Pulse propagation in a 1D array of excitable semiconductor lasers

International audience; Nonlinear pulse propagation is a major feature in continuously extended excitable systems. The persistence of this phenomenon in coupled excitable systems is expected. Here, we investigate theoretically the propagation of nonlinear pulses in a 1D array of evanescently coupled excitable semiconductor lasers. We show that the propagation of pulses is characterized by a hopping dynamics. The average pulse speed and bifurcation diagram are characterized as a function of the coupling strength between the lasers. Several instabilities are analyzed such as the onset and disappearance of pulse propagation, and a spontaneous breaking of the translation symmetry. The pulse propagation modes evidenced are specific to the discrete nature of the 1D array of excitable lasers. Linear oscillators coupled with springs to nearest neighbors exhibit wave propagation. This phenomenon is persistent when considering the continuous limit, i.e. when considering an elastic rope. In this limit, the wave dispersion relation is linear, unlike the discrete case of coupled systems where it is nonlinear. Here we study the propagation of localized nonlinear wave pulses in coupled excitable systems. Excitable oscillators play a fundamental role in understanding the activity of neurons, cardiac tissue, and oscillatory chemical reactions. Based on a model of a 1D array of excitable semiconductor lasers, we show that pulse propagation is characterized by a hopping dynamics and that it displays a rich variety of bifurcations. Counter-intuitively, we observe that pulses do not persist in the continuous limit.