Universal Fluctuations of the Random Lasing Threshold in a Sample of a Finite Area

TL;DR

This paper demonstrates that the distribution of lasing thresholds in finite-area random media is universal, governed by a single parameter, and depends on sample size and disorder, with implications for understanding random lasing behavior.

Contribution

The authors analytically derive the universal distribution of lasing thresholds in finite samples, revealing its dependence on a key dimensionless parameter and the effects of sample size and disorder.

Findings

Distribution of thresholds is universal and governed by a single parameter.

Threshold distribution narrows with increasing sample size.

Distribution broadens with increasing disorder strength.

Abstract

We consider the random lasing from a weakly scattering medium and demonstrate that the distribution of the threshold gain over the ensemble of statistically independent finite-size samples is universal. Universality stems from the facts that: (i) lasing threshold in a given sample is determined by the highest-quality mode of all the random resonators present in the sample, and (ii) the areal {\em density} of the random resonators decays sharply with the quality factor of the mode that they trap. We find analytically the shape of the universal distribution function of the lasing threshold. The shape of this function is governed by a single dimensionless parameter, $\beta$. This parameter increases as a power law with $\ln S$, where $S$ is the sample area (length, volume), and decreases as a power law with disorder strength. The powers depend on the microscopic mechanism of the light trapping. As a result, the distribution of the thresholds narrows with $S$ and broadens with the disorder strength.