Noise-induced peak intensity fluctuations in class B laser systems

Random perturbations and noise can excite instabilities in population systems that result in large fluctuations. Important examples involve class B lasers, where the dynamics are determined by the number of carriers and photons in a cavity with noise appearing in the electric-field dynamics. When such lasers are brought above threshold, the field intensity grows away from an unstable equilibrium, exhibiting transient relaxation oscillations with fluctuations due to noise. In this work, we focus on the first peak in the intensity during this transient phase in the presence of noise, and calculate its probability distribution using a Wentzel-Kramers-Brillouin approximation. In particular, we show how each value of the first peak is determined by a unique fluctuational momentum, calculate the peak intensity distribution in the limit where the ratio of photon-to-carrier lifetimes is small, and analyze the behavior of small fluctuations with respect to deterministic theory. Our approach is easily extended to the analysis of transient, noise-induced large fluctuations in general population systems exhibiting relaxation dynamics.