Mapping partially polarized light to incoherent superpositions of vector beams and vortex beams with orbital angular momentum

Fully polarized light, cylindrical vector beams, and beams with opposite orbital angular momentum (OAM) and their superpositions are respectively represented as points on the Poincaré sphere (PS), the higher-order Poincaré sphere (HOPS) and the OAM Poincaré sphere (OAMPS). Here, we study the mapping of inner points between these spheres, which we regard as incoherent superpositions of points on the surface of their respective sphere. We obtain points inside the HOPS and OAMPS by mapping incoherent superpositions of points on the PS, i.e., partially polarized states. To map points from the PS to the HOPS, we use a q-plate, while for mapping points from the HOPS to the OAMPS, we use a linear polarizer. Furthermore, we demonstrate a new polarization state generator (PSG) that generates efficiently partially polarized light. It uses a geometric phase (GP) blazed grating to split an unpolarized laser into two orthogonal polarization components. An intensity filter adjusts the relative intensity of the components, which are then recombined with another GP grating and directed to a waveplate, thus achieving every point inside the PS. The proposed PSG offers advantages over other methods in terms of energy efficiency, ease of alignment, and not requiring spatial or long-time integrations