Success rate analysis of the response of an excitable laser to periodic perturbations

Abstract: We use statistical tools to characterize the response of an excitable system to periodic perturbations. The system is an optically injected semiconductor laser under pulsed perturbations of the phase of the injected field. We characterize the laser response by counting the number of pulses emitted by the laser, within a time interval, $\Delta$T , that starts when a perturbation is applied. The success rate, SR($\Delta$T), is then defined as the number of pulses emitted in the interval $\Delta$T , relative to the number of perturbations. The analysis of the variation of SR with $\Delta$T allows to separate a constant lag of technical origin and a frequency-dependent lag of physical and dynamical origin. Once the lag is accounted for, the success rate clearly captures locked and unlocked regimes and the transitions between them. We anticipate that the success rate will be a practical tool for analyzing the output of periodically forced systems, particularly when very regular oscillations need to be generated via small periodic perturbations.