## 3 Proposed Design  
Figure 1 depicts the proposed design of the OAM-incorporated satellite-ground-underwater OWC system.  
As depicted, the system is composed of four transmitters/receivers that operate at 1550, 1550.8, 1551.6, and 1552.4 nm wavelengths for satellite-ground-underwater communication. A satellite-to-ground and a ground-to-underwater link is used for satellite-to-ground and ground-to-underwater communication. Four different OAM nodes are incorporated at specific wavelengths in each transmitter. Each transmitter uses a continuous wave laser as an input light source. The mode generator generates four different modes at Laguerre-Gaussian (LG) modes of [0,0], LG[0,2], LG[0,4] and LG[0,8]. In order to multiplex all of these different modes, a spatial multiplexer is used. After that, each incoming mode signal is modulated by a Mach-Zehnder modulator at 10 Gbps without a return to zero. Each transmitter combines these modulated signals using a power combiner. An additional power combiner combines all modulated+mode signals at specific wavelengths for transmission through the OWC link under atmospheric turbulence and link losses. At the receiver, a power splitter splits the received signals into different wavelength sections. In the first step, these signals are demultiplexed via a spatial demultiplexer and then split via a power splitter. Low gas filter (LPF) and bit error rate (BER) analyzer components are used on the first output of the power splitter to convert the optical signal to an electrical one. Using the second output of the power splitter, information is transmitted via UWOC for ground-to-satellite communications. Similarly, a spatial photodetector, and the LPF and BER components are used to obtain the original data. Figure 2 shows the generated OAM modes' two-dimensional (2D) and three-dimensional (3D) views with phase profiles [18].  
A multimode generator is used to convert the single-mode signals to multi-mode signals. The multimode generator used in the system attaches LG mode profiles to the input wavelength signals' X and Y polarizations. A Laguerre-Gaussian profile is attached to each polarization. In the proposed system, all spatial modes (LG[0,0], LG[0,2], LG[0,4], and LG[0,8]) are attached to both polarizations (X = Y), where 'LG[]' indicates the mode number starting from fundamental mode at [0,0] to the higher-order mode [0,[8]], taking  
Figure 1: Systematic diagram of OAM-incorporated satellite–ground–underwater OWC system.  
both X and Y polarizations as X = Y in the Laguerre-Gaussian beams. Mathematically, the LG mode is defined as [20; 21]:  
\[\rho_{g,l}(c,\omega)=\beta\left(\frac{2c^{2}}{\omega_{0}^{2}}\right)^{\frac{\theta }{2}}L_{g}^{l}\left(\frac{2c^{2}}{\omega_{0}^{2}}\right)exp\left(\frac{-c^{2}} {\omega_{0}^{2}}\right)exp\left(\frac{\pi c^{2}}{\lambda N_{0}}\right)\left\{ \begin{array}{ll}\cos\left(l\omega\right),&l<0\\ \sin\left(l\omega\right),&l\geq 0\end{array}\right. \tag{1}\]  
where \(c\) is the curvature radius, \(g\) and \(l\) are the x-and y-axis modes' dependencies, \(\omega_{0}\) is spot size, \(L_{g}\) and \(L_{l}\) are the Laguerre polynomials, \(N_{0}\) is the normalized radius, \(\theta\) is the beam divergence, and \(\beta\) is the atmospheric attenuation coefficient [22].  
Figure 2: _Cont._