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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.

With the help of generalized Huygens–Fresnel integral, an analytical expression for the self-healing of a partially coherent radially polarized twisted (PCRPT) beam is derived. The coherence and polarization properties of the PCRPT beam in self-healing propagation are studied in detail. It shows that the existence of the twist phase is a double-edged sword for the self-healing properties of the beam. With the increase of the twist factor, the self-healing ability of beam intensity distribution decreases. However, the anti-disturbance performance of beam polarization improves at the same time. Besides, the polarization and coherence distribution of the beam are proved that own a slight self-healing ability when the obstacle is small. Our results will be helpful to the fields of optical tweezers, microscopy, optical communication, and so on.

The probability density analysis formula of the single orbital angular momentum (OAM) mode of an annular vortex beam with a focusing mirror in a turbulent atmosphere is derived theoretically, and the effects of different parameters on the OAM spectrum are investigated numerically, and the results show that the OAM diffusion of the annular vortex beam is weaker than the Gaussian vortex beam in a turbulent atmosphere under the same conditions, and the annular vortex beam with a focusing mirror can more effectively reduce the crosstalk of OAM modes. Our findings will be useful for improving FSO system performance.

An analytical expression for a partially coherent azimuthally polarized beam with an astigmatic phase (PCAPBAP) is derived. The statistical properties of the PCAPBAP propagating in a paraxial-focused system are studied through numerical examples. It is shown that the beam’s shape changes in a unique way during propagation, and this type of change is related to the rotating factor of the astigmatic phase. Moreover, the influence of the rotating factor and source coherence length on the beam’s polarization and coherence is investigated in detail. The results show that the coherence and polarization properties of the beam also change obviously due to the astigmatic phase’s effect. This paper will be helpful to the fields of optical tweezers, optical needles, imaging, and so on.