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In this paper, we propose a novel (to our knowledge) vector beam by combining the radially polarized beams with the different polarization orders, which is called the grafted polarization vector beam (GPVB). Compared with the tight focusing of traditional cylindrical vector beams, GPVB can present more flexible focal field patterns by adjusting the polarization order of two (or more) grafted parts. Moreover, because the GPVB possesses the non-axisymmetrical polarization state distribution, which will lead to the spin-orbit coupling in its tight focusing, it can obtain the spatial separation of spin angular momentum (SAM) and orbital angular momentum (OAM) in the focal plane. The SAM and the OAM are well modulated by adjusting the polarization order of two (or more) grafted parts. Furthermore, we also find the on-axis energy flow in the tight focusing of the GPVB can be changed from positive to negative by adjusting its polarization order. Our results provide more modulation freedom and potential applications in optical tweezers and particles trapping.

In this paper, we focus on the study of the negative energy flow in the tight focusing of a radially polarized vortex beam. We know that, because of the coupling of the polarization state and the vortex charge, the on-axis energy flow in the focal region can be well modulated by changing the polarization order and the vortex charge of the incident vector beam. This shows that when the polarization order and the vortex charge satisfy the specific relation, the on-axis negative energy flow can be obtained in the focal region. Moreover, the initial phases of two polarization unit vectors also affect the evolution of the on-axis negative energy flow in the tight focusing of the radially polarized beam. The phase difference modulation of the two polarization unit vectors indicates two different modulations of the polarization state. Our work provides a more flexible modulation method for focal shaping and optical modulation.