Abstract
The phase fluctuation of Laguerre-Gaussian (LG) vortex beams induced by atmospheric turbulence affects the quantum phase associated with azimuth coordinates and affects the orbital angular momentum of the vortex beams. The measurement of orbital angular momentum is affected by the change in the classical phase and the quantum phase in the Hilbert space. This paper analyzes the additional random complex phase of the vortex beam generated by the atmospheric turbulence and discusses the effect of atmospheric turbulence on the orbital angular momentum of an LG vortex beam using the photon state-vector function. The distributions of the classical phase of vortex beams affected by turbulence of different strengths are calculated and compared with the case for LG vortex beams transmitted through free space. Results show that the atmospheric turbulence affects the phase value of LG vortex beams transmitted in the external field and significantly affects the beam phase structure in the near field. However, the effect of turbulence on the phase of vortex beams is insignificant for a transmission range z > 2000 m while the phase values vary slowly and gradually become constant.
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