# Extending UWOC System Applications through Photon Transmission Dynamics Study in Harbor Waters
## 3 The Simulation Results and Discussion
### Analytical Evaluation of the Received Aperture and FOV  
The study also examines how normalized power loss correlates with AL and the size of the Received aperture at the receiver's end, as illustrated in Figure 10. Our simulations reveal a consistent relationship between these variables across the four types of harbor water. Notably, as the size of the received aperture increases, the normalized power loss decreases. However, the rate of this decline slows and eventually stabilizes. This trend is attributed to the fact that a larger received aperture can capture more scattered photons, thus enhancing the absorption efficiency of the receiver. Additionally, it is evident that larger AL values correspond to greater normalized power losses. This relationship underscores the significant impact of communication distance and beam attenuation characteristics on the efficiency of photon reception in UWOC systems. Figure 10: Comparative analysis of normalized power loss relative to attenuation length and received aperture across four types of harbor water. (**a**) Harbor I; (**b**) Harbor II; (**c**) Harbor III; (**d**) Harbor IV. The relationship between normalized power loss, AL, and received FOV at the receiving end is further explored in Figure 11, focusing on the four types of harbor water. Simulation results indicate that the trends in normalized power loss correspond closely with both AL and the received FOV across these water types. In scenarios where the received FOV is relatively small (<0.2793 rad), there is a noticeable decrease in normalized power loss as the FOV increases. This decrease is attributed to the fact that a larger FOV allows more photons, particularly those deviating from the optical axis, to become On-target photons and be absorbed by the receiver. However, as the received FOV continues to expand beyond this point, the impact on normalized power loss diminishes. This plateau in the effect is due to the large FOV eventually encompassing almost the entire peak intensity region of the Gaussian beam on the Reception Plane. Consequently, further increases in FOV do not significantly affect the proportion of photons captured, thereby stabilizing the normalized power loss. In our final analysis, we examine the time delay spread at the receiving end in relation to AL, the size of the received aperture, and the received FOV across the four types of harbor water. This analysis is illustrated in Figures 12 and 13, and our findings indicate that, under constant harbor water conditions, the time delay spread increases with the rising AL. In the range of shorter ALs (2-10 AL), as shown in Figure 12, the time delay spread enlarges with an increase in the size of the received aperture. This trend is attributed to the fact that a larger aperture increases the likelihood of capturing multiple-scattered photons. However, in scenarios involving larger ALs (15-30 AL), the time delay spread exhibits minimal variation in response to changes in the received aperture size, remaining within the range of 1.05 \(\times\) 10\({}^{-7}\) s to 7.39 \(\times\) 10\({}^{-9}\) s. The primary reason for this is that at longer communication distances, most scattered photons become Off-target photons  
Figure 11: Analysis of normalized power loss in relation to attenuation length and received FOV across four types of harbor water. (**a**) Harbor I; (**b**) Harbor II; (**c**) Harbor III; (**d**) Harbor IV. due to multiple scatterings, and thus they are unlikely to be absorbed by the receiver. Consequently, in the range of 15-30 AL, the time delay spread remains relatively constant. In the case of a small received FOV (less than 0.8 rad), as depicted in Figure 13, there is a noticeable increase in the time delay spread as the FOV gradually expands. This pattern arises because a larger received FOV enhances the receiver's capability to capture a greater number of multiple-scattered photons. As a result, the time delay spread grows with the increasing FOV.