Random laser in the localized regime

We present detailed calculations of laser action in two-dimensional disordered systems in the localized regime. The systems are made of circular particles imbedded in an active dielectric medium, described by a population of four-level atoms. Without pumping the active medium, the existence of localized modes is studied as a function of the filling fraction and of the radius of the scattering particles. When pumping the active medium above threshold, we find that the localized modes of the passive system act as the regular modes of a conventional cavity. They are not modified by the presence of gain. By introducing local pumping of the atomic system, the spectrum of the laser emission is found to depend on the position of the pump in agreement with recent experimental results. It is shown that local pumping allows a selective excitation of individual localized modes.