  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.
