We report a strange bifurcation in a mutually delay-coupled semiconductor diode laser system. This system undergoes a series of transitions among different amplitude death islands as the coupled-cavity delay time and the optical coupling strength are varied. The dynamical behaviour of the system, within the bifurcation windows between consecutive death islands, is investigated as a function of the coupling strength η for a fixed delay time τ. The visibility and cross-correlation measures are used to unveil the signatures of global phase-locking stability. This robust phase stability of the system may open up new ways for diode laser stabilization technology. A stability analysis is presented for the understanding of the dynamics. © 2009 IOP Publishing Ltd.