Threshold of random lasers in the incoherent transport regime

We study the threshold of random lasers in the regime of incoherent transport. We present a time-dependent three-dimensional model based on the radiative transfer equation and rate equations, allowing us to describe the various transport regimes (ballistic, multiple scattering, diffusive). Numerical simulations based on this model allow us to describe the main features of the lasing threshold. We develop a modal theory of random lasers with incoherent feedback, based on the disordered-averaged modes of the radiative transfer equation. As a first example, we show that this approach predicts the lasing threshold for systems with sizes L ranging from L similar to l(s) (single-scatttering regime) to L >> l(*) (diffusive regime).