Based on the Spin Flip Model (SFM), vectorial chaotic synchronization characteristics of vertical-cavity surface-emitting semiconductor lasers (VCSELs) with isotropic optical feedback is numerically investigated. The results are as follows. First, when the external cavity round-trip time equals the propagation time of light from the transmitter to the receiver, both the x-linear polarization (LP) mode and the y-LP mode can realize very high complete synchronization. Second, when external cavity round-trip time is not equal to the propagation time and μ is near the lasing threshold, the better completely synchronized quality of the dominant y-LP mode can be temporarily achieved. In comparison, the governing x-LP mode can only realized poor synchronization quality. In addition, with the system governed by the mixed LP modes, each LP mode can obtain inferior synchronization quality. However, with injection current much greater than the threshold current, the completely governed y-LP mode can steadily achieve the best chaotic synchronization quality. At last, each LP mode of the injection can achieve good injection-locking synchronization with that of the receiver. While each dominant LP mode can obtaine poorer injection-locking synchronization quality than the corresponding suppressed LP mode, with equal power, two LP modes both can achieve almost identical high injection-locking synchronization quality. Namely, the LP state with less power can be obtain better injection-locking synchronization.

Spin-flip model (SFM) is a mostly used approach to analyzing the nonlinear dynamics of vertical-cavity surface-emitting laser (VCSEL), and therefore the value selections of some key parameters in this model are crucial. In this work, based on experimentally measured dynamical characteristics of a 1550 nm vertical-cavity surface-emitting laser (1550 nm-VCSEL) under free running and parallel optical injection, some key parameters (field decay rate k, total carrier decay rate N, linewidth enhancement factor , active medium birefringence rate p, spin relaxation rate s, and active medium linear dispersion rate a) are estimated. Through experimentally measuring the noise spectrum of the laser, the relaxation oscillation frequency and the damping rate of the relaxation oscillations are calculated, and the photon lifetime can be preliminary estimated. After further amending the photon lifetime by considering the effect of the gain saturation on the damping rate of the relaxation oscillations, the value of k is determined. Based on the function relation between the laser relaxation oscillation frequency and the electrical pumping, the value of N is obtained. By experimentally acquiring the dynamical distribution mapping of the laser under parallel optical injection, the minimum Hopf bifurcation point of the Hopf bifurcation curve can be found, and then the value of is roughly estimated. According to the frequency difference between the two polarization components of the laser in the measured optical spectrum, the value of p can be calculated. The value of s is obtained by using the relationship between s and p. On the basis of the above determined parameter values, the value of a can be specified by numerically simulating the optical spectrum of the laser and comparing with experimentally obtained results. Moreover, by comparing the experimentally measured dynamical mapping of optical injection VCSEL with corresponding dynamical mapping simulated on the basis of the above mentioned parameters, the value of is rectified. Finally, further simulated results agree with relevant experimental observations.

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