Spin angular momentum flux density of non-uniformly polarized vortex beams with tunable polarization angles in uniaxial crystals

Abstract

We propose the non-uniformly polarized vortex (NUPV) beams with the changing retardation angle and the tunable angle between polarization and radial direction, in which the radially polarized vortex (RPV) beam is a particular case. Based on the paraxial vector theory, the analytical propagation expressions of NUPV beams in uniaxial crystals orthogonal to the optical axis are derived and used to investigate the evolutions of spin angular momentum (SAM) flux densities, polarization states, and the Stokes parameters. The results show a more complex behavior of SAM such as rotation, creation and disappearance in cyclical ways can be found in anisotropic media, which is different from a monotonous rotation of SAM for hybridly polarized beams without a vortex. Besides, it is worth mentioning that the SAM of the NUPV beams also presents the more complex evolution in isotropic media rather than stable Gaussian-like structures, which indicate the more flexible polarization behavior of NUPV beams. Then the influence of refractive index ratio ne/no and topological charge number m on SAM is discussed. The results show the flexibility of polarization is strengthened by anisotropy or the embedded vortex. The polarization states and the Stokes parameters on the Poincaré spheres both verified the change in SAM. The presented work has potential values and broad prospects in polarization-sensitive sensing and detection.