Haus/Gross-Pitaevskii equation for random lasers

We report on experimental tests of the trend of random laser linewidth versus pumping power as predicted by a Haus master equation that is formally identical to the one-dimensional Gross-Pitaevskii equation in a harmonic potential. Experiments are done by employing picosecond pumped dispersions of titanium dioxide particles in dye-doped methanol. The derivation of the master equation is also detailed and shown to be in agreement with experiments analytically predicting the value of the threshold linewidth. (C) 2010 Optical Society of America