A mathematical formalism of the generalized Stokes field is developed to characterize the propagation properties of partially coherent higher-order vector vortex beams (PC-HOVVBs) in two configurations: (1) without double-slit and (2) with double-slit. Unlike the usual Stokes field, which solely characterizes the polarization of the beam, the generalized Stokes field is a unified representation that encodes both the polarization and coherence properties of the PC-HOVVBs. The generalized Stokes phase is shown to exhibit an explicit dependence on the choice of spatial coordinates. In the far-field interference patterns of PC-HOVVB, the emergence of new generalized Stokes vortices ($N$) is observed, revealing the information of the index ($\left|\eta \right|$) of the input beam as $N=2\left|\eta \right|$. The separation between these generalized vortices increases with decreasing source spatial correlation. This interdependence can be used to determine the spatial coherence width of the input beam. Furthermore, during propagation, these vortices undergo rotation, creation, and annihilation. The experimentally measured generalized Stokes intensity and phase at the double-slit plane were in good agreement with the theoretical predictions. The generalized Stokes field formalism developed in the article may find potential wherever the coherence and polarization properties are crucial, including polarization metrology, free-space optical communication, beam shaping, and quantum communication.

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• Angular momentum of light
• Beam control
• Beam polarization
• Classical optics
• Optical coherence
• Structured light