Angular momentum properties of a circularly polarized vortex beam in the paraxial optical systems.

The angular momentum (AM) properties of circularly polarized vortex beams (CPVBs) in two paraxial optical systems [free space and a gradient-index (GRIN) fiber] are demonstrated. The transverse light intensity, the longitudinal light intensity, the phase of the longitudinal electric field, the kinetic momentum, the total spin AM (SAM), the transverse-type SAM (t-SAM), the longitudinal-type SAM (l-SAM), and the orbital angular momentum (OAM) of CPVBs in the two paraxial optical systems are characterized. Spin-orbit coupling of CPVBs is studied during propagation in free space and in a GRIN fiber. When the OAM and the SAM of a CPVB have the same direction of rotation and when they have opposite directions of rotation, the spin-orbit coupling exhibits different characteristics in free space and in the GRIN fiber.