# Laser Transmission Characteristics of Seawater for Underwater Wireless Optical Communication
## 3 Results and Discussion
### Average AOA
#### 3.1.2 Average AOA at Different Offsets on the Receiving Plane  
To further analyze the laser divergence characteristics on the receiving plane at different offsets, AOA distributions at 0.01, 0.1, 1.0, 5, and 10 m offsets relative to the beam center were simulated. For simplicity, only the average AOA results are provided in this study. Figure 4 shows the variations in the average AOA with the attenuation length at the different offsets in clear water, coastal water, and turbid harbor water, respectively. In absorption-dominated clear water, the average AOA decreases continuously as the attenuation length increases because of rapidly attenuating laser power. For instance,  
Figure 4: Variations in the average AOA with the attenuation length at the different offsets in (**a**) clear water, (**b**) coastal water, and (**c**) turbid harbor water. Figure 3: Variations in the average AOA with the attenuation length in clear water (black line), coastal water (red line), and turbid harbor water (blue line). the average AOA of 10 m is approximately 63.4\({}^{\circ}\) at an attenuation length of 1, 15.2\({}^{\circ}\) at an attenuation length of 15, and 13.1\({}^{\circ}\) at an attenuation length of 25; the average AOAs at the offset of 0 m are 1.1\({}^{\circ}\), 0.75\({}^{\circ}\), and 0.15\({}^{\circ}\) at the attenuation lengths of 1, 15, and 25, respectively. Thus, the differences in the average AOAs between offsets 0 m and 10 m are 62.3\({}^{\circ}\), 14.5\({}^{\circ}\), and 12.9\({}^{\circ}\) at the above attenuation lengths. In scattering-dominated coastal and turbid waters, the average AOAs at large offsets decrease with increasing attenuation length and increase at small offsets since multiple scattering leads to spatial dispersion of the laser beam. Here are some examples. In coastal water, the average AOA at the offset of 10 m is 75.4\({}^{\circ}\), 23.1\({}^{\circ}\), and 20.2\({}^{\circ}\) at the attenuation lengths of 1, 20, and 35, respectively; the average AOAs at the offset of 0 m are 1.0\({}^{\circ}\), 1.2\({}^{\circ}\), and 14.4\({}^{\circ}\) at the attenuation lengths of 1, 20, and 35, respectively; the differences at these offsets are 74.4\({}^{\circ}\), 21.9\({}^{\circ}\), and 5.8\({}^{\circ}\) at the same attenuation lengths. In turbid harbor water, the average AOA at the offset of 10 m is 70.0\({}^{\circ}\), 47.5\({}^{\circ}\), and 39.7\({}^{\circ}\) at the attenuation lengths of 1, 20, and 35, respectively; the average AOAs at the offset of 0 m are 2.7\({}^{\circ}\), 19.3\({}^{\circ}\), and 27.4\({}^{\circ}\) at the attenuation lengths of 1, 20, and 35, respectively; the differences at these offsets are 67.2, 28.3\({}^{\circ}\), and 12.2\({}^{\circ}\) at the same attenuation lengths. Overall, the differences in the average AOAs at various offsets are more significant at smaller attenuation lengths but decreased considerably at larger ones. Figure 5 shows the AOA distribution with the attenuation length in clear water, coastal water, and turbid harbor water, demonstrating more specific characteristics of laser divergence. In summary, light concentrated at the small angles gradually diverges with increasing attenuation length, and the peak angle of the AOA distribution is gradually shifted toward larger angles. The higher the single scattering albedo \(\omega_{0}\), the faster the laser diverges and the more divergent it becomes. For example, at an attenuation length of 15, the peak angle of the AOA distribution is close to 0\({}^{\circ}\), whereas it is approximately 11.6\({}^{\circ}\) and 23\({}^{\circ}\) in coastal and turbid harbor waters, respectively. The peak angles of the AOA distributions at an attenuation length of 25 are approximately 8.5\({}^{\circ}\), 15.6\({}^{\circ}\), and 27\({}^{\circ}\), with corresponding full width at half maxima (FWHMs) of 21.8\({}^{\circ}\), 30.6\({}^{\circ}\), and 45.4\({}^{\circ}\) in clear water, coastal water, and turbid harbor water, respectively.