“…The mainstream passive methods for generating vortex light beams include spiral phase plates [16,17], forked diffraction gratings [18,19] and Pancharatnam-Berry phase optical elements (PBOEs) [20], etc. Among these, vortex retarders (VRs), as one of the PBOEs, are widely used in various applications due to their significant advantages, including increased insensitivity to chromatic aberration, which is particularly beneficial for scenarios requiring broadband light sources [21,22]. In VRs, the fast axis orientation is uniformly radial and varies continuously along the azimuthal direction, specifically following the following rule [21,22]:…”