# Extending UWOC System Applications through Photon Transmission Dynamics Study in Harbor Waters
## 3 The Simulation Results and Discussion  
In this paper, we primarily investigate the characteristics of UWOC with varying communication distances in four distinct types of harbor water. To facilitate this study,  
Figure 6: Schematic illustration of changes in the photon packet’s weight. certain parameters of the transmitter and receiver are predetermined and held constant, with the main variable parameters being the transmitted full divergence angle, the received aperture, and the received FOV. The transmitted full divergence angle significantly impacts the initial scattering angle \(\varphi_{0}\) of photon, as described in Equation (9), and the corresponding beam waist radius influences the initial position of photons, as indicated by Equations (5) and (8). These factors dictate the varied paths photons traverse, thereby affecting the number and time of photons reaching the Reception Plane. Consequently, this variation directly influences the normalized power loss and time delay spread. The received aperture and FOV determine the receiver's capability to collect photons, with the different number of photons received resulting in variations in received optical power. Moreover, the disparate photon counts lead to discrepancies in the statistical timing of photons arriving at the Reception Plane, ultimately affecting both normalized power loss and time delay spread. Reflecting the focus of our research, we have established a set of initial fixed parameters for use in our simulation model. These parameters, detailed in Table 2, include the laser wavelength, the number of photons transmitted, the single photon energy, and the total transmitted light energy. This approach ensures a consistent baseline for analyzing the impact of the aforementioned variable parameters on the performance of UWOC systems in different harbor water conditions. The specific settings for the transmitted full divergence angle, as outlined in Table 3, include values of 0.5 mrad, 5 mrad, 10 mrad, and 100 mrad. The Transmitted half divergence angle \((\theta_{div})\) of the Gaussian beam is defined as when the transmission distance \(z\rightarrow\infty\), the angle between the position with 1/e times the center maximum amplitude of the Far-field spot with z axis, as shown in the Figure 7 below. The Transmitted full divergence angle is \(2\theta_{div}\). The Far-field spot of the Gaussian beam is the spot determined by the position with 1/e times the center maximum amplitude, the spot radius \(w(z)\) in the propagation direction is shown in Equation (15), where \(w_{0}\) is the beam waist radius. \[w(z)=w_{0}\sqrt{1+\left(\frac{\lambda z}{\pi w_{0}^{2}}\right)^{2}} \tag{15}\]  
So, the Transmitted full divergence angle \(2\theta_{div}\) can be derived:  
\[2\theta_{div}=2\underset{z\rightarrow\infty}{lim}\frac{w(z)}{z}=\frac{2 \lambda}{\pi w_{0}} \tag{16}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Wavelength** & **Transmitted** & **Single** & **Transmitted** \\  & **Photon Number** & **Photon Energy** & **Light Energy** \\ \hline
532 nm & \(10^{13}\) & \(3.74\times 10^{-19}\) J & \(3.74\times 10^{-6}\) J \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Initial fixed parameters utilized in the simulation. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Transmitted full divergence angle** & 0.5 mrad & 5 mrad & 10 mrad & 100 mrad \\ (\(2\theta_{div}\)) & & & & \\ \hline
**Transmitted beam waist diameter (\(2w_{0}\))** & \(1.4\times 10^{-3}\) m & \(1.35\times 10^{-4}\) m & \(6.77\times 10^{-5}\) m & \(6.77\times 10^{-6}\) m \\ \hline
**Received aperture** & 25 mm & 50 mm & 100 mm & 200 mm & 400 mm \\ \hline
**Received FOV** & \(\frac{\pi}{90}\) rad & \(\frac{\pi}{30}\) rad & \(\frac{\pi}{22.5}\) rad & \(\frac{\pi}{15}\) rad & \(\frac{\pi}{7.5}\) rad & \(\frac{\pi}{2}\) rad & \(\frac{\pi}{1.5}\) rad & \(\pi\) rad \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Setting values for the transmitted full divergence angle, transmitted beam waist diameter, received aperture and received FOV.