## 3 Results and Discussions
To further determine the value range of \(E_{\rm inj}\) for modulating logic inputs, we calculate the evolutions of the polarization bistability of \(x_{\rm P}\)-PC, \(y_{\rm P}\)-PC, \(x_{\rm S}\)-PC and \(y_{\rm S}\)-PC under applied electric fields \(E_{\rm A}\) of 11 kV/mm and 25 kV/mm, respectively, as illustrated in Figure 4. From Figure 4a, it is evident that under an applied electric field \(E_{\rm A}\) of 11 kV/mm,  
Figure 3: The influence of the optical injection amplitude \(E_{\rm inj}\) on the correlation coefficient \(\rho_{\rm x,y}\) under different applied electric fields. (**a**) \(E_{\rm A}=11\) kV/mm. (**b**) \(E_{\rm A}=25\) kV/mm. Figure 2: Evolutions of dynamic state of \(x_{\rm S}\)-PC and \(y_{\rm S}\)-PC in parameter space of \(E_{\rm A}\) and \(E_{\rm inj}\). (**a**) \(x_{\rm S}\)-PC. (**b**) \(y_{\rm S}\)-PC. when \(E_{\rm inj}\) ranges from 0 to 3.9, \(x_{\rm p}\)-PC predominates, while \(y_{\rm p}\)-PC is suppressed. However, the extent of mutual suppression between them is not pronounced. When \(E_{\rm inj}\) varies between 3.9 and 4.5, both \(x_{\rm p}\)-PC and \(y_{\rm p}\)-PC display bistable loops, accompanied by an increased degree of mutual suppression. When \(E_{\rm inj}\) ranges from 4.5 to 10, \(x_{\rm p}\)-PC dominates completely, while \(y_{\rm p}\)-PC is nearly entirely suppressed. In Figure 4b, when \(E_{\rm inj}\) is below 3.9, the evolution of the polarization bistability for \(x_{\rm S}\)-PC and \(y_{\rm S}\)-PC is similar to that observed in Figure 4a. When \(E_{\rm inj}\) ranges from 3.9 to 4.7, both \(x_{\rm S}\)-PC and \(y_{\rm S}\)-PC demonstrate bistable loops. As \(E_{\rm inj}\) exceeds 4.7, the mutual suppression between \(x_{\rm S}\)-PC and \(y_{\rm S}\)-PC intensities, leading to the complete suppression of \(y_{\rm S}\)-PC by \(x_{\rm S}\)-PC. From Figure 4c, it is evident that under an applied electric field \(E_{\rm A}\) of 25 kV/mm, when \(E_{\rm inj}\) ranges from 0 to 3.9, \(y_{\rm p}\)-PC dominates, while \(x_{\rm p}\)-PC is suppressed. When \(E_{\rm inj}\) ranges from 3.9 to 4.7, both \(x_{\rm p}\)-PC and \(y_{\rm p}\)-PC exhibit bistable loops, with an increased degree of mutual suppression observed between them. When \(E_{\rm inj}\) ranges from 4.7 to 10, \(y_{\rm p}\)-PC dominates completely, while \(x_{\rm p}\)-PC is entirely suppressed. The polarization bistability evolutions of \(x_{\rm S}\)-PC and \(y_{\rm S}\)-PC depicted in Figure 4d closely resemble those observed in Figure 4c. In our scheme, the mean comparison mechanism is employed to demodulate \(x_{\rm p}\)-PC and \(y_{\rm p}\)-PC and \(x_{\rm S}\)-PC and \(y_{\rm S}\)-PC to obtain logic outputs \(O_{1}\) and \(O_{2}\) (as described below). The bit error rate of \(O_{1}\) and \(O_{2}\) is influenced by the extent of mutual suppression between \(x_{\rm p}\)-PC and \(y_{\rm p}\)-PC, as well as between \(x_{\rm S}\)-PC and \(y_{\rm S}\)-PC. A higher degree of mutual suppression correlates with a lower bit error rate. Therefore, based on the above analysis, it can be inferred that the value of \(E_{\rm inj}\) used for modulating the logic input should be greater than 4.7. Considering that maximizing the correlation coefficient \(\rho_{x_{\rm S}}\) is desirable and ensuring that \(x_{\rm S}\)-PC and \(y_{\rm S}\)-PC maintain a chaotic state, we opt to choose appropriate values of \(E_{\rm inj}\) within the range of 5.35 to 5.46 for modulating the logic inputs. Assume that the optical injection amplitude \(E_{\rm inj}\) is equal to the sum of three square wave signals, i.e., \(E_{\rm inj}=E_{\rm inj1}+E_{\rm inj2}+E_{\rm inj3}\), where \(E_{\rm inj1}\) and \(E_{\rm inj2}\) are modulated as optical logic inputs \(I_{1}\) and \(I_{2}\), and \(E_{\rm inj3}\) is modulated as an optical clock signal \(I_{3}\). Since the logic input can be either 0 or 1, there are eight possible input combinations: (0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 1), (1, 0, 0), (1, 0, 1), (1, 1, 0) and (1, 1, 0).