Field-matched mode sorter for optical vortex knots

Optical vortex knots are topologically structured light fields whose phase or polarization singularities trace linked or knotted trajectories during propagation, making them promising candidates for high-dimensional optical information carriers. Their use in communication or quantum-information protocols, however, requires a practical readout method that can distinguish a chosen knot alphabet with low crosstalk. Here, we demonstrate a proof-of-principle sorter for optical vortex knots using up to six optimized phase-only elements. The sorter maps each input knot to a predefined output region and is optimized directly from the output intensity distributions to enhance correct assignment, suppress crosstalk, and avoid degenerate mappings between distinct knots. We apply the method to an alphabet composed of the Hopf link, trefoil, and cinquefoil optical vortex knots. We empirically investigate the performance-to-cost trade-off across phase-plane counts and find that four planes give high distinguishability for the three-knot alphabet at reasonable optimization cost. We also benchmark the sorter under common experimental imperfections, and establish that the sorting mechanism is field-matched rather than topological: it responds to the transverse field at a chosen plane, whether or not a given perturbation preserves the knot's topology. These results extend optical mode sorting to topologically structured light and provide a readout route for knot-based high-dimensional optical communication.