A Mathematical Model of the Dynamics of an Optically Pumped Codoped Solid State Laser System

This is a study of a mathematical model for the dynamics of an optically pumped codoped solid state laser system. The model comprises five first order, nonlinear, coupled, ordinary differential equations which describe the temporal evolution of the dopant electron populations in the laser crystal as well as the photon density in the laser cavity. The analysis of the model is conducted in three parts. First, a detailed explanation of the modeling process is given and the full set of rate equations is obtained. The model is then simplified and certain qualitative properties of the solution are obtained. In the second part the equilibrium solutions are obtained and a local stability analysis is performed. The system of rate equations is solved numerically and the effects, on the solution, of varying physical parameters is discussed. Finally, the third part addresses the oscillatory behavior of the system by tracking the eigenvalues of the linearized system. A comparison is made between the frequency of oscillations in the linear and nonlinear system. Pertinent physical processes--back transfer, Q-switching, and up-conversion--are then examined. The laser system consists of thulium and holmium ions in a YAG crystal operated in a Fabrey-Perot cavity. All computer programs were written in FORTRAN and currently run on either an IBM-PC or a DEC VAX 11/750