## 5 Numerical Analysis
### Channel Capacity of the Link  
In this sub-section, we apply the conclusions obtained in the previous section, select the optimized source parameter value, and select the 4-QAM/256-QAM modulation schemes to discuss the influence of various factors in weak turbulence absorption seawater on the average information capacity of OAM link. We know that the turbulence fluctuation of long wavelength OAM signal is lower than that of short wavelength signal [31] for a given absorption coefficient, and the loss of OAM signal transmitted in long absorption seawater channel is higher than that in short channel \begin{table}
\begin{tabular}{l l l} \hline \hline
**Modulation System** & **Length of the Channel \(z\) (m)** &
\begin{tabular}{l} **Optimum** **Half Width \(\widetilde{w}_{opt}\)** \\ **(m)** \\ \end{tabular} \\ \hline
4-QAM/256-QAM & 50 & 0.0021 \\
4-QAM/256-QAM & 100 & 0.0032 \\
4-QAM/256-QAM & 150 & 0.0038 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The Relationship between the Optimal Half-width of the POV and the Channel Length. Figure 8: The bandwidth-limited ABER of POV carrier link versus the half beam-width \(\widetilde{w}\) and topological charge \(m_{0}\) under modulation of **(a)** 256-QAM, **(b)** 256-QAM, **(c)** 4-QAM and **(d)** 4-QAM. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Modulation System** & **OAM Topological Charge \(m_{0}\)** &
\begin{tabular}{l} **Optimum** **Half Width \(\widetilde{w}_{opt}\)** \\ **(m)** \\ \end{tabular} \\ \hline
4-QAM/256-QAM & 1 & 0.0036 \\
4-QAM/256-QAM & 2 & 0.0037 \\
4-QAM/256-QAM & 3 & 0.0038 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The Relationship between the Optimal Half Beam-width of POV and the Topological Charge of OAM. for a given signal wavelength. However, the absorption coefficient of seawater depends on the wavelength of light [39]. Therefore, seawater absorption as well as signal wavelength are two important factors for the performance research of optical communication system with OAM mode carrier. In Figure 9, we give the evolution of capacity of underwater communication link using 4-QAM/256-QAM modulation under four absorption seawaters conditions; the four absorption seawater and four signal wavelength are 410 nm (\(n_{\rm I}=0.3588\times 10^{-9}\)), 470 nm (\(n_{\rm I}=0.4487\times 10^{-9}\)), 510 nm (\(n_{\rm I}=1.0549\times 10^{-9}\)) and 570 nm (\(n_{\rm I}=3.4010\times 10^{-9}\)). Figure 9 reveals that as the absorption coefficients of seawater in the two links are similar, the link with a long signal wavelength has a large capacity, while when the signal wavelengths in the two links are similar, the link with a small absorption coefficient has a large capacity. This result suggest that the carrier wavelength should be adjusted according to the absorptivity of seawater in order to keep the underwater communication link in the optimal state of large capacity. Figure 10 show the AIC curves of the 4-QAM/256-QAM modulation system for different turbulence strength versus the ratio of temperature and salinity fluctuation. As can be found, the AIC decreases with the increase of temperature and salinity fluctuation. That is, the salinity fluctuation has a greater impact on the AIC than the temperature fluctuation, this conclusion is consistent with the research conclusions of other types of optical vortices [11; 12]. The evolution of the AIC of OAM signal carried by POV with the turbulent inner scale and turbulent outer scale of seawater is shown in Figure 11. As can be seen from Figure 11, AIC increases with the increase of turbulent inner scale, but it decreases with the increase of turbulent outer scale. According to the theory of turbulence effect, the turbulent inner scale mainly produces the forward scattering of the emitted beam. Therefore, as the turbulent inner scale increases, the uniform area in the seawater increases, and the wavefront distortion of OAM signal mode passing through the channel decreases; that is, the transmittance of the OAM signal mode increases.