Characterization and generation of eight-point vector vortex beams based on multiaxial super-geometric modes

We propose a novel, to our knowledge, approach in which the transformation of superposed rings of multiaxial super-geometric modes into superposed points enables the generation of eight-point vector vortex beams. Specifically, the eight-point vector vortex modes are numerically constructed by converting the decomposed multiaxial geometric modes from a ring-shaped distribution to a point-shaped configuration, indicating that they belong to a class of special transverse modes in frequency-degenerate laser cavities. Subsequently, the intensity patterns of eight-point vector vortex modes are investigated under different astigmatism parameters, revealing shapes such as four-star, S , Z , five, and X . Importantly, the global geometric morphology of these eight-point vector vortex modes can be flexibly tailored on demand through the precise adjustment of their intrinsic astigmatism parameters, thereby confirming the controllability and predictability of the beam configurations. Our work provides a potentially useful foundation for developing applications such as vectorial optical trapping and optical tweezers.