An investigation of a mathematical model of an optically pumped Ti(3+):Al2O3 laser system
Abstract
During the last several years, solid state lasers were developed that have the potential for meeting rigorous performance requirements for spacebased remote sensing of the atmosphere. In order to design a stable and efficient laser and to understand the effect on laser output of changes in the physical and design parameters, an understanding of the development of the dynamical processes of the laser is necessary. Typically, the dynamical processes in a laser system are investigated via rate equations describing the evolution of the occupancy in the electronic levels and of the photon density in the laser cavity. There are two approaches to this type of study. Most often, for the sake of simplicity, the spatial variations of the dynamic variables in the laser system are disregarded and the mathematical model consists of a system of first order nonlinear ordinary differential equations (ODE). The second approach is to take into account both spatial and temporal variations in the dynamic variables in the laser cavity. The resulting model consists of a first order semilinear system of partial differential equations (PDE). The model which was studied was studied was generic in the sense that it was a fourlevel laser system, but the parameters used in the numerical study were specific to Titaniumdoped sapphire. For simplicity, a constant, spatially uniform pumping scheme was considered. In addition, a simplification of the model was made so that it treats a single lasing wavelength with a narrow bandwidth. The purpose was to investigate both versions of the mathematical model and to determine whether the numerical solutions are similar both qualitatively and quantitatively. The systems of ordinary differential equations were solved numerically using a RungeKuttaFehlberg algorithm which was very efficient for typical values of the physical parameters. A numerical scheme, based on the Modified Euler method, for computing solutions to the system of partial differential equations was developed and implemented. The PDE model was solved numerically at the expense of greatly increased computer time.
 Publication:

1989 NASAASEE Summer Faculty Fellowship Program in Aeronautics and Research
 Pub Date:
 September 1989
 Bibcode:
 1989asee.nasa..133R
 Keywords:

 Aluminum Oxides;
 Design Analysis;
 Laser Cavities;
 Laser Outputs;
 Mathematical Models;
 Partial Differential Equations;
 Solid State Lasers;
 Stability;
 Titanium Oxides;
 Algorithms;
 Electron Energy;
 Energy Levels;
 Lasing;
 Nonlinear Equations;
 Photon Density;
 Remote Sensing;
 Simplification;
 Spatial Distribution;
 Temporal Distribution;
 Lasers and Masers