In recent years, the vortex beams with OAM have attracted the attention of scholars  [1], [2], [3], [4], [5]. The vortex beam containing OAM has a phase term expimϕ [6], where m is called the OAM mode or topological charge. The beams carrying OAM of various m are orthogonal to one another, and the m can theoretically take on any integer value [7], [8]. This has inspired the use of the spatial dimensional resources of OAM beams as information carriers and their application to the field of free-space optical communication, and high-capacity communications of Gbit/s [9], [10] and Tbit/s [11], [12] have been achieved. However, as the vortex beam propagates through the atmosphere, the wave front distortion caused by atmospheric turbulence will cause the input mode power to spread over adjacent OAM modes, increasing the BER [13], [14], [15], [16]. In order to clearly clarify the OAM mode component of the beam, Molina-terriza expanded the beam as a linear superposition of the spiral harmonic functions expimϕ to form a spiral spectrum [17]. Therefore, in order to comprehend and optimize the optical communication system, it is crucial to analyze the spiral spectral properties of vortex beams in a turbulent atmosphere.

In 2013, Yang et al. discovered an anomalous vortex beam (AVB) [18], which has unique advantages in many fields, including optical communications [19], lidar detection [20], and optical trapping [21], [22]. Many studies of vortex beams have been based on elegant Laguerre-Gaussian beams (ELGBs) [23] and Bessel-Gaussian beams (BGBs) [24], but they have not been used and developed to a large extent, one reason being that they are difficult to generate. It has been found that an AVB can be turned into an ELGB after far field transmission, i.e., the AVB can be considered as a virtual source that generates ELGB and BGB as well [18]. Most previous studies have shown that ELGBs are less affected by the turbulent atmosphere than LGBs [23], [25], and it has also been further demonstrated in the literature [19] that AVBs in a weakly turbulent atmosphere are less affected by turbulence than LGBs. Therefore, it is necessary to study the propagation properties of AVBs.

But quite a few of these studies focus on isotropic turbulence and describe these statistics using the Kolmogorov model. However, we know that optical turbulence is mostly inhomogeneous and anisotropic in the free atmosphere (above 2 km from the ground) [26]. In light of this, it is possible that the traditional isotropic Kolmogorov spectrum is inadequate for the free atmosphere. Additionally, laser beams are virtually partially coherent light in practical optical systems. As a result, this paper will study the transmission characteristics of the PCAVB in an anisotropic turbulent atmosphere and discuss the effects of asymmetric anisotropic turbulence and source parameters on the OAM mode crosstalk of the PCAVB signals. The study can be applied to atmospheric laser communication to provide some theoretical guidance and reference value for its beam selection.