## 3 Proposed System Concept Architecture  
### PAT and Beam Divergence Control  
In our previous research, we introduced an UOWC system concept using OPA antennas for electronic beam steering for PAT and beam divergence control purposes [8]. The system enables bidirectional communication between underwater vehicles whose transmitters and receivers are not aligned along the same axis. The proposed system based on OPA antennas is able to steer a laser beam electronically without mechanical movement, offering high precision and speed. A two-dimensional OPA antenna is designed, allowing beam steering in azimuth and elevation angles and control over the beam width. Controlling beam divergence is critical for pointing, acquisition, and communication. A wide beamwidth is advantageous for the pointing and acquisition phase, simplifying the alignment process, while a narrow beamwidth during the communication phase increases the link range and data throughput. Beam divergence control is managed by subdividing the antenna array into smaller subarrays, as suggested in prior work. Each subarray steers the beam to a slightly different angle, broadening the overall beam. This method allows for controlled beam divergence by manipulating angular displacements.  
The mathematical foundation for OPA operation is based on Fraunhofer diffraction theory, where the far-field radiation pattern is the sum of the radiated field by each antenna element:  
\[E(\theta,\phi)=\sum_{n=1}^{N}\sum_{m=1}^{M}E_{n,m}(\theta,\phi)=\int_{0}^{2\pi }\int_{0}^{\pi}AF(\theta_{0},\phi_{0})\,E_{i}(\theta,\phi)\,d\theta\,d\phi. \tag{12}\]  
\(AF(\theta_{0},\phi_{0})\) is the array factor for the desired angle \((\theta_{0},\phi_{0})\), and \(E_{i,j}(\theta,\phi)\) is the transmitted field by a single antenna element. By adjusting the phase shifts between the antenna elements, we can control the angle at which the radiation from the antenna elements constructively interferes in order to achieve the highest directivity in the desired direction [8].  
The link budget calculation for the UOWC system using the proposed OPA transceiver system, considering only attenuation due to absorption and scattering (excluding turbulence), can be expressed using [PERSON]'s law, as follows:  
Figure 2: PDFs of the normalized irradiance for different ratios of temperature to salinity fluctuations \(w\) over 20 m distance.  
\[P_{r}=P_{t}\,\eta_{\rm MZM}\,\eta_{t}\,D_{t}\,\eta_{r}\,D_{r}\left(\frac{\lambda}{4 \pi L}\right)^{2}e^{-c(\lambda)\cdot L}, \tag{13}\]  
where \(P_{r}\) is the received power, \(P_{t}\) is the transmit power, \(\eta_{\rm MZM}\) is the efficiency of the Mach-Zehnder modulator, \(\eta_{t}\) and \(\eta_{r}\) are the efficiencies of the transmitter and receiver, respectively, \(D_{t}\) and \(D_{r}\) are the directivities of the transmitter and receiver, respectively. The term \(\left(\frac{\lambda}{4\pi L}\right)^{2}\) corresponds to the path loss of a spherical wave that has traveled a distance \(L\). Parameter values were selected according to Table 1 in the numerical evaluation for link budget calculation.  
The system concept employs a continuous-wave (CW) laser as the light source, modulated using an IQ Mach-Zehnder Modulator (MZM) for complex-valued modulation. For OPA antenna design at the transmitter and receiver side, photonic integrated circuits (PICs) on a silicon waveguide platform with \(\lambda/2\)-pitch are assumed, as suggested in [26], employing 3 dB splitters, phase shifters, and grating couplers.