Route to Chaos in a Ring of Three Unidirectionally-Coupled Semiconductor Lasers

Complex dynamics of a ring of three unidirectionally-coupled semiconductor lasers are studied with respect to the coupling strength. While uncoupled, the lasers stay in a continuous-wave regime; they begin to oscillate as the coupling strength reaches a certain threshold value. When the coupling further increases, the dynamics exhibit a route to chaos via a sequence of Hopf bifurcations resulting in periodic, quasiperiodic, and chaotic oscillations. In the chaotic range, different synchronization states, ranging from asynchronous behavior to phase and near synchronization, are observed. The analytical solution yields a large number of fixed points.