We introduce a new class of partially coherent beams with non-uniform correlation structure called radially polarized rectangular Hermite non-uniformly correlated (RPRHNUC) beams and study the propagation properties of this kind of beams in free space and atmospheric turbulence. How the mode orders and coherence lengths affect the resistance of such beams to turbulence is also investigated. RPRHNUC beams possess the self-focusing properties. This kind of beams will prove useful in free-space optical communications and other fields.
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