Dynamics of topological monopoles annihilation on a fibre in a thick and thin nematic layer.

We study topological defect annihilation on a glass fibre with homeotropic surface anchoring of nematic liquid crystal molecules. The fibre is set parallel to the nematic director of a planar cell with variable thickness and we create pairs of Saturn ring and Saturn anti-ring using the laser tweezers. In thick cells we observe in the whole region of defect separation a Coulomb-like pair attraction with no background force, [Formula: see text] with [Formula: see text]. In cells with thickness comparable to glass fibre diameter, we observe the Coulomb-like attraction only at small separations of the defect pair. For separations larger than the fibre diameter, the pair interaction force is independent of separation. This string-like force is attributed to the formation of defect lines, connecting both monopoles and are indeed visible only on extremely confined fibre, where the fibre diameter is practically equal to the nematic layer thickness. Numerical simulations confirm the formation of defect lines connecting both rings.