Bernhardi, Edward H.

### Abstract:

This thesis consists of three main parts. An introduction to diode-pumped solid-state lasers, thermal modelling of solid-state lasers and rate-equation modelling of solid-state lasers. The first part explains the basic components and operation principles of a typical diode-end-pumped solid-state laser. The stimulated emission process, solid-state laser gain media, various pump geometries and a basic end-pumped laser resonator configuration are among the topics that are explained. Since thermal effects are one of the main limiting factors in the power-scaling of diode-pumped solid-state lasers, the second part of this thesis describes numerical and analytical thermal models that determine the thermal lens and thermally induced stresses in a laser crystal. As a first step, a time-independent numerical thermal model which calculates the three-dimensional temperature distribution in the laser crystal is implemented. In order to calculate the time dependent thermally induced stresses in a laser crystal, a coupled thermal-stress finite element analysis model was implemented. Even though some steady-state analytical solutions for simple crystal geometries do exist, the finite element analysis approach was taken so that the time dependent thermally induced stresses could be calculated for birefringent crystals of various geometries. In order to validate the numerical results, they are compared to experimental data and analytical solutions where possible. In the last part, the population dynamics inside the laser gain medium are described and modelled with a quasi-three-level rate-equation model. A comprehensive spatially resolved rate-equation model is developed and discussed. In order to simplify the implementation of the rate-equation model as a computer simulation, the spatial dependence of the laser parameters is ignored so that the model reduces to a singleelement plane-wave model. The simplified rate-equation model is implemented and solved numerically. The model is applied to a four-level CW and Q-switched Nd:YLF laser as well as a quasi-three-level QCW Tm:GdV04 laser. The models' predictions are thoroughly verified with experimental results and also with analytical solutions where possible.