Impacts Of Mismatched Parameter On The Leader-laggard Synchronization Between Two Mutually Coupled VCSELs

Mutually coupled vertical-cavity surface-emitting lasers (VCSELs) system have attracted considerable interests due to their important application in bidirectional chaos secure communication fields. The nonlinear dynamics, polarization properties and chaos synchronization of mutually coupled scheme have been studied extensively. For completely symmetrical (identical parameter) mutually coupled VCSELs, the chaos synchronization characteristics behave in an unstable way due to stochastic noise, and stochastic leader-laggard synchronization is usually observed in a time dependent manner. In order to realize the stable chaos synchronization, the asymmetric system based on the mismatched external parameter (such as coupling strength mismatch, frequency detuning) has been proposed, and the influences of mismatched external parameters on the leader-laggard relationship has been investigated. However, all the works mentioned above did not take the mismatched intrinsic parameters into account. Since there is always exists the inevitable mismatch of intrinsic parameters in mutually coupled VCSELs, therefore, it is essential to investigate the influences of mismatched intrinsic parameters on the leader-laggard relationship between two mutually coupled VCSELs.In this paper, based on the framework of spin-flip model (SFM) of VCSELs, the theoretical model of mutually coupled VCSELs has been established, and the impacts of mismatched intrinsic parameter on the leader-laggard chaos synchronization of the system have been investigated numerically. The results show that:firstly, the cross-correlation coefficient appears two peaks about0.8because of spontaneous symmetry-breaking phenomena, which indicates that the chaos synchronization characteristics behave in an unstable way, and the system presents stochastic leader-laggard relationship between the two VCSELs; secondly, for two VCSELs with identical intrinsic parameter, the switching point of leader-laggard caused by continually varying frequency detuning or injection rate detuning is located at zero frequency detuning or zero injection rate detuning, which indicates that the VCSEL with higher frequency or subject to lower injection level plays a leader role; thirdly, for two VCSELs with mismatched intrinsic parameter, the switched point of leader-laggard will deviate from zero frequency detuning or zero injection rate. Therefore, compared with the results obtained under matched intrinsic parameter, the opposite result has been observed in the range between zero detuning and switching point. Additionally, the offsets of switching point induced by different intrinsic parameters are different, and the influence of line-width enhancement factor is found to be the most significant. The simulation results above agree with the experimental results well.