The dynamics of two mutually coupled but non-identical semiconductor lasers are studied experimentally, numerically and analytically for weak coupling. The lasers have dissimilar relaxation oscillation frequencies and intensities, and their mutual coupling strength is asymmetric. We find that the lasers may entrain to the relaxation oscillation frequency of either one of the lasers. The form of entrainment is a special form of synchronization, called localized synchronization, where one laser exhibits strong oscillations and the other one weak oscillations. We perform a bifurcation analysis to explain the mechanism of entrainment by taking advantage of the inherently large parameters in a semiconductor laser, the linewidth enhancement factor (alpha) and the ratio of the carrier and photon lifetime T.
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