Statistics of chaos in a bursting laser

We demonstrate experimentally how semiconductor lasers subjected to double optical feedback change the statistics of their chaotic spiking dynamics from Gaussian to long-tail power-law distributions associated to the emergency of bursting. These chaotic regimes, which are features of excitable complex systems, are quantified by the tail exponent a and appear by changing the ratio between the feedback times. Transitions to bursting occur in the neighborhood of low-order Farey fractions. The physics behind these transitions is related to the variation of threshold pump current in the compound system as obtained from a deterministic set of rate equations. Numerical integration also verifies the observed chaos transitions indicating the possibility of controlling the bursting chaotic statistics.