We introduce a general strategy for the synthesis of vector partially coherent beams (PCBs) with a prescribed non-uniform correlation structure. With it, we characterize a specific family of such beams, termed radially polarized Hermite non-uniformly correlated (RPHNUC) beams. These beams possess unusual propagation properties compared to vector PCBs with uniform correlation structure; for example, they maintain their dark hollow core and evolve multi-ring structures. These beams may prove useful in free-space optical communications, optical trapping, and polarization-sensitive imaging. (C) 2020 Optical Society of America
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