Abstract
We consider a modified version of the spin-flip model (SFM) that describes optically pumped quantum dot (QD) spin-polarized vertical-cavity surface-emitting lasers (VCSELs). Maps showing different dynamical regions and those consisting of various key bifurcations are constructed by direct numerical simulations and a numerical path continuation technique, respectively. A comparison between them clarifies the physical mechanism that governs the underlying dynamics as well as routes to chaos in QD spin-VCSELs. Detailed numerical simulations illustrate the role played by the capture rate from wetting layer (WL) to QD ground state, the gain parameter, and the amplitude-phase coupling. By tuning the aforementioned key parameters in turn we show how the dynamical regions evolve as a function of the intensity and polarization of the optical pump, as well as in the plane of the spin relaxation rate and linear birefringence rate, which is of importance in the design of spin lasers promising potential applications. By increasing the capture rate from WL to QD our simulation accurately describes the transition from the QD spin-VCSEL to the quantum well case, in agreement with a previous mathematical derivation, and thus validates the modified SFM equations.
Highlights
Instabilities and nonlinear dynamics in semiconductor lasers, driven by external perturbations, have received considerable attention [1,2,3], due to their potential applications in chaos-based communications [4, 5], random-number generation [6, 7], chaotic lidar [8], microwave generation [9], reservoir computing [10], and compressive sensing [11]
Spin-vertical-cavity surface-emitting lasers (VCSELs) offer faster polarization dynamics oscillating at a frequency mainly determined by the amount of birefringence in the cavity [40,41,42] and, in a very recent report, it has been demonstrated that direct modulation frequencies far beyond 100 GHz can be expected through polarization modulation in these lasers [43]
Limited knowledge of instabilities and effects of some key parameters on the dynamics of QD spin-VCSELs has been provided in a single publication from our group [48], where the largest Lyapunov exponent (LLE) method is used as a gauge for the dynamic behavior
Summary
Instabilities and nonlinear dynamics in semiconductor lasers, driven by external perturbations, have received considerable attention [1,2,3], due to their potential applications in chaos-based communications [4, 5], random-number generation [6, 7], chaotic lidar [8], microwave generation [9], reservoir computing [10], and compressive sensing [11]. In the case of QW spin-VCSELs, understanding instabilities and complicated dynamical behavior has been a topic of intense research This motivates research on the characterization of dynamics using various approaches, including asymptotic analysis [36], the calculation of the largest Lyapunov exponent (LLE) [27], and bifurcation analysis combining direct numerical simulations and path numerical continuation [47]. The latter method has provided a full picture of various dynamics accessible to QW spin-VCSELs, and uncovered rich bifurcation scenarios leading to chaos as well as certain auxiliary phenomenon [47], e.g., hysteresis. Our method allows us to map out the transition from the QD case to the QW case, further validating the modified SFM equations used throughout this study
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