## 3 Results and Discussions
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** \\ \hline Linewidth enhancement factor \(a\) & 3 & Noise strength \(N_{\rm oil}\) & 100 \(\rm dBw\) \\ Field decay rate \(k\) & 300 \(\rm ns^{-1}\) & Polar angle \(\theta\) & \(\pi/2\) \\ Spin relaxation rate \(\rm\tau_{s}\) & 50 \(\rm ns^{-1}\) & Azimuth \(\varphi\) & \(\pi/2\) \\ Nonradiative carrier relaxation \(\rm\tau_{e}\) & 1 \(\rm ns^{-1}\) & Crystal temperature F & 293 \(\rm K\) \\ Dichroism \(\rm\gamma_{a}\) & 2 \(\rm ns^{-1}\) & Poled period of crystal \(\Lambda\) & 5.8 \(\times\) 10\({}^{5}\) m\({}^{-1}\) \\ Birefringence \(\rm\tau_{P}\) & 60 \(\rm ns^{-1}\) & Duty ratio \(D\) & 0.5 \\ Delay time \(\rm\tau\) & 5 ns & Crystal length \(L\) & 15 mm \\ Effective area of light spot \(\rm S_{A}\) & 7.0686 \(\rm\mu m^{2}\) & Refractive index of o-light \(n_{1}\) & 2.24 \\ Length of laser cavity \(L_{\rm v}\) & 3 \(\rm\mu m\) & Refractive index of e-light \(n_{2}\) & 2.17 \\ Effective refractive index of active layer \(n_{\rm g}\) & 3.6 & Frequency detuning \(\Delta\omega_{\rm s}\) & 0 GHz \\ Volume of active layer V & 21.206 \(\rm\mu m^{3}\) & Frequency detuning \(\Delta\omega\) & 150 GHz \\ Normalized bias current \(\rm\mu_{M}=\mu_{S}\) & 1.2 & Wavelength of VCSEL \(\Lambda\) & 1550 nm \\ Optical injection strength \(k_{\rm x}=k_{y}\) & 10 \(\rm ns^{-1}\) & Optical injection strength \(k_{\rm injx}=k_{\rm injy}\) & 500 \(\rm ns^{-1}\) \\ Threshold current of VCSEL \(l_{\rm th}\) & 6.8 mA & Bit duration time \(T\) & 10 ps \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The main system parameters. Here, we calculate the dependence of the correlation coefficient \(\rho_{\rm x,y}\) on the optical injection amplitude \(E_{\rm inj}\), as shown in Figure 3. Under the condition of \(E_{\rm A}=11\) kV/mm as depicted in Figure 3a, as \(E_{\rm inj}\) increases from 0 to 2.8, \(\rho_{\rm x}\) gradually rises to 0.73. As \(E_{\rm inj}\) further increases to 4.2, \(\rho_{\rm x}\) shows a declining trend, dropping from 0.73 to 0.41. With \(E_{\rm inj}\) increasing to 4.4, \(\rho_{\rm x}\) rapidly rises from 0.41 to a peak of 0.97. As \(E_{\rm inj}\) progresses from 4.4 to 10, \(\rho_{\rm x}\) slowly decreases to 0.84. For \(\rho_{\rm y}\), as \(E_{\rm inj}\) increases from 0 to 3.6, it swiftly rises from 0 to 0.82; with a further increase in \(E_{\rm inj}\) to 10, \(\rho_{\rm y}\) decreases slowly to 0.45. From Figure 3b, it is observed that when \(E_{\rm A}=25\) kV/mm, the evolution curve of \(\rho_{\rm x}\) with \(E_{\rm inj}\) closely matches that in Figure 3a. However, the evolution of \(\rho_{\rm y}\) differs: as \(E_{\rm inj}\) increases from 0 to 3.6, \(\rho_{\rm y}\) increases from 0 to 0.82; as \(E_{\rm inj}\) continues to 4.2, \(\rho_{\rm y}\) decreases slowly to 0.77; then, as \(E_{\rm inj}\) rises from 4.2 to 4.4, \(\rho_{\rm y}\) swiftly increases to a maximum of 0.98. Finally, as \(E_{\rm inj}\) progresses to 10, \(\rho_{\rm y}\) decreases gradually from 0.98 to 0.9. In our approach, a stronger correlation is advantageous for enhancing the storage performance of data selection logic operations. Therefore, it is concluded that under the condition where the \(E_{\rm A}\) equals 11 kV/mm, \(\rho_{\rm x}\) reaches a relatively high value around \(E_{\rm inj}=4.4\), peaking at 0.97. Similarly, \(\rho_{\rm y}\) achieves a relatively high value around \(E_{\rm inj}=3.6\), reaching a maximum of 0.82. When the \(E_{\rm A}\) is 25 kV/mm and \(E_{\rm inj}\) approaches 4.4, both \(\rho_{\rm x}\) and \(\rho_{\rm y}\) reach relatively high values, with \(\rho_{\rm x}\) peaking at 0.96 and \(\rho_{\rm y}\) at 0.98.