Generation of vector beams with liquid crystal disclination lines.

We report that light beams, guided along liquid crystal defect lines, can be transformed into vector beams with various polarization profiles. Using finite-difference time-domain numerical solving of Maxwell equations, we confirm that the defect in the orientational order of the liquid crystal induces a defect in the light field with twice the winding number of the liquid crystal defect, coupling the topological invariants of both fields. For example, it is possible to transform uniformly polarized light into light with a radial polarization profile. Our approach also correctly yields a zero-intensity region near the defect core, which is always present in areas of discontinuous light polarization or phase. Using circularly polarized incident light, we show that defects with noninteger winding numbers can be obtained, where topological constants are preserved by phase vortices, demonstrating coupling between the light's spin, orbital angular momentum, and polarization profile. Further, we find that an ultrafast femtosecond laser pulse traveling along a defect line splits into multiple intensity regions, again depending on the defect's winding number, allowing applications in beam steering and filtering. Finally, our approach describing the generation of complex optical fields via coupling with topological defect lines in optically birefringent nematic fluids can be easily extended to high-intensity beams that affect nematic ordering.