## 3 Simulation Results of Gaussian Beams  
After a laser-fed SMF passes through the emitting collimator, the beam radius evolution of a Gaussian beam over 200 m is shown in Figure 1. At this range, the Gaussian beam gradually approaches at \(y=kx\), where \(k=\omega_{0}/z_{R}\). In this case, the Gaussian beam can be seen as a point source at \(z=0\) with a half-divergent angle \(\theta=\omega_{0}/z_{R}\) in rad. Figure 1 depicts the passage of the collimated beam through the divergent lens, and the corresponding \(\theta\) is 0.14 mrad. In contrast to transmission distances spanning hundreds of meters, indoor OWC only requires a few meters. Figure 2 depicts the focusing process of the collimated optical beam after passing through the divergent lens. The emitting collimator's output facet is positioned at \(z=0\), while the thin lens marked by an arrow, neglecting its thickness, is situated at \(z=40\) mm. Since the separation between the emitting collimator and the divergent lens is constrained to several centimeters, the optical beam retains its collimation. As a matter of fact, its collimation distance is sufficient to extend a few meters away, and this characteristic accounts for the negligible geometrical path loss observed in indoor OWC employing narrow optical beams. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Optics** & **Size 1** & **FL 2** & **CA 3** & **Beam Waist** & **NA 4** \\ \hline Fixed Col. 5  & 24 mm & 37.20 mm & X & 3.5 mm & 0.24 \\ Lens 6  & 25 mm & 20.00 mm & 22.5 mm & X & 0.54 \\ Zoom Col. 7  & 1.2-inch & Adjustable & 20.5 mm & X & 0.25 \\ \hline \hline \end{tabular}  
* Outer Diameter; 2 Focal length; 3 Clear Aperture; 4 Numerical Aperture; 5 Collimator with a fixed focal length; 6 Focusing lens; 7 Collimator with a adjustable focal length.  
\end{table} 
Table 1: Parameters of the optics used in simulations and experiments. Figure 2: The focusing process of a collimated optical beam. The divergence of the optical beam can be adjusted by lenses. As the optical beam encounters a lens, the beam waist of this lens is expressed as:  
\[\omega_{01}=\frac{\omega_{00}f}{z_{R}}, \tag{5}\]  
where \(\omega_{00}\) and \(\omega_{01}\) are the beam waist of the emitting collimator and the divergent lens with a focal length of \(f\), respectively. \(z_{R}\) is the Rayleigh length of the emitting collimator. After the optical beam reaches its beam waist of 2.81 um as calculated by Equation (5), it diverges at the same rate as focusing, and the corresponding half-divergent angle \(\theta\) is 9.92\({}^{\circ}\), which equals the divergent angle calculated by \(atan(\omega_{00}/f)\). As a result, the beam radius evolution, as determined by Equation (3), can be effectively substituted with a simplified geometric optics approach. Following free-space transmission, the optical beam is collected by the receiving collimator. During this stage, geometrical path loss arises when the diameter of the coverage area exceeds that of the receiving collimator's clear aperture (CA). To evaluate the geometrical path loss, it is critical to establish the receiving model of divergent Gaussian beams. At a target transmission distance \(z\), the optical power within transverse distance \(r\) of a Gaussian beam is the integral of Equation (1) from 0 to \(r\):  
\[P(r,z)=\int_{0}^{r}I(r,z)dr=P_{o}\bigg{(}1-exp\bigg{(}\frac{-2r^{2}}{\omega^{2 }(z)}\bigg{)}\bigg{)}, \tag{6}\]  
where \(\omega(z)\) is the radius of the coverage area at a transmission distance \(z\). Assuming the receiving collimator with a CA of \(\varphi_{c}\) is located at a transverse distance \(r\), and the intensity distribution between the two circles with an on-axis dot and tangent to the receiving collimator is uniform [16], then the optical power captured by the receiving collimator can be derived from Equation (6) as:  
\[P_{colli}(r,z,\varphi_{c})=\left\{