Euclidean matrix theory of random lasing in a cloud of cold atoms

TL;DR

This paper presents an analytic Euclidean matrix theory for random lasing in cold atom clouds, covering all densities and comparing with diffusion theory, to predict lasing thresholds and intensities.

Contribution

It introduces a novel Euclidean matrix approach based on Green's functions to analyze random lasing across different densities, extending beyond existing models.

Findings

Lasing threshold and intensity are calculated analytically.

The Euclidean matrix approach aligns with diffusion theory at certain regimes.

The theory applies from low to high atomic densities.

Abstract

We develop an ab initio analytic theory of random lasing in an ensemble of atoms that both scatter and amplify light. The theory applies all the way from low to high density of atoms. The properties of the random laser are controlled by an Euclidean matrix with elements equal to the Green's function of the Helmholtz equation between pairs of atoms in the system. Lasing threshold and the intensity of laser emission are calculated in the semiclassical approximation. The results are compared to the outcome of the diffusion theory of random lasing.