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

Optical vortices have attracted significant interest due to their distinctive topological properties and wideranging applications, including free-space communication, quantum information processing, image analysis, and the manipulation of microscopic particles. Vortex formation typically arises from the interaction between light and chiral structures. 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 donutshaped beam induces the formation of vortex triad loops. These loops consist of a central vortex with low amplitude, surrounded by a ring exhibiting diverse vortex configurations. 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 triad loops, we derive an amplitude equation from first principles, offering insight into the underlying mechanisms driving their emergence.