Noise-induced peak intensity fluctuations in class B laser systems

TL;DR

This paper investigates how noise causes large fluctuations in the initial peak intensity of class B lasers during transient relaxation oscillations, using a WKB approximation to analyze the probability distribution of these peaks.

Contribution

It introduces a novel application of WKB methods to derive the distribution of first peak intensities in noisy laser systems, extending to general population dynamics with relaxation.

Findings

Derived the probability distribution of the first peak intensity.

Showed how each peak value relates to a unique fluctuational-momentum.

Analyzed small fluctuations relative to deterministic predictions.

Abstract

Random perturbations and noise can excite instabilities in population systems that result in large fluctuations. An interesting example involves class B lasers, where the dynamics is 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 (WKB) 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.