Statistical theory of multimode random lasers

We present a semiclassical laser theory for multimode lasing in optical resonators with overlapping modes. Nonlinear saturation and mode competition are characterized in terms of left and right eigenmodes of a non-Hermitian operator. The theory is applied to wave-chaotic cavities and weakly disordered random media. In the limit of sufficiently strong pumping, we find that the mean number of laser peaks increases with the 1/3 power of the pump strength.