Investigation Of Dynamical Behavior And Reservoir Computing Based On Mutually Coupled Quantum Dot Spin-VCSELs

The research of laser source has become an important field of optical physics,among which semiconductor lasers have attracted researchers to conduct extensive investigations in succession due to their outstanding characteristics that were constantly being discovered.In particular,the point of nonlinear dynamics on semiconductor lasers has been focusing considerably critical attention,for instance various semiconductor lasers have shown a wide variety of dynamic behaviors,the common ones include steady state,period,period-doubling,and chaotic state.For more semiconductor lasers,the rich dynamic behavior is of great significance to their development.Exploring and controlling the rich dynamic behavior of such semiconductor lasers in a specific environment is a very important hot topic in the current research field.Likewise,various extended model structures based on semiconductor lasers have gradually appeared,and investigations on that could even fully exhibit the potentials of semiconductor lasers.Furthermore,more recent studies have raised a multitude of fascinating topics based on diversified semiconductor lasers,thus,the attention to semiconductor lasers has not diminished in any way.Compared with the traditional distributed feedback laser(DFB)and edge-emitting semiconductor laser(EEL),the vertical-cavity surface-emitting laser(VCSEL)has more superior performance,such as low threshold current,low threshold voltage,high power output,low loss and high conversion efficiency.Meanwhile,due to the tremendous contributions to deal with theoretical and experimental analysis in spintronics field,taking a consideration for electron spin combining with VCSEL represents an exciting view of research,namely spin-VCSEL,which is regarded as a specific design of spintronic devices and it can be controlled by injection of spin-polarized electrons into the laser active region to realize the adjustment of output optical polarization.Moreover,since the coupling of spin-up(down)electrons to the left(right)-circularly polarized optical field in a quantum confined active material,spin-VCSEL can supply high-quality and even faster output for the polarization dynamics with hardly necessary external perturbation.At present,spin-VCSELs can be divided into quantum well(QW)type and quantum dot(QD)type according to the different materials of active region.In this paper,we propose a mutually coupled QD spin-VCSELs model using double QD spin-VCSELs on the basis of the single QD Spin-VCSEL model.Further we consider that extending this structure to the field of artificial intelligence neural networks,that is,RC system based on mutually coupled QD spin-VCSELs.Consequently from which both the dynamical behavior and application of mutually coupled QD spin-VCSELs are studied.Based on the solitary QD spin-VCSEL model,this model of our mutually coupled QD spin-VCSELs driven with optical pumping using circularly polarized light based on two QD spin-VCSELs is presented,and the rate equation of which is also described by using the expanding spin-flip model.Compared with the conventional solitary model,we systematically study the influence of key parameters on the output dynamical behavior of the model and produce numerous bifurcation maps combining with the idea of bifurcation analysis to visually display different dynamical regions,which are associated with more plentiful dynamical regimes in two dimensional planes with a variety of two parameters,and the detailed direct numerical simulations accurately reveal the dependence of dynamical behavior on external and internal parameters through introducing mutual coupling scheme.We then find that the roles played by the mutual coupling strength and delay time are remarkably significant in intensifying the regime of complex dynamical oscillation.Beyond that,the crucial effects of capture rate,gain parameter,linewidth enhancement factor and frequency detuning in regard to determining the evolvement of dynamical behavior in the mutually coupled QD spin-VCSELs model are evidently shown in the plane of the optical pump intensity and polarization.Through a comprehensive investigation of the dynamical behavior dependent on key parameters,it provides a practical reference and theoretical basis for regulating and even controlling the dynamical mechanism expressed in the current model.Therefore,the involved efforts are enlightening and foresighted to promote a deeply research in the field of QD lasers-based expansion.Inspired by artificial intelligence neural networks,RC as a brain-inspired information processing technology derived from recurrent neural network(RNN)has become a typical contribution.The model of mutually coupled QD spin-VCSELs is extended to the field of optical neural network,and an optical reservoir computing(RC)system based on our proposed model is implemented successfully.In which Santa-Fe time series prediction task is utilized to quantitatively evaluate the prediction performance of the presented system.Different effects of optical pump intensity,optical pump polarization,mutual coupling strength,external signal injection strength,and external signal injection frequency detuning on prediction performance are revealed systematically and completely in various two-dimensional maps as well.The results show that better prediction performance regions have appeared at smaller optical pump intensity,smaller mutual coupling strength,larger external signal injection strength and negative external signal injection frequency detuning.Moreover,for the purpose of reaching the trade-off between prediction performance and data processing rate,the conversion of the data processing rate can be achieved by adjusting the time scale of this RC system flexibly,where the fastest data processing rate can be even up to 50 Gbps.Therefore,this research not only expands the application field of QD spin-VCSEL,but also provides a promising way for high-speed data processing and neuromorphic computation in the future.