Generation of vortex rosette via donut-shaped beams in optical valves

Optical vortices have attracted significant interest due to their distinctive topological properties and wide-ranging applications, including free-space communication, quantum information, image analysis, and micromanipulation. Vortex formation can arise from the interaction of light with structured or anisotropic media, including chiral systems. Among the most effective platforms for generating optical vortex beams are optical valves and liquid crystal cells, which leverage molecular self-organization to produce complex light fields. We show, both experimentally and theoretically, that illuminating an optical valve with a donut-shaped beam generates a vortex rosette, consisting of a low-amplitude central vortex surrounded by a ring of interacting vortex-antivortex pairs. This structure imparts a nontrivial topological charge to the transmitted light, endowing it with novel characteristics akin to those of a q-plate. To elucidate the origin of these vortex rosettes, we derive an amplitude equation from first principles, offering insight into the underlying mechanisms driving their emergence.