Abstract
A simple expression for the correlations of beams radiated by Schell-model sources carrying a prescribed astigmatic phase (cross phase) in 3D space is derived. The z-coherence of such sources upon free-space propagation is investigated in detail. It is demonstrated that the z-coherence does not decrease to zero with an increasing separation of two axial points. Our results show that the initial cross phase, coherence, and correlation state of such sources affect the distribution of the z-coherence. Furthermore, the cross phase plays a role in maintaining z-coherence, which will be useful in applications where high z-coherence is required.
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