## 4 Secure Optical Communication  
In this section, we investigate the effect of \(\tau_{PD}\) on the message encoding and decoding based on chaos synchronization between the transmitter and receiver laser. As described in the previous Section 3, the transmitter laser's pump magnitude is modulated with a message and transmitted to the receiver laser. The message recovery is performed by subtracting the receiver laser output from the transmitted output signal and then filtering the difference using a fifth-order Butterworth filter. A digital message signal with 1.2 Gbit/s bit rate is encoded at the transmitter laser. In Figure 9a, we present the original message \(m(t)\) (red) together with the recovered message \(m^{\prime}(t)\) (blue). The eye diagram, Figure 9b, shows that the message is successfully recovered with less error, where the eye diagram is very open. Apart from the synchronization performance, the quality of the recovered message would also depend on the chaos pass filtering [54]. The recovered message is shown in Figure 9 obtained prior to the intra-cavity propagation delay \(\tau_{PD}\) correction in the receiver laser. To quantify the recovered message quality, BER is evaluated and expressed as \(exp(-Q^{2}/2)/\sqrt{2\pi}Q\). The quality factor is defined as \(Q=\xi_{1}-\xi_{0}/\sigma_{1}+\sigma_{0}\) where \(\xi_{1}(\xi_{0})\) is the mean power of bits \"1\" (\"0\"), and \(\sigma_{1}(\sigma_{0})\) corresponding standard deviation. It must be stated that the lesser BER value indicates the message recovery quality is better in the communication system. The BER of the recovered message prior to the \(\tau_{PD}\) correction in the receiver laser is \(5.43\times 10^{-12}\). The evaluated intra-cavity propagation delay \(\tau_{PD}\) is corrected in receiver laser's output and we repeated the message recovery process. Thus, the obtained BER value is found to be \(4.10\times 10^{-12}\), which is evidently lesser than that of the BER of the recovered message signal obtained prior to the \(\tau_{PD}\) correction to the receiver laser output. To further compare the influence of \(\tau_{PD}\) and communication performances with the other schemes such as chaos masking (CMA) and chaos modulation (CMO), the BER is measured for each of the schemes. For CMA scheme, the \(C_{m}\) and \(\tau_{PD}\) are found to be 0.82 and 27.6 ps, respectively. The BER value prior to the \(\tau_{PD}\) correction is \(4.70\times 10^{-3}\), and after the correction it is \(4.59\times 10^{-3}\). In the case of CMO, the \(C_{m}\) is measured to be 0.85 and the corresponding \(\tau_{PD}\) is 28.2 ps. And the BER value without (with) the \(\tau_{PD}\) correction is \(1.28\times 10^{-1}\) (\(1.27\times 10^{-1}\)). It is evident that the \(\tau_{PD}\), although small value in relative scales, has a noticeable and measurable effect on the recovery of a message in all three schemes. To ascertain if \(\tau_{PD}\) correction is going to be a non-ignorable quantity in the recovery process we repeated this study for various injection rates and frequency detunings between TL and RL. We focus our investigation on the influence of the intra-cavity propagation delay \(\tau_{PD}\) on message encoding/decoding for various injection rates \(\eta\) between the transmitter and receiver laser. Figure 9: Results of unidirectional message encoding and decoding using CSK scheme for \(J_{m}=1.10I_{lh}\), \(J_{R}=1.08I_{lh}\), \(\kappa=9\) ns\({}^{-1}\), \(\eta=15\) ns\({}^{-1}\), \(\Delta f=0\), \(\tau_{ext}=10\) ns, and \(\tau_{f}=0\) under transmitter-receiver configuration. (**a**) The original message \(m(t)\) (red) and the recovered one \(m^{\prime}(t)\) (blue), and (**b**) the eye diagram of the recovered message. The digital message transmitted at 1.2 Gbit/s bit rate with \(b=0.2\) modulation depth. The encoding message signal at 1.2 Gbit/s bit rate with a modulation depth of \(b=0.2\), \(\Delta f=0\), and the injection rate \(\eta\) is varied from 10 ns\({}^{-1}\) to 70 ns\({}^{-1}\).