Mapping bifurcation structure and parameter dependence in quantum dot spin-VCSELs.

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.

Nonlinear dynamics of solitary and optically injected two-element laser arrays with four different waveguide structures: a numerical study.

We study the nonlinear dynamics of solitary and optically injected two-element laser arrays with a range of waveguide structures. The analysis is performed with a detailed direct numerical simulation, where high-resolution dynamic maps are generated to identify regions of dynamic instability in the parameter space of interest. Our combined one- and two-parameter bifurcation analysis uncovers globally diverse dynamical regimes (steady-state, oscillation, and chaos) in the solitary laser arrays, which are greatly influenced by static design waveguiding structures, the amplitude-phase coupling factor of the electric field, i.e. the linewidth-enhancement factor, as well as the control parameter, e.g. the pump rate. When external optical injection is introduced to one element of the arrays, we show that the whole system can be either injection-locked simultaneously or display rich, different dynamics outside the locking region. The effect of optical injection is to significantly modify the nature and the regions of nonlinear dynamics from those found in the solitary case. We also show similarities and differences (asymmetry) between the oscillation amplitude of the two elements of the array in specific well-defined regions, which hold for all the waveguiding structures considered. Our findings pave the way to a better understanding of dynamic instability in large arrays of lasers.

Locking bandwidth of two laterally-coupled semiconductor lasers subject to optical injection.

We report here for the first time (to our knowledge), a new and universal mechanism by which a two-element laser array is locked to external optical injection and admits stably injection-locked states within a nontrivial trapezoidal region. The rate equations for the system are studied both analytically and numerically. We derive a simple mathematical expression for the locking conditions, which reveals that two parallel saddle-node bifurcation branches, not reported for conventional single lasers subject to optical injection, delimit the injection locking range and its width. Important parameters are the linewidth enhancement factor, the laser separation, and the frequency offset between the two laterally-coupled lasers; the influence of these parameters on locking conditions is explored comprehensively. Our analytic approximations are validated numerically by using a path continuation technique as well as direct numerical integration of the rate equations. More importantly, our results are not restricted by waveguiding structures and uncover a generic locking behavior in the lateral arrays in the presence of injection.