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.

Polarization state generator for the generation of complex light with controllable degree of polarization

“…The concept of DoP, extended also to vector beams and OAM beams [13], can be of particular relevance in the context of ultrafast laser pulses emitted in the femtosecond or even attosecond regimes. Although a complete spatiotemporal characterization of their polarization properties is possible thanks to the development of interferometric techniques [17], the extension to higher frequency regimes of ultrafast extreme-ultraviolet vector beams [18,19] is not trivial.…”

“…In Ref. [13] we provide a demonstration, based on the density matrix formalism, that the value of p is not modified in the one-to-one mapping between the classical PS, the HOPS and OAMPS spheres, when the light beam emerging the PSG passes through the q-plate and through a linear polarizer, respectively. These mappings include the inner points of the spheres.…”

“…While in the first row the projection of the vector beam onto the polarizer results in a Hermite-Gaussian beam, the fully unpolarized case results in a ring shaped intensity profile. Measurements using the modal decomposition were included in [13] showing how the value of p is also maintained in the OAMPS.…”

“…The proposed PSG system bears advantages over other methods proposed to generate beams with controlled DoP that require either long paths [10], long temporal integrations [11] or spatial averaging [12]. We show that by taking the beam with controlled DoP as the input to a q-plate we can map any state in the polarization PS onto the HOPS, and finally project it onto the OAMPS through a linear polarizer, this mapping including the inner points in the corresponding PS [13].…”

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

“…In this work, we extend this method to map the inner points between the three spheres [4] and extend the degree of polarization (DoP) concept to vector beams and OAM modes. We achieve an incoherent superposition of vector beams and scalar beams by performing an incoherent superposition of polarization states (thus obtaining a partially polarized state), where the control of each beam in the superposition is determined by the DoP of the input polarization mixed state.…”