Analytical approach to thermal lensing in end-pumped Yb:YAG thin-disk laser

Thermal lensing in the thin-disk laser influences the output beam quality and optical efficiency significantly. In this paper, an analytical approach is taken to study the production mechanisms, features, and influences of thermal lensing in the end-pumped thin-disk laser. We calculate the distributions of temperature, stress, strain, and expansion in the disk and the curvature of the crystal using an analytic method. The expressions of the thermal lens focal length depending on the radius are presented. The optical path difference, a major cause of thermal lensing, is induced by the thermo-optical effect, the photoelastic effect, and inhomogeneous distribution of thermal expansion and the excited population. Thermal lensing is found to be aspheric with undesired aberrations and birefringence effects. Furthermore, a convex mirror due to the axial temperature gradient occurs in a free disk, and the convex mirror is found to be spherical in the center region of the disk. Based on the results of our analysis, the aspect ratio and size of the laser mode of the gain region may be adjusted to limit the damaging effects of thermal lensing.