Evolution of partially coherent Stokes skyrmions in free space.

Optical skyrmions are structured-light states with nontrivial topology, yet their behavior under reduced spatial coherence remains poorly understood. Here, we investigate the free-space propagation of partially coherent Stokes skyrmions (PCSSs) and show that, in the low-coherence regime, reduced coherence disrupts the averaged polarization texture, while the conventional gradient-based skyrmion-number evaluation becomes statistically unstable, whereas vector fidelity provides a complementary measure of structural degradation. For high-order skyrmions, the fidelity exhibits a pronounced non-monotonic dependence on coherence length, with a deep minimum at an intermediate coherence scale. This anomaly is associated with coherence-dependent anti-alignment of the averaged Stokes texture, consistent with relative modal phase evolution and partial-coherence-induced filtering of modal-correlation terms. These results provide useful guidance for understanding, characterizing, and designing coherence-tolerant skyrmionic vector fields.