First-principles statistics of lasing modes in random lasers
In plain words
A random laser has no mirrors: light bounces among random scatterers in a material with gain until it lases. A theory that predicts how many modes lase, what they look like and how their output fluctuates from shot to shot is still missing.
Precise statement
Multimode random laser with saturable gain in a disordered medium of scattering mean free path l, size $L >> l$, from the diffusive regime ($kl >> 1$, $k$ the wavenumber) toward localization. Quantities: number of lasing modes versus pump, their spatial profiles and the shot-to-shot emission statistics (including Levy-type heavy tails). SALT (steady-state ab initio laser theory) solves single disorder realizations; an answer is an ensemble theory that predicts these statistics with no fitted parameters and is checked against an experiment with characterized disorder.
What would settle it
Comparison of measured mode number, spectra and intensity statistics in a sample of known l and gain with ensemble-averaged first-principles laser simulations.