Initial-state dependence of the route to chaos of an external-cavity laser

External-cavity semiconductor lasers (ECLs), consisting of a laser diode in front of a mirror to reflect light back into the laser diode, are among the most important dynamical systems because of their ultrafast dynamics, their tunability, and the numerous existing applications. The dynamics of an ECL is greatly influenced by the existence and stability of numerous modes of the external cavity. In such high-dimensional nonlinear systems, numerous attractors, located around various modes of the external cavity, can coexist in phase space for a given set of parameters, a phenomenon called generalized multistability. In this work, we propose a procedure that allows one to select experimentally different modes of the external cavity as different initial states. We use this procedure to reveal experimentally generalized multistability in an ECL through the demonstration that different routes to chaos exist in an ECL, depending on the initial state selected. In particular, we show that the famous quasiperiodic route to chaos is only observed for specific choices of initial conditions.