# Extending UWOC System Applications through Photon Transmission Dynamics Study in Harbor Waters
## 3 The Simulation Results and Discussion
### Analytical Examination of the Full Divergence Angle in Transmission
This observation underscores the significance of divergence  
Figure 8: Comparative analysis of normalized power loss relative to attenuation length and transmitted full divergence angle across four types of harbor water. (**a**) Harbor I; (**b**) Harbor II; (**c**) Harbor III; (**d**) Harbor IV. angle control in minimizing power loss in UWOC, particularly in environments with scattering particles. Differences in the simulation results depicted in Figure 8a-d have been calculated, for example with a full divergence angle of 100 mrad and an AL of 30, the power loss of Harbor II, III, and IV are found to be 14.00 dB, 31.59 dB, and 41.59 dB lower, respectively, than that of Harbor I. So, the normalized power loss of Harbor II, III, and IV is 3.98%, 0.069%, and 0.0069% times that of the Harbor I. In our next analysis, we examine the time delay spread in relation to both the AL and the transmitted full divergence angle across the four types of harbor water, as depicted in Figure 9. We observe that under identical harbor water condition, the time delay spread increases with both the increase in AL and the transmitted full divergence angle. Conversely, for a given AL and divergence angle, the time delay spread decreases as the quality of harbor water deteriorates. This trend mirrors the observed behavior in normalized power loss, indicating that the influence of communication distance \(z\) on time delay spread is more significant than water quality; in other words, the impact of water quality is overshadowed by the substantial losses induced by the communication distance \(z\). We consider that increase in scattering events may boost the incidence of forward scattering, which could reduce the variability in the paths photons travel to the Reception Plane, thus resulting in a decrease in time delay spread. Additionally, Figure 9d highlights a specific scenario where the AL ranges from 2-5 and the transmitted full divergence angle is between 0.5 mrad and 5 mrad. In this case, the  
Figure 9: Variation of time delay spread in relation to attenuation length and transmitted full divergence angle across four types of harbor water. (**a**) Harbor I; (**b**) Harbor II; (**c**) Harbor III; (**d**) Harbor IV. time delay spread is notably low, ranging only from 1.09 \(\times\) 10\({}^{-11}\)-1.22 \(\times\) 10\({}^{-11}\) s. This minimal spread can be attributed to the relatively short transmission distance, approximately 0.45 m to 1.14 m, which is insufficient to contribute significantly to the time delay spread. This finding emphasizes the importance of considering both the transmission distance and beam divergence characteristics when assessing the time delay in UWOC. The results in Figure 9a-d have been also numerically analyzed, the time delay spread of Harbor II, III, and IV is 30.56%, 9.67%, and 0.49% times that of the Harbor I, when full divergence angle is 100 mrad, AL is 30. The differences of normalized power loss are much smaller than that of time delay spread. This indicates that the influence of absorption and scattering on power loss is much greater than that of scattering on time delay spread.