## 2 OAM Light and Ocean Turbulence Channel Model
\(\eta\) is the Kolmogorov microscale (internal ocean scale), which takes \(\delta=8.284\times(\sqrt{k_{x}^{2}+k_{y}^{2}}\eta)^{3/4}+12.978(\sqrt{k_{x}^{2} +k_{y}^{2}}\eta)^{2}\), \(A_{T}=1.863\times 10^{-2}\), \(A_{S}=1.9\times 10^{-4}\), \(A_{TS}=9.41\times 10^{-3}\), and \(\eta=1\times 10^{-3}\) m.  
\[C_{n}^{2}=10^{-8}\chi_{T}\varepsilon^{-1/3} \tag{5}\]  
where \(\chi_{T}\) is the temperature variance dissipation rate and \(\varepsilon\) is the turbulent dynamic dissipation rate. When studying the transmission characteristics of light in ocean turbulence, it is usually necessary to obtain sufficient data under long-distance conditions; however, the light propagation experiments carried out in the ocean require very large human and material resources, and the process is particularly difficult to control. Existing studies have shown that the effect of ocean turbulence on light propagation in free space can be equivalent to the free propagation of light between several random phase screens [20; 23; 24]. At present, there are three commonly used methods for generating random phase screens: the power spectrum inversion method (Fourier transform method), Zenick polynomial method, and fractal method. The basic idea of the power spectrum inversion method is to form a complex Gaussian random number matrix with a mean value of 0 and variance of 1 in the frequency domain, and then filter it with the turbulence power spectrum density function. Finally, the inverse Fourier transform is used to obtain the random phase screen. The core idea of the Zernick polynomial method is to decompose the wavefront distortion into the orthogonal Zernick polynomial in the circle domain, and the coefficients of each order polynomial are obtained by the power spectrum function. The fractal method is based on the principle that the distorted wavefront caused by turbulence is a fractal plane, so that the fractal Brownian motion is used to simulate the distorted wavefront caused by turbulence. The method uses the phase structure function and obtains the function value at each point on the random phase screen through interpolation. The effect of ocean turbulence on optical transmission can be approximately equivalent to the spatial phase disturbance; therefore, multiple random phase screens can be used coaxially to simulate ocean turbulence, in a variety of random phase screen generation methods. The power spectrum inversion method has a fast calculation speed and is suitable for a variety of power spectrum models [24]. Therefore, this section uses the power spectrum inversion method to generate random phase screens to simulate ocean turbulence channels. Figure 1 shows the ocean turbulence channel model based on a random phase screen. Assuming that the random phase screen is perpendicular to the transmission direction of OAM light (that is, the optical axis \(z\)), taking the LG beam as an example, in the spatial domain, let the light field of the beam at the light source be \(LG_{0}(x,y)\). \(LG_{0}(x,y)\) is a complex number, the value of the modulo is related to the intensity of the light field, and the angle represents the phase of the light field. Let the spatial frequency domain transfer function of the LG beam propagate in free space as [25]  
\[U_{P}\big{(}\kappa_{x},\kappa_{y}\big{)}=\exp\Big{(}i\Delta z\sqrt{k^{2}-\kappa _{x}^{2}-\kappa_{y}^{2}}\Big{)} \tag{6}\]  
Before reaching the first random phase screen, the LG beam is equivalent to transmitting in free space, and the light field when it reaches the first random phase screen is shown in Equation (7):  
\[LG_{-1}(x,y)=FT^{-1}\big{\{}FT[LG_{0}(x,y)]U_{P}\big{(}\kappa_{x},\kappa_{y} \big{)}\big{\}} \tag{7}\]  
where \(FT^{-1}\) represents the inverse Fourier transform and \(FT\) represents the Fourier transform. After the LG beam passes through the random phase screen, its light field phase is disturbed and the light field of the LG beam becomes  
\[LG_{+1}(x,y)=LG_{-1}(x,y)\exp[i\phi(x,y)] \tag{8}\]  
where \(\phi(x,y)\) is the random phase screen.