# Wireless-Channel Key Distribution Based on Laser Synchronization
## 4 Numerical Results
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Active region length & \(L\) & 350 \(\mu\)m \\ Active region width & \(w\) & 2.5 \(\mu\)m \\ Active region thickness & \(d\) & 0.2 \(\mu\)m \\ Group refractive index & \(n_{g}\) & 3.7 \\ Internal loss & \(\alpha_{0}\) & 3000 m\({}^{-1}\) \\ Confinement factor & \(\Gamma\) & 0.3 \\ Index grating coupling coefficient & \(k_{i}\) & 6000 m\({}^{-1}\) \\ Linear recombination coefficient & \(A\) & \(3\times 10^{8}\) s\({}^{-1}\) \\ Bimolecular recombination coefficient & \(B\) & \(1\times 10^{-16}\) m\({}^{3}\)s\({}^{-1}\) \\ Auger recombination coefficient & \(C\) & \(1.3\times 10^{-41}\) m\({}^{6}\)s\({}^{-1}\) \\ Transparency carrier density & \(N_{0}\) & \(1.5\times 10^{24}\) m\({}^{-3}\) \\ Linear gain coefficient & \(gL\) & \(3\times 10^{-20}\) m\({}^{2}\) \\ Nonlinear gain saturation coefficient & \(\varepsilon_{\text{NL}}\) & \(1\times 10^{-23}\) m\({}^{3}\) \\ Linewidth enhancement factor & \(a_{H}\) & 3 \\ Inversion parameter & \(n_{sp}\) & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter values of DFB lasers used in simulations. laser outputs decreases, and the BER between Alice and Bob increases. This degradation in performance is due to the decrease in received power as the distance increases, leading to a deterioration of the receiver's signal-to-noise ratio (SNR), which ultimately affects laser synchronization. When the transmit power of the drive signal is set to \(P_{t}=13\) dBm, the maximum transmission distance that satisfies a cross-correlation greater than 0.9 and BER lower than \(3.8\times 10^{-3}\) is approximately 200 m. We can improve the received SNR to extend the maximum distance by increasing the transmit power. When \(P_{t}\) is set to 27 dBm, the maximum distance can reach 1000 m. It is worth noting that the distribution distance between Alice and Bob (\(d_{AB}\)) depends on their orientation relative to the drive. If the drive is positioned exactly in the middle between Alice and Bob, \(d_{AB}\) will be twice the transmission distance. Continuing with the more general case where the distance from the drive to Alice and Bob is unequal, the simulation results are shown in Figure 8. The distance from the drive to Bob (\(d_{DB}\)) is adjusted while maintaining the distance from the drive to Alice at \(d_{DA}=100\) m. When \(d_{DB}\) is less than 240 m, the cross-correlation of the laser outputs remains above 0.9. This indicates that synchronization exhibits robustness to unequal distances. Therefore, it is also feasible to place the drive at either Alice or Bob, in which case the distribution distance \(d_{AB}\) is equal to the transmission distance. Figure 8: Effect of unequal distances on laser synchronization. The distance from the drive to Alice is fixed at \(d_{DA}=100\) m (solid blue curve). As a reference, the results for equal distances from the drive to Alice and Bob (\(d_{DA}=d_{DB}\)) are also plotted (dashed gray curve). The transmit power is set to \(P_{t}=13\) dBm. Figure 7: Effects of transmission distance \(d\) on the (**a**) laser synchronization and (**b**) BER between Alice and Bob. The distance from the drive to Alice and Bob is equal (\(d_{DA}=d_{DB}=d\)). The threshold coefficient of dual-threshold quantization is set to \(C_{+}=0.8\).