Dimensional signature on noise-induced excitable statistics in an optically injected semiconductor laser

Noise-induced excitability is a prevalent feature in many nonlinear dynamical systems. The optically injected semiconductor laser is one of the simplest such systems and is readily amenable to both experimental and theoretical analysis. We show that the dimensionality of this system may be tuned experimentally and that this has a strong signature on the interspike statistics. The phase of the slave laser is resolved experimentally in the frame of the master laser, allowing an examination of the dynamics at extremely low injection strengths where intensity measurements alone cannot determine the dynamics fully. Generic phase equations are found for the different dimensional scenarios. When the dimensionality is greater than 1, we show that a precursor of a homoclinic bifurcation generates a noise-induced frequency and that the homoclinic bifurcation admits a bistability in the system.