It is generally true that the orbital angular momentum (OAM) mode persistently degenerate when a vortex beam propagates in the atmospheric turbulence. Here, however, we unveil an interesting self-recovery effect of OAM mode of the circular beam (CiB) in weak non-Kolmogorov turbulence. We show that the CiB displays the self-focusing effect and has clear focus in the weak non-Kolmogorov turbulence if we choose proper complex parameters, and the detection probability of the original OAM mode reaches the maximum at the focus. Our study proposes a method to alleviate the turbulent effects on OAM-based communication.
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