Modelling of passively Q-switched lasers with intracavity Raman conversion

We present a model of passively Q-switched Raman lasers by utilizing the rate equations. The intracavity fundamental photon density, Raman photon density and the initial population-inversion density of the gain medium are assumed to be of Gaussian spatial distributions. These rate equations are normalized by introducing some synthetic parameters and solved numerically, and a group of general curves are generated. From these curves we can understand the dependence of the Raman laser pulse characteristics on the parameters about the pumping, the gain medium, the Raman medium and the resonator. An illustrative calculation for a passively Q-switched Nd$^{3 + }$:GdVO$_{4}$ self-Raman laser is presented to demonstrate the usage of the curves and related formulas.