In this paper, we propose a numerical approach to simulate the degree of coherence (DOC) of a partially coherent beam (PCB) with a Schell-model correlator in any transverse plane during propagation. The approach is applicable for PCBs whose initial intensity distribution and DOC distribution are non-Gaussian functions, even for beams for which it is impossible to obtain an analytical expression for the cross-spectral density (CSD) function. Based on our approach, numerical examples for the distribution of the DOC of two types of PCBs are presented. One type is the partially coherent Hermite–Gaussian beam. The simulation results of the DOC agree well with those calculated from the analytical formula. The other type of PCB is the one for which it is impossible to obtain an analytical expression of CSD. The evolution of the DOC with the propagation distance and in the far field is studied in detail. Our numerical approach may find potential applications in optical encryption and information transfer.

A partially coherent beam under the combined action of a Hermite-Gaussian correlated function and vortex phase, named the HGCSMLG_0l beam has been explored both theoretically and experimentally. The statistical properties, such as the intensity and distribution of the degree of coherence (DOC) on propagation are analyzed in detail, based on the deduced equations. We find that the intensity is determined dominantly by the non-conventional correlated function when the coherence length is comparatively small and by vortex phase when the coherence length is large. The modulus of the DOC is not vulnerable to coherence width, rather, it is affected by both non-conventional correlated function and vortex phase. Our results are verified well by the experiment results.

We introduce a novel type of twisted partially coherent beams with a nonconventional correlation function, named the twisted Hermite-Gaussian correlated Schell-model (THGCSM) beam. The condition that a twist phase can be imposed on a partially coherent beam is addressed for Schell-model fields endowed with rectangular symmetry. Further, the analytical formula for the THGCSM beam propagating in free space has been derived with the help of the generalized Collins formula. The propagation properties, such as the spectral density and the spectral degree of coherence (SDOC) of the THGCSM beam, also have been studied in detail by some numerical examples. The numerical results show that the twist phase plays a role in resisting beam splitting, caused by the correlation structure, and induces the rotation of the distribution of the SDOC on propagation. Moreover, it is interesting to find that when the beam carries a twist phase, this will endow the beam the ability to maintain its distribution of the SDOC on propagation and enhance the self -reconstruction capability of the SDOC. Our results may provide new insights into nonconventional partially coherent beams with twisted phase and may be useful in some applications, such as optical communications and information recovery.

In this letter, we conducted a detailed investigation of the statistical properties, such as spectral density, spectral degree of coherence (SDOC), orbital angular momentum (OAM) flux density, and propagation factor M², of a twisted Gaussian Schell-model (TGSM) beam carrying the cross phase in a turbulent atmosphere. Our findings revealed that atmospheric turbulence induces degeneration of the intensity distribution and spectral degree of coherence of a Gaussian Schell-model beam with the cross phase during propagation, while the twist phase acts as an antidote to degradation. Furthermore, we observed that the z-component of the time-averaged angular momentum flux is determined by the twist phase, whereas the cross phase influences the distribution of the OAM flux density in the beam. Additionally, we explored the variations in the propagation factor M² of a TGSM beam with the cross phase in a turbulent atmosphere. Notably, we discovered that the deleterious effects of the atmospheric conditions can be mitigated by modulating both the twist and the cross phases. This work contributes valuable insights for information transfer and optical manipulations.