Detection of Poincaré beam coordinates on the hybrid-order Poincaré sphere via Stokes vortex mapping

Poincaré beams can be mapped on the hybrid-order Poincaré sphere using longitude and latitude coordinates. Mapping on a geometrical sphere is crucial in the study of the topological aspects and applications of singular beams. Currently, there is a dearth of methods that enable the mapping of Poincaré beams on these spheres. This paper presents a simple and robust detection method to determine the coordinates of Poincaré beams on a hybrid-order Poincaré sphere (HyOPS). The method requires only a single intensity measurement obtained through a fixed linear polarizer. The transmitted intensity pattern contains unique null points whose positions encode both longitude and latitude coordinates of the beam. This approach eliminates the need for polarizer rotation or multiple projections, thereby reducing experimental errors and improving reproducibility. The method is applicable to beams belonging to all three types of HyOPS, where the beams are formed by linear/circular state superpositions. Experimental results demonstrate accurate mapping of beam coordinates, consistent with theoretical predictions.