Fractional angular momentum borne on rotating vortex solitons

We predict the existence of vortex solitons with one and two embedded off-centered phase singularities in competing media trapped in a rotating harmonic potential. The Coriolis force induced by the rotation of external potentials shifts the singularity of the single-charge vortex soliton from the origin to the periphery. In this process, the angular momentum carried by per photon varies continuously from 1 to 0. For vortex solitons with two separated opposite-charge singularities, the counterclockwise rotation leads to a variation of angular momentum per photon from 0 to -1, and vice versa. Particularly, for vortex solitons nesting two singularities of the same charge, two branches of vortices with symmetrical singularities and asymmetric singularities coexist when the rotation frequency exceeds a critical value. The angular momentum per photon still varies continuously with the rotation frequency. Linear stability analysis collaborated by direct propagation simulation demonstrates that rotating asymmetric vortex states carrying fractional angular momentum are extremely robust, provided that their power is high enough.