Ho:Tm lasers. I. Theoretical

Energy transfer dynamics pertinent to Ho:Tm lasers are modeled in two steps: a calculation of the parameters controlling the energy transfer process and a calculation of the population densities of all manifolds influencing the laser process. Energy transfer parameters are modeled with the classical dipole-dipole approximation, but several important changes are implemented to better describe laser materials such as Ho:Tm laser materials. This approach was used to calculate energy transfer parameters using measured energy levels coupled with quantum mechanical calculations although spectroscopically measured parameters could be used in principle. Given the energy transfer parameters, a rate equation approach is used with the eight manifolds required for an accurate description of the Ho:Tm laser. Population densities of all eight manifolds can be predicted as a function of time whether or not lasing occurs. Results of the modeling process are compared with experimental results for both Ho:Tm:YAG and Ho:Tm:YLF with different concentration and a variety of different mirror reflectivities and different pump pulse lengths in a companion paper.