Propagation of the COAM matrix of a twisted Gaussian Schell-model beam

The Coherence-Orbital Angular Momentum (COAM) matrix elements of an optical beam describe its mode-to-mode radial correlations. An analytic expression for the COAM matrix of a Twisted Gaussian Schell-Model (TGSM) beam propagating in a vacuum is derived and analyzed in detail, with the help of the Huygens–Fresnel integral. Additionally, we show how to recover the cross-spectral density of the TGSM beam from its COAM matrix, expressing the result in an elegant symmetric form. Due to the unique properties of the TGSM beam, the analysis of its individual OAM correlations will deliver further insight for their applications to imaging, laser communication, optical tweezers, and other modalities. •Analytical formula for OAM correlations of a radiating TGSM beam in vacuum is derived.•Source OAM correlations for different beam parameters are structurally different.•Structure of OAM correlations of a radiating TGSM beam resembles diffraction patterns.•Spectral density of a radiating TGSM beam decreases slowly under certain conditions.