The polarization distribution of a structured light field, such as a vector vortex beam (VVB), is defined by a uniform ellipticity and a polarization azimuth that varies across the transverse plane. On the standard Poincaré sphere, polarization of this beam traces a ring at a fixed latitude and can be uniquely mapped to a single point on the higher-order Poincaré spheres (HOPS). Precise determination of the corresponding HOPS coordinates is crucial for fully exploiting these beams in applications like chirality detection and circular dichroism experiments. However, there are few techniques available to reliably identify these coordinates in HOPS. In this work, we introduce an experimental approach to determine the HOPS coordinates of VVBs using only one intensity measurement. Our method utilizes a spiral phase plate in conjunction with a linear polarizer to generate intensity nulls in the transmitted beam. These intensity nulls encode both the latitude and longitude of the beam on the HOPS, providing a simple, non-interferometric, and efficient characterization strategy.
Bhardwaj et al. (Fri,) studied this question.