Mode statistics in random lasers

TL;DR

This paper models random laser ensembles using random matrix theory to analyze the average number of lasing modes, their fluctuations, and the effects of coupling regimes and mode competition on mode statistics.

Contribution

It provides a novel analysis of mode statistics in random lasers, challenging previous claims and highlighting the impact of mode competition on mode distribution.

Findings

No power-law dependence of average mode number on pump strength in strong coupling regime

Power-law behavior observed in relative fluctuations of mode number

Mode competition causes the distribution of excited modes to deviate from binomial

Abstract

Representing an ensemble of random lasers with an ensemble of random matrices, we compute average number of lasing modes and its fluctuations. The regimes of weak and strong coupling of the passive resonator to environment are considered. In the latter case, contrary to an earlier claim in the literature, we do not find a power-law dependence of the average mode number on the pump strength. For the relative fluctuations, however, a power law can be established. It is shown that, due to the mode competition, the distribution of the number of excited modes over an ensemble of lasers is not binomial.