Geometrical-phase lens based optical system for the spin-splitting of vector beams

In this work, we present a new optical lens system based on a polarization directed flat lens (geometric phase lens) designed to provide circular polarization split focusing in two real foci located at two different axial planes. We find the conditions to obtain two real back focal planes of the system, and the same focal length of opposite sign. In this situation, the system acts as a bifocal SAM split system with equal scale for both real foci. We experimentally demonstrate the optical spin dependent dual focus effect of the system. Then, we illuminate the system with vortex and vector beams generated by a q-plate and provide theoretical explanation within the Jones matrix formalism for the different orbital angular momentum (OAM) and spin angular momentum (SAM) states experimentally observed at the two focal planes. Finally, we show the interference of the two split focused components of the vector beam at the intermediate plane between the two focal planes. The resulting spiral interference pattern indicates the sign and value of the vector beam's topological charge. It can also be used to identify the vector beam of a given charge by the shift on the interference fringes. Therefore, the optical system can be useful as a new tool for analyzing OAM and SAM beams.