Interferometric method to detect degenerate index states of polarization singularities

An innovative interference-based method for detecting degenerate index states of polarization singularity is presented here. Index degeneracy occurs when different combinations of spin and orbital angular momentum states are superposed to form the polarization singularity. The technique presented here utilizes the interference of a polarization singular beam with a spherical reference beam to create distinct interference patterns. The interference fringes generated by the setup consist of the fork as well as spiral fringes. Two observations, one on the interference pattern and the other on the projection of the interference pattern on one of the linear basis states pertaining to $S_{2}$ Stokes polarization parameter. This allows straightforward identification and quantification of degenerate index states of polarization singular beam. Beyond resolving index degeneracies, the method can also be extended to determine the coordinates on the Hybrid-order Poincaré Sphere (HyOPS) as well as the relative phase shift between orthogonal components in the input polarization beam. Both simulation and experimental results validate the proposed method.