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Plasmonic vortex lenses (PVLs), producing vortex modes, known as plasmonicvortices (PVs), in the process of plasmonic spin-orbit coupling, provide apromising platform for the realization of many optical vortex-basedapplications. Very recently, it has been reported that a single PVL cangenerate multiple PVs. This work exploits the representation theory of finitegroups, reveals the symmetry origin of the generated PVs, and derives a newconservation relation based on symmetry principles. Specifically, the symmetryprinciples divide the near field of the PVL into regions, designate integers,which are the topological charges, to the regions, and, particularly, give anupper bound to the topological charge of the PV at the center of the PVL.Further application of the symmetry principles to the spin-orbit couplingprocess leads to a new conservation relation. Based on this relation, atwo-step procedure is suggested to link the angular momentum of the incidentfield with the one of the generated PVs through the symmetries of the PVL. Thistheory is well demonstrated by numerical calculations. This work provides analternative but essential symmetry perspective on the dynamics of spin-orbitcoupling in PVLs, forms a strong complement for the physical investigationsperformed before, and therefore lays down a solid foundation for flexiblymanipulating the PVs for emerging vortex-based nanophotonic applications.

Symmetry-compatible angular momentum conservation relation in plasmonic vortex lenses with rotational symmetries