Modeling of thermal lensing in cw end-pumped solid state lasers

Thermal focusing acts as a key role in limiting and degrading the laser performance in a continuously end-pumped solid-state laser. In order to evaluate the deleterious effect caused by thermal lensing in such a laser scheme, heat transfer equation is solved to obtain the temperature distribution in an edge-cooled and axially Gaussian beam heated rod in the form of a power series, taking into account only the radial heat flow, which is a reasonable simplification of the real situation. Also, under the two assumptions of thin disk and long rod, the induced stress- and strain-field are deduced, respectively. Thus the analytical expressions for the induced thermal focusing length are determined over the extent of axially average pump spot size, considering all the following three elements contributing to thermal focusing: thermal dispersion, surface deformation and stress-induced birefringence, and regarding the rod as thin lens and thick lens, respectively. The results are applied to cubic crystals, such as Nd:YAG and Nd:GSGG, and the homogeneous medium of silicate Nd:glass. It can be seen that with ten watt of pump power, the effective focusing lengths of these materials are in the order of millimeters and much more serious than those predicted by other authors.