# Evaluation of Optimal Visible Wavelengths for Free-Space Optical Communications
## 4 Results and Discussion
### Summary of Findings
#### 4.4.2 Theoretical Consistency with Fog Attenuation Models  
Although the present experiments were conducted under controlled indoor conditions without atmospheric interference, the observed wavelength-dependent performance trends align with classical theoretical models of fog attenuation. These include the [PERSON], [PERSON], and [PERSON] models, which predict how optical signal attenuation varies with wavelength under different visibility conditions [11; 12; 13]. The [PERSON] model, based on the Beer-Lambert law, expresses attenuation as \(\gamma\propto\lambda^{-q}\), where \(\gamma\) is the attenuation coefficient, \(\lambda\) is the wavelength, and q is a visibility-dependent parameter typically ranging from 0.5 to 1.6 [11]. For example, in moderate fog (visibility V = 2 km), q \(\approx\) 1.3, and, in lighter fog (V = 6 km), q \(\approx\) 0.7. Under such conditions, shorter wavelengths like 405 nm experience greater attenuation, while longer wavelengths, such as 650 nm, retain a clear transmission advantage. This trend is strongly reflected in our experimental results, where the 650 nm diode demonstrated the highest optical output power and quantum efficiency compared to the 532 nm and 405 nm. The [PERSON] model further extends [PERSON]'s work by refining the range of applicability and showing that longer wavelengths (typically in the 850-1550 nm range) experience reduced attenuation in light fog or haze [12]. Although the model is primarily used in the infrared regime, the attenuation behavior it describes also broadly applies to visible wavelengths, reinforcing the practical advantage of red light in short-range FSO links. The Al Naboulsi model further distinguishes between advection and radiation fog. In cases of moderate fog, particularly radiation fog, attenuation varies with wavelength and is lowest in the longer visible and near-infrared bands [13]. This again corroborates our observation that the 650 nm diode outperforms the 405 nm and 532 nm sources, especially under conditions simulating moderate atmospheric disturbances. To visually emphasize this consistency, Figure 5 presents a side-by-side comparison of the normalized experimental quantum efficiency and theoretical attenuation curves based on the Kruse model. The figure plots normalized attenuation curves for visibility values of 2 km (moderate fog) and 6 km (light fog), alongside the experimental data points at 405 nm, 532 nm, and 650 nm. The comparison illustrates a clear inverse relationship: wavelengths with higher theoretical attenuation correspond to lower measured efficiency, and vice versa. As shown, the 650 nm diode achieved the highest efficiency and corresponded to the lowest predicted attenuation, whereas the 405 nm diode experienced both reduced efficiency and higher theoretical losses. This supports the qualitative alignment between fog attenuation theory and practical system performance. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Wavelength (nm)**} & **This Work** & **[PERSON] et al. (2018)** & **[PERSON] et al. (2018)** & **Summary of Observed** \\  & **(\%)** & **—Q-Factor [9]** & **—Relative Efficiency [14]** & **Behavior** \\ \hline
650 nm (Red Laser) & \(55.1\) & \(4.87\) & Highest (stable day/night performance) & Best optical output and stability \\ \hline
532 nm (Green Laser) & \(19.9\) & \(4.42\) & Moderate (sensitive to atmospheric changes) & Susceptible to scattering and power degradation \\ \hline
405 nm (Violet Laser) & \(34.0\) & Not reported & Lowest (degraded under humidity and haze) & High drive requirement, lower atmospheric resilience \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparative summary of wavelength performance across studies. While future work will extend these findings through controlled fog-chamber testing and real-world FSO deployment, the present study establishes a solid, clear-air baseline.