Light transport and localization in diffusive random lasers

We develop an analytical theory for diffusive random lasers by coupling the transport theory of the disordered medium to the semi-classical laser rate equations, accounting for ( coherent) stimulated and ( incoherent) spontaneous emission. From the causality of wave propagation in an amplifying, diffusive medium we derive a novel length scale which we identify with the average mode radius of the lasing quasi-modes. We show further that loss at the surface of the laser-active medium is crucial for stabilizing a stationary lasing state. The solution for the transport theory of random lasers for a layer geometry with appropriate surface boundary conditions yields the spatial profile of the light intensity and of the population inversion. The dependence of the intensity correlation length on the pump rate is in qualitative agreement with experimental and numerical findings.