# 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  
In this study, we analyze the variation characteristics of laser power in relation to both the attenuation length and the divergence angle. Figure 8 illustrates the normalized power loss received as a function of the AL and the transmitted full divergence angle. The AL is defined as the product of the attenuation coefficient \(c(\lambda)\) and the communication distance \(z\), expressed mathematically as \(\text{AL}=c(\lambda)\times z\). Simulation results indicate a consistent trend across all four types of harbor water: as AL increases, there is a corresponding increase in the attenuation loss of received power. Notably, the attenuation of received optical power initially occurs at a rapid rate and then stabilizes. This pattern is attributed to the gradual divergence of the light beam, which leads to a swift attenuation of light energy over a short distance. As the transmission distance extends, the light beam enters a state of full scattering. In this phase, the proportion of energy attenuation due to light scattering gradually diminishes, making absorption the predominant factor affecting light transmission. This trend is particularly evident in Figure 8a, highlighting the dynamic interplay between scattering and absorption in determining the attenuation characteristics of UWOC. Furthermore, our analysis reveals that a larger transmitted full divergence angle correlates with greater normalized optical power attenuation loss. This trend holds consistently across the four types of harbor water. The normalized power loss of four harbor water in Figure 8 is different based on the same AL, which is inconsistent with the traditional Beer-Lambert law. This indicates that the Beer-Lambert law is completely inapplicable in harbor water due to the extreme scattering property, which is also confirmed by the reference [52], and the common approach in many studies of directly deriving communication distance by dividing the attenuation coefficients of two different water types proves to be inapplicable in the context of harbor water. The Monte Carlo algorithm is the valid solution for these highly scattering communi  
Figure 7: Schematic Transmitted divergence angle and Far-field light spot. cation scenarios. This finding underscores the complexity of the relationship between water quality, communication distance, and light attenuation in UWOC, challenging assumptions that may hold true in other types of aquatic environments. In addition, with the same AL and divergence angle, it is shown that the normalized power loss is decreasing (\(\downarrow\)) as the water quality deteriorates (\(c\uparrow\)) and the communication distance decreases (\(z\downarrow\)) in Figure 8. It can be concluded that in harbor water, the influence of communication distance on normalized power loss is more significant; in other words, the impact of water quality is overshadowed by the sheer magnitude of communication distance \(z\)-induced losses. This phenomenon is attributed to that intensified photons scattering in more deteriorating water might increase the diversity of photons reaching the Reception Plane, this diversification may offset some of the power loss, leading to a reduction in normalized power loss. Our findings also indicate that the differences in normalized power loss among smaller divergence angles, specifically 0.5 mrad, 5 mrad, and 10 mrad, are relatively minor compared to a larger angle like 100 mrad. The primary reason for this is that a smaller transmitted full divergence angle confines the light spot within a more limited range. This confinement results in reduced geometric loss and diminishes the likelihood of photons being scattered by particles in the water. Consequently, a smaller divergence angle ensures that a higher number of photons can reach the photosensitive surface of the receiver and be effectively absorbed.