Controlled negative energy flow in the focus of a radial polarized optical beam

The controlled and continuous negative energy flow (from negative to positive) on the optical axis in the focal region is obtained by adjusting the polarization distribution of the input second-order radially polarized beam (the polarization topological charge is equal to 2). Moreover, the similar evolution of negative energy flow also can be achieved for the tightly focused vector beams with polarization topological charge -2. It is because both the beams with polarization topological charges 2 and -2 can possess the same polarization and spin flow density distributions with the help of the polarization modulation. The results provide a potential method for modulating the effects induced by the spin-orbit coupling in tight focusing of optical beam.