Optical solitons have long been of considerable interest because of their important applications, such as all-optical information processing (e.g., all-optical switches, and all-logic gates), optical manipulation and beam control. It is shown that an annular optical soliton may be formed when a fully coherent vortex beam propagates in a strongly nonlocal nonlinear medium (SNNM). The annular optical soliton with vortex has more advantages in applications than the Gaussian-like optical soliton without vortex. In practice, partially coherent beams are often encountered, and the partial coherence is one of the main features of laser beams. However, when a partially coherent vortex beam propagates in an SNNM, an optical soliton cannot be formed due to partial coherence. This paper aims to find partially coherent vortex solitons.

Based on the extended diffraction integral principle and the ABCD matrix of SNNM, the analytical propagation formula of twisted partially coherent vortex (TPCV) beams in SNNM is derived in this paper. It is found that an annular optical soliton may be formed in SNNM because of the twist feature of TPCV beams, even if the spatial coherence is extremely low. The conditions for the formation of annular optical solitons of TPCV beams in SNNM are also given in this paper. In addition, it is shown that the intensity and the gradient force of annular optical solitons increase as the partial coherence of TPCV beams decreases, which can be applied to optical manipulation.

On the other hand, under certain conditions, an optical soliton may also be formed, when a TPCV beam and a twisted Gaussian Schell-model (TGSM) beam are combined coaxially and incoherently in SNNM. The conditions for the formation of optical solitons of the combined beams in SNNM are independent of the beam coherence degree, the topological charge, and the proportion of sub-beam power. Furthermore, the gradient force can be manipulated by the beam coherence degree, and the profile of optical solitons can be manipulated by the topological charge and the proportion of sub-beam power. The results obtained in this study are useful for optical manipulation, material processing, and beam control.