First-Passage-Time Analysis of the Pulse-Timing Statistics in a Two-Section Semiconductor Laser under Excitable and Noisy Conditions

A two-section semiconductor laser can exhibit excitability for certain parameter settings. When used as a photonic spiking neuron, it is relevant to investigate its sensitivity to noise due to, e.g., spontaneous emission. Under excitable conditions, the system emits irregularly timed noise-triggered pulses. Their statistics is analyzed in terms of a first-passage time distribution for the fluctuating intensity to reach the threshold for excitable response. Two analytic approximations valid for short and long times, respectively, are derived which very well explain measured and simulated pulse-repetition time distributions. This provides physical insight into the noise-triggered spiking mechanism.