## 3 Simulation Results and Discussions
### RIN Spectra of \(LD\) for Various States  
Variations in the RIN of the LD with the LEF and SEF at various states of the LD, such as the CW, PO, PD, and chaos state, with two different values of OFB intensity, \(K_{ex}=0.01\) (weak OFB) and \(K_{ex}=0.1\) (moderate OFB), are presented in Figures 4 and 5. Figure 4 plots the RIN spectra at the OFB intensity \(K_{ex}=0.01\) in the weak OFB regime, the LEF \(\alpha=1\), 3, and 5, and the SEF \(C=10^{-4}\), \(10^{-5}\), and \(10^{-6}\). It is clear from Figure 4(a1-c1) that when the laser operates in the CW state and when the SEF \(C=10^{-4}\) and the LEF \(\alpha=1\), 3, and 5, there is no difference in the RIN value with the OFB (dashed line) and solitary laser RIN (solid line) at a higher frequency regime (relaxation frequency \(f_{r}\)). A frequency shift in the RIN peak is noticed and moves towards increasing frequency, where the relaxation frequency is \(f_{r}=5.5\), 5.9, and 6.2 GHz when the LEF \(\alpha=1\), 3, and 5, respectively. Moreover, in a low-frequency regime and by increasing the LEF, the RIN is enhanced to a level higher than the solitary laser RIN level. By transmitting to the PO state, when the LEF \(\alpha=1\) and the SEF \(C=10^{-4}\), \(10^{-5}\), and \(10^{-6}\), the peak value of the RIN with OFB is enhanced to higher values (four orders of magnitude) (dashed line) compared with the solitary laser RIN (solid line) at the relaxation frequency \(f_{r}\), as shown in Figure 4(a1-a3). A small shift in the RIN peak is noticed and moves towards increasing frequency, where the relaxation frequency is \(f_{r}=1.2\), \(2\), and \(5.5\) GHz by increasing the SEF \(C=10^{-6}\), \(10^{-5}\), and \(10^{-4}\), respectively. At low frequency and by decreasing the SEF, the RIN is enhanced to almost one order of magnitude higher than the solitary laser noise. Under the PD state, the RIN behaves as under the PO state except that another peak is observed in the RIN spectrum, which represents a doubling in the period. By increasing the intensity of the OFB \(k_{ex}=0.1\), we investigated the impacts of the LEF and SEF on the RIN spectra over various states of the LD in the OFB medium regime. Figure 5 shows the RIN spectra at the OFB intensity \(K_{ex}=0.1\) in a moderate OFB regime, an LEF \(\alpha=1\), \(3\), and \(5\), and an SEF \(C=10^{-4}\), \(10^{-5}\), and \(10^{-6}\). When the laser operates in the CW state at an SEF \(C=10^{-4}\) and an LEF \(\alpha=1\), as shown in Figure 5(a1), the RIN shows a second harmonic peak, and its value of the relaxation frequency \(f_{r}\) (dashed line) is lower than the solitary laser RIN (solid line) by about two orders of magnitude. A frequency shift was found between the RIN with OFB (\(f_{r}=4.9\) GHz) and the solitary laser RIN (\(f_{r}=5.7\) GHz). The frequency shift increases by decreasing the SEF \(C=10^{-6}\) and \(10^{-5}\), where the RIN with OFB occurs at (\(f_{r}=1.25\) and \(2.1\) GHz) and the solitary laser RIN occurs at (\(f_{r}=0.75\) and \(1.25\) GHz), as shown in Figure 5(b1,c1), respectively. At a low frequency, the RIN is enhanced to higher values (almost one order of magnitude) than the solitary laser RIN level and increases by decreasing the SEF, as shown in Figure 5(b1,c1). Under the PO state, when the LEF \(\alpha=3\) and the SEF \(C=10^{-5}\), the peak intensity of the RIN with OFB is enhanced to higher values (four orders of magnitude) (dashed line) and shifted in the direction of increasing frequency comparing with the solitary laser RIN (solid line) at the relaxation frequency \(f_{r}\), as shown in Figure 5(b2). Figure 5(b2) exhibits a frequency shift between the RIN with OFB (\(f_{r}=3.6\) GHz) and the solitary laser RIN (\(f_{r}=2.0\) GHz). At low frequency, the RIN is enhanced to higher values (almost one order of magnitude) than the solitary laser RIN and increases by decreasing the SEF, as shown in Figure 5(b2,b3,c3).