Time-dependent theory for random lasers in the presence of an inhomogeneous broadened gain medium such as PbSe quantum dots.

Time-dependent model is presented to simulate random lasers in the presence of an inhomogeneous gain medium. PbSe quantum dots (QDs) with an arbitrary size distribution are treated as an inhomogeneous gain medium. By introducing inhomogeneity of the PbSe QDs in polarization, rate, and Maxwell's equations, our model is constructed for a one-dimensional disordered system. By employing the finite difference time-domain method, the governing equations are numerically solved and lasing spectra and spatial distribution of the electric field are calculated. The effect of increasing the pumping rate on the laser characteristics is investigated. The results show that the number of lasing modes and their intensities increase with pumping rate. It is also demonstrated that the emission spectra depend on the standard deviation of the Gaussian distribution function. Increasing the standard deviation leads to reduction of the laser intensity.