Model for a Random Laser

The laser action in random media is studied numerically for a planar system of resonant scatterers pumped by an external laser. The eigenmodes of the finite system (quasistates) are “lossy” in the absence of gain because of the leakage of light outside the medium and can be characterized by their decay rates. Lasing occurs when the gain compensates the decay rate of the quasistate with the longest lifetime. The dependence of the lasing threshold on the number of scatterers (size of the system) is found to be $I\propto 1/\sqrt{N}$, which agrees with recent experiments. We demonstrate that this dependence is strongly related to the fluctuations of quasistate decay rates and discuss the nature of these fluctuations.