction from models 1 and 2 (see text for details). Insets: false color intensity distributions of the nonvortex and vortex output beams fields.

Figure 6

Illustration of the director distributions that correspond to model 1 (axial symmetry) and model 2 (radial symmetry).