Extending the degree of polarization concept to higher-order and orbital angular momentum Poincaré spheres

Abstract

In this work, the density matrix formalism that describes any standard polarization state (fully or partially polarized) is applied to describe vector beams and spatial modes with orbital angular momentum (OAM). Within this framework, we provide a comprehensive description of the mapping between the corresponding Poincaré spheres (PSs); namely: the polarization PS, the higher-order PS (HOPS) and the orbital angular momentum PS (OAMPS). Whereas previous works focus on states located on the surface of these spheres, here we study vector and scalar modes lying inside the corresponding PS. We show that they can be obtained as the incoherent superposition of two orthogonal vector (or scalar) modes lying on the corresponding sphere surface. The degree of polarization (DoP) of a classical polarization state is thus extended to vector beams and OAM modes. Experimental results validate the theoretical physical interpretation, where we used a q-plate to map any state in the polarization PS onto the HOPS, and a linear polarizer to finally project onto the OAMPS. Three input states to such q-plate-polarizer system are considered: totally unpolarized, partially polarized, and fully polarized light. For that purpose, we design a new polarization state generator, based on two geometric phase gratings and a randomly polarized laser, which generates partially polarized light in an efficient and controlled way. We believe that the extension of the DoP concept to vector and OAM beams introduces a degree of freedom to describe spatially polarization and phase variant light beams.