The cross-talk among different orbital angular momentum (OAM) modes induced by the turbulent atmosphere is a challenging effect commonly occurring in OAM-based free-space optical (FSO) communication. The aim of this study is to propose a simple method to reduce the crosstalk and demonstrate its effect by analytical derivation and numerical simulation. It is found that the crosstalk is largely reduced by using a focusing mirror. Our results will be useful in free-space optical communication.

We introduce a radially polarized partially coherent twisted beam based on the unified theory of coherence and polarization. We also derive expressions of this beam propagating in free space and examine the influence of twist factor and coherence of the source plane on its propagation properties. It is found that both twist factor and coherence of the source plane affect its average intensity, polarization, and coherence. Those results also show that the beam is rotating with beam propagation, and the beam’s rotation is independent of coherence of the source plane.

The recently introduced concept of Stokes fluctuations generalizes both the Hanbury Brown–Twiss effect and the notion of scintillation. Here we apply this new framework to the specific example of a Gaussian Schell-model (GSM) beam. We derive formulas for Stokes scintillations and Stokes fluctuation correlations, which explicitly express the dependence of these quantities on the GSM source parameters. It is found that the normalized Stokes scintillations vary significantly with position. Also, they can be either positively or negatively correlated.

The theoretical model for studying the self-healing of the spatial coherence of a light beam is constructed. Based on this model, the evolution of the degree of coherence for a partially coherent Gaussian Schell-model beam is studied in detail. This study shows the existence of the self-healing effect of the partial coherence for this beam. The self-healing process is determined by the disturbing strength of the turbid medium, the beam width, and the initial coherence. An example of the application of the self-healing property is provided in the case of ghost imaging, if the initial beam is blurred by certain turbid media.

Convolution expression for partially coherent beams that are partially blocked by an opaque obstacle is derived in detail in a paraxial $ABCD$ optical system. The examples are showed to how the formula can be applied to study the self-healing for different beams and different obstructions. In particular, this approach can be used to conveniently deal with any partially coherent Schell-model beams partially blocked by any shape obstacle. Furthermore, the self-healing ability characterization based on the similarity degree of intensity to intensity is proposed. Our method not only can be used to estimate the self-healing ability of beams in theory, but also can be applied to characterize the self-healing ability of beams in experiment. It offers a good and convenient method for investigating or comparing the self-healing ability of different beams, including fully coherent beams and partially coherent beams.

The analytical formula of the probability density of a single orbital angular momentum (OAM) mode for pin-like optical vortex beams (POVBs) in turbulent atmosphere is derived. Its OAM spectrum in the receiving plane is obtained by the numerical calculation. For comparison, the OAM spectrum of commonly Gaussian vortex beams is showed, too. Those results show that POVBs show good performance on resisting the cross talk of the OAM mode induced by the turbulence in some cases, such as smaller radius of the receiving aperture, longer propagation distance, and stronger turbulence. Our finding has application in free-space optical communication based on the OAM mode.