Closed-form expression for mutual intensity evolution of Hermite-Laguerre-Gaussian Schell-model beams

We derive a comprehensive closed-form expression for the evolution of the mutual intensity (MI) of Hermite-Laguerre-Gaussian Schell-model beams (HLG-SMBs) during propagation through rotationally symmetric optical systems. We demonstrate that the MI of the beam associated with a given HLG mode at any transverse plane can be presented as a linear superposition of the MIs of the SMBs associated with the equal and lower index modes of the same type, but of complex argument. The obtained expression allows easy analysis of the evolution of the intensity distribution and the CCF of such beams and, in particular, an understanding of the coherence singularity formation and modification during the beam propagation.