The overall phase shift and lens effect calculation using Gaussian boundary conditions and paraxial ray approximation for an end-pumped solid-state laser

In this work, the inhomogeneous equation of heat conduction was exactly solved by applying inhomogeneous boundary conditions for laser crystals of aspect ratio=1 (aspect ratio=radius of the laser rod/length of the laser rod). We have shown that the paraxial ray approximation leads the solution to be a function of r(2), that is, the approximation is equivalent to a situation in which a homogeneous pump source is used. The solution was then used to derive expressions for the overall phase shift, focal length of the thermal lens and the end effect induced curvature of the end face. The expressions were then applied to Nd:YAG laser medium. The result shows a meaningful correction of the order of 0.001 cm to the focal length of Nd:YAG rod for 3 W source power and beam waist of 100 mu m.