Free-space creation of multipole high-order non-integer Bessel beams

Bessel beams with integer vortex phases and vector vortex polarization have attracted attention for their stable, nondiffracting propagation. Research has focused on integer-order beams, while non-integer beams face challenges due to phase-polarization coupling, limiting their stable propagation in free space. We generate stable multipole high-order non-integer Bessel beams (NBBs) through phase-polarization control. Furthermore, using optical pen technology, we precisely manipulate the beam's position, number, topological charge, and polarization order. Applications include laser processing, optical imaging, communications, and quantum sensing.