Nonlinear dynamics and complexity of spin-VCSELs with negative optoelectronic feedback subject to key parameters

A novel model based on optically pumped spin-polarized vertical-cavity surface-emitting laser (spin-VCSELs) with negative optoelectronic feedback (NOEF) is implemented and analyzed in this paper. The bifurcation analysis is used to systematically study the influence of key parameters on the output dynamic behavior of the proposed model. In addition, plentiful dynamical regimes are generated in a variety of mapping diagrams, which visually show several different color regions. The direct numerical simulations in detail explain the evolution process of the system from steady state, periodic state, period-doubling state, and quasi-periodic state to chaotic state, and reveal the dependence of the rich dynamic behaviors of the model on the NOEF parameters. We find that the enhancement of feedback intensity and feedback delay time can make the system easier to enter the complex dynamic regions. At the same time, the \(C_0\) $C_0$ complexity algorithm is used to estimate the complexity of the proposed model. The results show that the introduction of NOEF has a significant effect on the complexity enhancement. Furthermore, the positive effects of pumping intensity, pump ellipticity and linewidth enhancement factor on the dynamic behavior evolution of the model are also evident in the mapping diagrams. Conversely, the spin-flip relaxation rate can suppress complex dynamic behavior. By studying the dynamic behavior of external and internal parameters, it provides a theoretical basis for adjusting the dynamic mechanism and to explore the extended model of spin-VCSELs based on NOEF.