Noise-induced pulse-timing statistics in an integrated two-section semiconductor laser with saturable absorber

We have analyzed and explained the generation of irregularly timed, spontaneous-emission triggered optical pulses from a two-section semiconductor laser with saturable absorber, operating near threshold in a regime of excitability. Here we focus on the statistics of the spontaneously emitted pulses. The numerical simulations and analytical theory are based on the Yamada model. The observed irregular pulse train intervals exhibit an initial refractory time, followed by a time interval until the next emitted pulse. The latter is analyzed in terms of a first-passage-time distribution for the intensity to diffuse from its equilibrium value to hit a larger threshold intensity for the first time. Analytic asymptotic short-time and long-time approximations have been derived