Abstract
In this paper, the nonlinear dynamics of a novel model based on optically pumped spin-polarized vertical-cavity surface-emitting lasers (spin-VCSELs) with optical feedback is investigated numerically. Due to optical feedback being the external disturbance component, the complex nonlinear dynamical behaviors can be enhanced and the regions of different nonlinear dynamics in size can be extended with appropriate parameters of spin-VCSELs. According to the equations of the modified spin-flip model (SFM), the comparison of bifurcation diagrams is first presented for the clear presentation of different routes to chaos. Meanwhile, numerous bifurcation diagrams in color are illustrated to demonstrate the rich dynamical regimes intuitively, and the crucial effects of optical feedback strength, feedback delay, linewidth enhancement factor, and spin-flip relaxation rate on the region evolvement of complex dynamics of the proposed model are revealed to investigate the dependence of dynamical behaviors on external and internal parameters when the optical feedback scheme is introduced. These parameters play a remarkable role in enhancing the mechanism of complex dynamic oscillations. Furthermore, utilizing combination with time series, power spectra, and phase portraits, the various dynamical behaviors observed in the bifurcation diagram are simulated numerically. Correspondingly, the powerful measure 0–1 test is employed to distinguish between chaos and non-chaos.
Highlights
It shows that the output of spin-polarized VCSEL is feedback by the Mirror to enhance the complexity of its nonlinear dynamics
It can be observed that optical feedback intensity and optical feedback delay time are important factors that significantly affect the dynamical behaviors of spin-VCSELs with optical feedback
Based on the presented expanding spin-flip model (SFM) equations, we have first investigated the nonlinear dynamics of optically pumped spin-VCSELs with optical feedback through numerical simulations
Summary
The nonlinear dynamics of semiconductor lasers (SLs) [1,2,3,4,5,6] has received extensive attention thanks to their high complex dynamical behaviors and the widespread application in fields such as random bit generation [7,8], reservoir computing [9,10], chaos-based optical communications [11,12,13,14], chaotic radar [15,16], and other relevant areas [17,18,19]. The theoretical analysis and experimental results about the regions of stability and instability in optically pumped 1300 nm dilute nitride spin-VCSELs have been reported in detail [32], in which the importance of the linewidth enhancement factor and linear birefringence rate for high-frequency applications has been revealed. The stability and instability analysis of optically pumped quantum dot spin-VCSELs has been investigated numerically in [35,36], and various bifurcation diagrams have been presented to demonstrate the impact of key parameters on the dynamical properties in this laser system [37]. The effects of optical feedback delay, optical feedback strength, linewidth enhancement factor, and spin-flip relaxation rate on the regions of complex dynamics of the proposed model are revealed to investigate the dependence of dynamical behaviors on external and internal parameters through the optical feedback scheme introduced. The results of the 0–1 test are consistent with the characteristics of different dynamic states and the corresponding regimes in the mapping
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