The ocean is an important part of the Earth, covering 70% of the Earth's surface. Therefore, marine optical communication is an important field for researchers in optical communication technology. Vortex beams, which carry orbital angular momentum (OAM), can be considered as a new degree of freedom. By leveraging the orthogonal and infinite properties of the OAM mode, these beams can enhance the capacity and spectral efficiency of communication systems. Additionally, the array beam is composed of several single beams with different arrangement modes. Previous studies have shown that the array beam not only improves the transmission power but also suppresses the influence of turbulence on beam transmission. Therefore, researchers developed linear, rectangular, and radially distributed laser arrays. Current research mainly focuses on array beam transmission in the atmosphere, and there is a paucity of studies on transmission characteristics in the ocean. However, these methods are based on Nikishov stable stratified sea spectra with an infinite outer scale, and there have been few studies on the drift characteristics and beam propagation of array vortex beams. Therefore, this study aims to investigate the transmission characteristics of single vortex beams, radial array vortex beams, and rectangular array vortex beams in an unstable stratified ocean considering external scales and analyze the influence of distance on their light intensity and phase. The results of this study provide a theoretical foundation for the development of underwater optical communication technologies.

In marine media, refractive index fluctuations are controlled by temperature and salinity fluctuations. In this study, the low-frequency components were superimposed on a phase screen simulated using the power spectrum inversion method to compensate for the absence of low-frequency components. The field phase in the beam propagation path changes after the beam passes through multiple random phase screens. The process of a beam passing through multiple random-phase screens was similar to beam propagation in ocean turbulence. When the three vortex beams pass through the ocean turbulence, their light intensities dispersed. Therefore, 500 sets of data were averaged after the three vortex beams passed through the phase screen. It is then calculated according to the definitions of the beam drift, beam spread, and light intensity flicker.

When the transmission distance is constant, the drift of the single vortex beam is the largest, and the drifts of the two vortex beams are relatively small. Additionally, the larger the r0 and xd of the array vortex beam, the smaller the drift. When x_d=y_d=6w₀, r₀=6w₀, the drift of the radial array vortex beam is greater than that of the rectangular array vortex beam. This is because the sub-beams at the four corners of the rectangular array vortex beam are relatively far from the center [Fig. 5(b)]. Additionally, the beam width of the two arrays of vortex beams slowly with an increase in w₀. The radius of the single vortex beam decreases when it reaches a certain level and then begins to increase monotonically. When fixed, the outer scale of the turbulence minimally impacts the beam widths of the three vortices [Fig. 6(e)].

After the two arrays of vortex beams transmit for a certain distance, they no longer maintain the initial array distribution, and the sub-beams affect each other and produce interference fringes. Under the same conditions, the drift of the single vortex beam is larger and the beam width is smaller than those of the two array vortex beams. However, the drift of the radial array vortex beam is larger and the beam width is smaller than those of the rectangular array vortex beams. The scintillation of the single vortex beam is larger than those of the two array vortex beams, and that of the rectangular array vortex beam is larger than that of the radial array vortex beam. At strong turbulence and long distances, the widths of the three vortex beams gradually decrease.