Stability maps of injection-locked laser diodes using the largest Lyapunov exponent

In this paper, we discuss the dynamics of a semiconductor laser subject to optical injection using the method of the Largest Lyapunov Exponent (LLE). The system's stability is investigated as a function of the frequency detuning omega, the injection strength K and the linewidth enhancement factor a. Chaotic regimes and locking stability areas are found by integrating the rate equations,and calculating the LLE for each solution in the (K-omega) plane. Periodic solutions are tracked inside the chaotic islands and very good agreement is demonstrated with experimental data in the literature. The LLE's strength lies in the ability to map the amount of chaos and the amount of stability inside the stable locking regions. We also demonstrate that as we increase the linewidth enhancement factor, the system becomes more chaotic on average and the LLE is greater for each map. (C) 2003 Elsevier Science B.V. All rights reserved.