Optically polarized selective transmission of a fractional vector vortex beam by the polarized atoms with external magnetic fields

We investigate the role of external magnetic fields and linearly polarized pump light, especially when their directions are parallel or vertical, on the propagation of the fractional vector vortex beams (FVVBs) through a polarized atomic system. Herein, the different configurations of external magnetic fields lead to various optically polarized selective transmissions of FVVBs with different fractional topological charge α caused by the polarized atoms, which is theoretically demonstrated by the atomic density matrix visualization analysis and experimentally explored by Cesium atom vapor. Meanwhile, we find that the FVVBs-atom interaction is a vectorial process due to the different optical vector polarized states. In this interaction process, the atomic optically polarized selection property provides potential for the realization of the magnetic compass based on warm atoms. For the FVVBs, due to the rotational asymmetry of the intensity distribution, we can observe some transmitted light spots with unequal energy. Compared with the integer vector vortex beam, it is possible to obtain a more precise magnetic field direction by fitting the different "petal" spots of the FVVBs.