Time dependent theory for random lasers

A model to simulate the phenomenon of random lasing is presented. It couple s Maxwell's equations with the rate equations of electronic population in a disordered system. Finite difference time domain methods are used to obtai n the field pattern and the spectra of localized lasing modes inside the sy stem. A critical pumping rate P-r(c) exists for the appearance of the lasin g peaks. The number of lasing modes increases with the pumping rate and the length of the system. There is a lasing mode repulsion. This property lead s to a saturation of the number of modes for a given size system and a rela tion between the localization length xi and average mode length L-m.