## 4 Secure Optical Communication
The effect of \(\tau_{PD}\) on the quality of message recovery with varying \(\eta\) is shown in Figure 10. For each of the values of \(\eta\), the quality of signal recovery as evaluated in terms of BER, prior to (after) the \(\tau_{PD}\) correction is shown in a red (blue) trace. We make two inferences from Figure 10. First, the BER is found to decrease up to the injection rate of \(\eta=17\) ns\({}^{-1}\) and BER increases for stronger injection. For stronger injection, the receiver tends to exactly reproduce the transmitter output, which consists of the chaotic output carrier together with the message signal. Hence, when stronger injection is applied, apart from the chaotic carrier subtraction, a part of the message signal itself will be eliminated in the process of decoding the signal [27; 28]. Secondly, it is evident from Figure 10 that the BER value is consistently less (blue trace) if message recovery is carried out after the \(\tau_{PD}\) correction to the receiver's output, which is implying that quality of the message recovery will improve if the intra-cavity propagation delay correction is incorporated in the receiver laser system. Next, we investigate the role of frequency detuning on quality of message recovery and thus the influence of intra-cavity propagation delay \(\tau_{PD}\). The injection rate is kept as \(\eta=15\) ns\({}^{-1}\) and varied frequency detuning \(\Delta f\). The obtained results are presented in Figure 11. It is evident from the figure that, the BER of the recovered message is found lesser near zero detuning. For \(\Delta f\) range \(-2\) GHz to \(-5\) GHz, where the better correlation found between TL and RL (see Figure 7), the quality of message recovery is worse (BER is more) since the receiver exactly reproduces the transmitter chaotic carrier output together with the message signal [27; 28]. As we have seen from Figure 7 that the synchronization quality is very sensitive while varying frequency detuning, where that affects message recovery excessively. The analysis of message recovery is restricted within the \(-5\) GHz to \(+5\) GHz detuning boundaries in the Figure 11 since RL is driven into the chaotic state only for \(\Delta f\) within \(-5\) GHz to \(+5\) GHz. As far as the influence of \(\tau_{PD}\) in the message recovery is concerned, in comparison with the BER (red trace) prior to the \(\tau_{PD}\) correction, the BER is found to decrease (blue trace) after \(\tau_{PD}\) correction in the recovery process. Figure 10: Estimation of BER values of the recovered messages as a function of injection rate for BR = 1.2 Gbit/s, \(b=0.2\), and \(\Delta f=0\). Red and blue traces correspond to BER value prior to and after the intra-cavity propagation delay \(\tau_{PD}\) correction, respectively, in the receiver laser. To further investigate the effect of intra-cavity propagation delay on communication performance, Figure 12 shows the BER of the recovered message for a different modulation depth of 1.2 Gbit/s bit rate message signal. Other parameters kept the same as in Figure 9. BER of the recovered message is evaluated for different message depth values, for before (red trace) and after (blue trace) the \(\tau_{PD}\) correction in the recovery process, and shown in Figure 12. Prior to the \(\tau_{PD}\) correction, as the message depth gradually increased from 0.01 to 1, the BER decreases dramatically from 0.12 to \(5.29\times 10^{-21}\). Moreover, there is a consistent improvement in the quality of message recovery (BER 0.12 to \(1.80\times 10^{-21}\)) after the \(\tau_{PD}\) correction (blue trace) as compared to the quality of signal recovery performed without the correction (red trace). Figure 13 shows the BER of the recovered message for different message bit rates at modulation depth \(b=0.2\). As shown in Figure 13, the BER is increased as the bit rate increases (blue and red  
Figure 11: Estimation of BER values of the recovered messages as a function of frequency detuning for BR = 1.2 Gbit/s, \(b=0.2\), and \(\eta=15\,\mathrm{ns}^{-1}\).