Light beam carrying natural non-integer orbital angular momentum in free space

Light beam with optical vortices can propagate in free space only with integer orbital angular momentum. Here, we invert this scientific consensus theoretically and experimentally by proposing light beams carrying natural non-integer orbital angular momentum. These peculiar light beams are actually special solutions of wave function, which possess optical vortices with the topological charge l+0.5, where l is an integer. Owing to the interaction of phase and polarization singularity, these vortex beams with fractional topological charge can maintain their amplitude and vortex phase even when they propagate to an infinite distance. This work demonstrates another state of optical vortices in free space, which will fundamentally inject new vigor into optics, and other relate scientific fields.