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.

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.