Crank-Nicholson method for rate equations in powder random lasers

Abstract

In this work, we show the resolution of the rate equations in powder random lasers by using the Crank-Nicholson finite difference method. Light propagation in our powders is described by the model of light diffusion. The generalized time-dependent random laser equations describing our system are formed by three differential coupled equations: two diffusion equations for the pump and emitted light and a rate equation for the density of the dopant molecules in the excited state. The system has been solved for two pumping schemes (one-photon and two-photon excitation) and for a wide range of temporal incident pulses (from femtoseconds to nanoseconds).