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.