Haus/Gross-Pitaevskii equation for random lasers

TL;DR

This paper experimentally tests the Haus/Gross-Pitaevskii equation's predictions on how the linewidth of a random laser varies with pumping power, using dispersions of Titanium dioxide particles in dye-doped methanol.

Contribution

It demonstrates the applicability of the Haus master equation, equivalent to the Gross-Pitaevskii equation, to describe random laser linewidth behavior.

Findings

Experimental results agree with the theoretical predictions of the master equation.

The threshold linewidth value is analytically predicted and confirmed experimentally.

The derivation of the master equations aligns with observed laser behavior.

Abstract

We report on experimental tests of the trend of random laserlinewidth versus pumping power as predicted by an Haus master equation that is formally identical to the one-dimensional Gross- Pitaevskii equation in an harmonic potential. Experiments are done by employing picosecond pumped dispersions of Titaniumdioxide particles in dye-doped methanol. The derivation of the master equations is also detailed and shown to be in agreement with experiments analytically predicting the value of the threshold linewidth.