## 1 Introduction  
Orbital angular momentum (OAM) is a new dimension that can be encoded, which can be adopted by optical [1, 2, 3, 4] and acoustic [5, 6, 7] communication systems to improve the information capacity of links. Although acoustic OAM has the advantages of low loss of underwater communication and perfect theoretical [5, 6, 7] and experimental model compared with underwater optical OAM transmission, its fatal weakness is the low channel capacity and signal transmission rate of underwater acoustic communication link. Therefore, as underwater communication and detection technology requires higher communication link channel capacity and signal transmission rate, OAM optical communication has become one of the new focuses in the field of underwater communication. However, due to the presence of various constituents in the ocean and oceanic turbulence, seawater scattering and absorption inevitably limit the transmission of information carried by OAM modes over optical communication links [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]. Therefore, in order to reduce the above negative effects of seawater and consider the relationship between signal transmission probability and channel capacity, a lot of studies have been conducted from the perspectives of OAM detection probability and link channel capacity. The disturbance degree of ocean turbulence to the detection probability of OAM mode of partially coherent Laguerre-Gaussian beams increases with the increase in beam radial mode order, OAM mode topological charge and ocean turbulence strength, and fully coherent vortex beams provided better performance than partially coherent ones [8]. The partially coherent elegant Laguerre-Gaussian beams are also more affected by turbulence as compared to the fully coherent elegant Laguerre-Gaussian beams, and one can choose optimum beam source to mitigate the influence of oceanic turbulence [9]. Although the detection probability of fractional OAM mode is lower than that of adjacent integer OAM mode, the channel capacity of the link can be increased by using fractional OAM mode when the available OAM topological charges are limited [10]. Compared with Laguerre-Gaussian beams, the Bessel Gaussian beam transmitted in turbulent seawater has stronger anti-turbulence and better OAM transmission performance [11]. For partially coherent modified Besselcorrelated vortex beam, the effect of high-anisotropic ocean turbulence on OAM signal is weaker than that of low-anisotropic ocean turbulence. In addition, the mode with low OAM quantum number can be selected to improve the information transmission of the link, and the OAM mode with large energy level difference between neighboring OAM can be used to reduce the impact of turbulence, to improve the information capacity of the optical communication link [12]. The channel capacity of the link increases as the pulse width of the half-modulated input pulse increases and the Bessel cone angle decreases. Channel capacity is more sensitive to salinity fluctuations than temperature fluctuations. In anisotropic and isotropic turbulence, the internal and external scales of turbulence have different effects on channel capacity [13]. An airy-OAM beam with a smaller topological charge, larger main ring radius, and longer wavelength has larger detection probability [14]. The Lommel Gaussian beam, which has a small asymmetric coefficient, low OAM quantum number, optimal waist width, and long transmission window wavelength, has a low probability of crosstalk introduced by turbulence. [15]. The self-focusing characteristic of a perfect optical vortex beam is beneficial to the propagation of the OAM mode, and the perfect optical vortex beam with smaller topological charge, smaller initial radius, and optimized half-ring width can reduce the degradation effect of the PV beam caused by turbulence [16].