Light diffusion and localization in three-dimensional nonlinear disordered media

By using a three-dimensional finite-difference time-domain parallel code, the linear and nonlinear propagation of light pulses in a disordered assembly of scatterers, generated by a molecular dynamics code, is simulated. We calculate the static and dynamical light diffusion constant and the transmission in the presence of localized states. We numerically demonstrate the ``modulational instability random laser'': at high input peak power, energy is transferred to localized states from the input pulse, resulting in a power-dependent nonexponential time decay of the transmitted pulse.