Stokes polarimetry with Poincaré–Hopf index beams

Abstract

Polarization structured beams have immense potential in various applications. Poincaré–Hopf (PH) index beam contains structured polarization distribution represented by a ring corresponding to a constant latitude on the standard Poincaré sphere. These structured beams can be represented by points on a recently introduced higher order Poincaré sphere (HOPS). For every PH index, HOPS can be constructed. Beams exhibit diverse properties depending on the polarity and magnitude of the PH index. Two examples of positive PH index beams are the most commonly encountered beams with radial and azimuthal polarization distributions. Negative PH index beams are polarization structured optical beams in which the symmetry in the polarization distribution is not readily discernible. There can be a set of holonomically constrained polarization transformations that can be represented as trajectories on the surface of HOPS. With the advent of nanostructured metasurface optics, it is possible to fabricate elements that perform this set of holonomically constrained transformations. This mapping is useful in the study of the acquisition of topological phases of these beams. Further identifying the coordinates of the input and output beams can be useful in the study of chirality and dichroism. Chirality is due to differential phase shifts, whereas circular dichroism is due to differential absorption between the right and left handed circular polarization components. We present here a method called Stokes polarimetry on HOPS beams that can precisely locate the HOPS latitude and longitude coordinates for a given beam. This method is based on single intensity measurement and is envisaged to play a paramount role in the practical use of HOPS and unveiling its potential.