We present a detailed analysis of topological binding and elastic interactions between long, and micrometer-diameter fiber, and a microsphere in a homogeneously aligned nematic liquid crystal. Both objects are surface treated to produce strong perpendicular anchoring of the nematic liquid crystal. We use the opto-thermal micro-quench of the laser tweezers to produce topological defects with prescribed topological charge, such as pairs of a Saturn ring and an anti-ring, hyperbolic and radial hedgehogs on a fiber, as well as zero-charge loops. We study the entanglement and topological charge interaction between the topological defects of the fiber and sphere and we observe a huge variety of different entanglement topologies and defect-mediated elastic bindings.We explain all observed phenomena with simple topological rule: like topological charges repel each other and opposite topological charges attract. These binding mechanisms not only demonstrate the fascinating topology of nematic colloids, but also open a novel route to the assembly of very complex topological networks of fibers, spheres and other objects for applications in liquid crystal photonics.
Creating, imaging, and transforming the topological charge in a superconductor, a superfluid, a system of cold atoms6, or a soft ferromagnet is a difficult—if not impossible—task, because of the shortness of the length-scales and lack of control. The length scale and softness of defects in liquid crystals allow for the easy observation of charges, but it is difficult to control charge creation. Here we demonstrate full control over the creation, manipulation and analysis of topological charges that are pinned to a microfibre in a nematic liquid crystal. Oppositely charged pairs are created via the Kibble-Zurek mechanism by applying a laser-induced local temperature quench in the presence of symmetry-breaking boundaries. The pairs are long-lived, oppositely charged rings or points that either attract and annihilate, or form a long-lived, charge-neutral loop made of two segments with a fractional topological charge.
We study anisotropic Stimulated Emission Depletion (STED) from dye molecules, which are collectively ordered in a host liquid crystal. Due to the ordering of fluorescent emitters, the STED efficiency depends on the polarization of the depletion beam and time-delay of the STED pulse. The depletion efficiency is highest at lower temperatures in the highly ordered smectic-A phase and deteriorates in the higher temperature nematic and isotropic phases. We demonstrate by temporal tuning of STED that it is possible to generate an arbitrary sequence of nanosecond fluorescent pulses with variable width and variable delay. Our results show that the STED mechanism in principle allows for very fast (GHz) and efficient control of light by light, which could in the future be used for all-optical control of the flow of light in photonic microdevices based on liquid crystals. Using STED anisotropy and time-control, new modalities of STED imaging in quid crystals could be developed.