Partially coherent Mathieu–Gauss beams

We present a theoretical study and experimental generation of Mathieu-Gauss beams in the partially coherent regime. By means of a rotating ground glass diffuser and a spatial light modulator, we demonstrate independent control over both the spatial coherence and ellipticity parameter of MG beams. We characterize the coherence structure and propagation properties of these partially coherent beams through a special case of the cross spectral density, namely the cross-correlation function. Our findings reveal that partially coherent Mathieu-Gauss beams retain structural features in their cross-correlation function even as their intensity profile deteriorates on propagation due to reduced spatial coherence. Furthermore, we show that their cross-spectral density remains nearly invariant during propagation, highlighting their potential for free-space optical communications and imaging through inhomogeneous media. These results not only contribute to the fundamental understanding of partially coherent structured beams but also open new avenues for applications in quantum optics, optical trapping, and beam shaping technologies.