Improved coupled-mode theory for the dynamics of semiconductor laser arrays

Exploring new chaotic synchronization properties in the master-slave configuration based on three laterally coupled semiconductor lasers with self-feedback

We have developed a theory model for a three-element laser array where three lasers are laterally coupled using the coupled mode theory and Maxwell equations. New chaotic synchronization properties have been observed systematically in the master-slave configuration, consisting of the driving three-element laser array with self-feedback and the response three-element laser array subjected to the parallel injection or cross injection. Under the parallel injection, the dynamic evolutions of high-quality complete chaotic synchronization between laser elements in different parameter spaces seriously depend on the self-feedback mode of the driving laser elements, such as one, two and all of them with self-feedback. It is found that when only the driving middle one or all of the driving laser elements are subject to self-feedback, high-quality complete chaotic synchronization of all laser elements can be achieved in the same large region of the most of the parameter spaces. In addition, we report here for the first time (to our knowledge) the interestingly symmetrical properties of leader/ laggard chaotic synchronization in the configuration under the cross-injection. Namely, the leader/ laggard chaotic synchronization with high quality between laser elements periodically varies with the delay differences, under the key parameters limited to a certain range. The varying traces of these synchronizations are like sine wave. The mirror symmetry between the laggard chaotic synchronization with in-phase (anti-phase) and the leader one with in-phase (anti-phase) can be achieved by the optimization of the structural parameters of laser waveguides. With the optimization of the related operating parameters, for one of the side-lasers, its leader/ laggard chaotic synchronization can be achieved the anti-symmetry between in-phase and anti-phase. On the other hand, for two symmetrical side-lasers, their leader/ laggard chaotic synchronization with in-phase and anti-phase can reach the anti-symmetry.

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.

Validity of the coupled-oscillator model for laser-array dynamics

We show that the coupled-oscillator model accurately describes the dynamics of laser arrays. Excellent qualitative and quantitative agreement is obtained between this model and the results of experiments on Nd:YAG laser arrays. Recent claims of instantaneous phase locking are shown to be in error.