# Wireless-Channel Key Distribution Based on Laser Synchronization
## 3 Experimental Results  
### Laser Synchronization Induced by a Common Wireless Signal  
The drive signal utilized in our experiment is a Gaussian noise characterized by a 3-dB bandwidth of 2.8 GHz and a central frequency of 6.7 GHz. The spectrum of the drive signal is shown in Figure 2a. The generation of broad-spectrum and synchronized outputs by the lasers requires a drive signal with an adequately broad bandwidth. The power loss is 37 dB, as the received power is approximately \(-24\) dBm and the transmit power is 13 dBm. The modulation depth is adjusted to 0.7 with an amplifier gain of 44 dB. The currents for the DFB lasers are set to 24.20 mA (2.12 \(I_{th}\)) and 23.50 mA (2.19 \(I_{th}\)) to achieve identical relaxation oscillation frequencies of 5.5 GHz. The injection strengths are adjusted to \(-8.43\) dB and \(-8.70\) dB to induce injection locking. The optical frequency detuning of the center frequencies of the DFB lasers and drive light is approximately 1.6 GHz, as illustrated in Figure 2b. As shown in Figure 2a, the laser outputs exhibit broad spectra characterized by a 3-dB bandwidth of approximately 2 GHz. This characteristic renders them suitable for the generation of high-speed random bits. The laser outputs have center frequencies that are approximately 1.3 GHz greater than those of the drive signal. This phenomenon arises as a result of the drive signal's spectrum encompassing the laser's relaxation oscillation frequency, thereby generating a light injection effect that enhances the relaxation oscillation frequency [32]. The spectral characteristics of the laser output and the drive light exhibit a comparable configuration, as illustrated in Figure 2b. The laser output maintains a fixed center frequency in accordance with that of the drive light. Figure 2: (**a**) RF spectra for the drive signal and the DFB laser outputs. (**b**) Optical spectra for the drive light and the DFB\({}_{\text{A}}\) output with and without optical injection. We introduce a measure of cross-correlation to evaluate the quality of the laser synchronization and the correlation between the laser output and the drive signal. The cross-correlation of temporal waveforms \(x(t)\) and \(y(t)\) is defined as  
\[CC_{xy}=\frac{\langle(x(t)-\overline{x})(y(t)-\overline{y})\rangle}{\sigma_{x} \sigma_{y}}, \tag{1}\]  
where \(<\)\(>\) denotes time average, \(\overline{x}\) and \(\overline{y}\) are the mean values, \(\sigma_{x}\) and \(\sigma_{y}\) are the standard deviations. If \(CC_{xy}=1\), it indicates that \(x(t)\) and \(y(t)\) are completely identical. Conversely, if \(CC_{xy}=0\), it means that they are completely uncorrelated. Figure 3a shows the temporal waveforms of the transmitted wireless drive signal, the signals received by antennas \(\mathrm{Rx_{A}}\) and \(\mathrm{Rx_{B}}\), and the response outputs of the DFB lasers. The received signals of both users maintain a high similarity, which satisfies the conditions for common-signal-induced synchronization. The temporal waveforms produced by the lasers demonstrate a significant resemblance. The corresponding linear correlation shown in Figure 3b is also evident in their corresponding correlation plot, which has a cross-correlation of 0.95. This observation demonstrates that Alice and Bob have successfully executed high-quality chaotic synchronization. In addition, as shown in Figure 3c, the cross-correlation between the laser output and the drive signal is 0.67, which is comparatively lower than that between the laser outputs. This indicates that only limited information about the synchronized outputs can be obtained from the drive signal, which satisfies our condition for key distribution. The effects of external parameter mismatches, such as center wavelength, bias current, and injection power, on the cross-correlation between laser outputs is illustrated in Figure 4. A mismatch of these external parameters for the lasers between Alice and Bob would lead to the reduction of the cross-correlation coefficient.