## 4 Discussion  
We show that SOP and DOP are preserved when passed through experimentally generated underwater turbulence, simulated underwater bubbles, and simulated atmospheric turbulence. In experiment, we see that minor unexpected changes to the properties of the bubbles between trials do not significantly affect the results. We also note that the DOP is not exactly preserved, as the input states are slightly outside of confidence interval for most measured output states. We suspect this is caused by error in experimental state generation and measurement, and is not a direct result of the bubbles. A more sensitive state generation and detection setup can reduce this error. We can significantly decrease the time scales needed to obtain results if we collect multiple intensity measurements at the same time. Measurements can be made anywhere on the entire Poincare sphere if \(I(0^{\circ},\,0^{\circ})\), \(I(0^{\circ},\,90^{\circ})\), \(I(0^{\circ},\,45^{\circ})\), and \(I(45^{\circ},\,45^{\circ})\) are measured  
Figure 4: Measured DOP of the output states through underwater turbulence compared to the measured DOP of the input states for different arbitrary partially polarized states. Experimental and stationary bubbles simulation results are compared. (**a**) The output DOP with respect to the input DOP for an arbitrary basis. Input and output DOP are equal at the black like (\(y=x\)). Experimentally obtained data is shown in red and stationary bubbles simulation results are shown in blue. The error bars represent 99% confidence interval. We see DOP is preserved for arbitrary states. (**b**) Arbitrary input and output states in the Poincare sphere representation. Experimental input states are orange triangles, experimental output states are green diamonds, stationary bubbles simulation input states are red squares, stationary bubbles simulation output states are blue circles. On the Poincare sphere: D = diagonal, A = anti-diagonal, L = left, R = right, V = vertical, H = horizontal. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**State**} & \multicolumn{2}{c}{\(s_{1}/s_{0}\)} & \multicolumn{2}{c}{\(s_{2}/s_{0}\)} & \multicolumn{2}{c}{\(s_{3}/s_{0}\)} & \multicolumn{2}{c}{**DOP**} \\ \cline{2-9}  & **Input** & **Output** & **Input** & **Output** & **Input** & **Output** & **Input** & **Output** \\ \hline
0 & 0.03 & 0.04 & 0.06 & \(-\)0.02 & 0.05 & 0.10 & 0.08 & 0.11 \\
1 & 0.08 & 0.11 & \(-\)0.11 & \(-\)0.15 & 0.29 & 0.33 & 0.32 & 0.38 \\
2 & 0.12 & 0.13 & \(-\)0.32 & \(-\)0.25 & 0.43 & 0.43 & 0.55 & 0.51 \\
3 & 0.18 & 0.17 & \(-\)0.45 & \(-\)0.36 & 0.62 & 0.68 & 0.79 & 0.79 \\
4 & 0.25 & 0.25 & \(-\)0.43 & \(-\)0.47 & 0.78 & 0.73 & 0.93 & 0.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Measured mean normalized Stokes parameters of the input and output arbitrary partially polarized states through experimental underwater turbulence. simultaneously. A polarimeter that uses a rotating wave-plate/polarizer scheme, where the intensity is continuously measured as a function of time as the wave-plate/polarizer spin can result in near instantaneous detection. The measurements would need to be taken at a faster rate than the fluctuations. Some time averaging may still be necessary unless the entire state observes uniform turbulence across the entire beam profile. DOP and SOP show promise as a method of encoding information in FSO communication that is preserved when passed through atmospheric turbulence or underwater bubbles. The sender and receiver only need passive optics to encode and decode the respective data; no active optics are necessary. Turbulence resilience without the need of active optics could be particularly beneficial for advancements in ground-to-satellite communication, as bypassing active optics can result in significant weight savings [39]. We believe the methods presented here can work in tandem with other correction and security measures to continue to improve upon FSO communication.