A method for the generation of tunable multi-degree-of-freedom rotations of vector beams on demand along a propagation direction is theoretically proposed. This generation can be achieved by a suitable vector superposition of three monochromatic non-coplanar beams, including a plane wave with elliptical polarization and two Bessel–Hermite–Gauss (BHG) beams with orthogonal polarization, the parameters of which were systematically chosen to obtain the different longitudinal characteristics of the field, i.e., the state of polarization (SoP), phase, and intensity. On one hand, both the incidence angles of the two BHG beams and the additional phase of the plane wave affect the rotation of the beam intensity and phase, but the incidence angle does not affect the rotation of the SoP. Moreover, the additional phase can lead to a change of the rotation angle of the SoP. On the other hand, the weight coefficients of the two BHG beams periodically change the beam intensity distribution along the propagation direction. Interestingly, the beam is non-diffracting, which means that energy is only exchanged internally and is conserved as a whole. This approach may find applications in dynamic multi-beam optical tweezers, atom guiding, materials processing, microscopy, and optical communications.

理论上提出了一种沿传播方向按需生成矢量光束可调谐多自由度旋转的方法。这可以通过三个单色非共面光束的适当矢量叠加来实现，包括一个椭圆偏振的平面波和两个正交偏振的 Bessel-Hermite-Gauss (BHG) 光束，其参数被系统地选择以获得场的不同纵向特性，即偏振态 (SoP)、相位和强度。一方面，两束BHG光束的入射角和平面波的附加相位都会影响光束强度和相位的旋转，但入射角不影响SoP的旋转。而且，额外的相位会导致 SoP 的旋转角度发生变化。另一方面，两个 BHG 光束的权重系数沿传播方向周期性地改变光束强度分布。有趣的是，光束是非衍射的，这意味着能量仅在内部交换并且作为一个整体是守恒的。这种方法可能会在动态多光束光镊、原子引导、材料加工、显微镜和光通信中找到应用。