Physical meaning of the deviation scale under arbitrary turbulence strengths of optical orbital angular momentum

The recently so-called deviation scale [Phys. Rev. A99, 013828 (2019)PLRAAN1050-294710.1103/PhysRevA.99.013828] bridges the connection between the result of the infinitesimal propagation equation (IPE) prediction and that of the single phase screen (SPS) approximation. Thanks to the multiple phase screen (MPS) approach, in this paper we elaborate the physical meaning of the deviation scale: the spatial accumulation of slight intensity modulation of incident orbital angular momentum (OAM)-carrying beam splits the original vortex into multiple individual vortices with a topological charge (TC) of +1 and regenerates the vortex-antivortex pairs with a TC of +1 and with a TC of -1, leading to a significant deviation between these two different results only when the disruption of this compound effect on the phase distribution of the incident OAM-carrying beam becomes more significant. Other than that, we also show that the appearance of the deviation scale cannot be predicted only by the Rytov variance, which can be predicted through the vortex-splitting ratio of the received optical field alone or with the help of the normalized propagation distance.