Analytic spatial and temporal temperature profile in a finite laser rod with input laser pulses

In this communication, we present an analytic expression of the thermal load in a cylindrical laser rod. We consider a pump beam with Gaussian temporal and spatial profile, which permits, using superposition of the single pulse solution, an explicit calculation of the optical path length difference across the radial direction of the rod and of the transient thermal focal length changes for a variable pump repetition rate and pulse width. We have chosen to model Ti:A_l2O_3 as a specific example, however our solution is completely general and can be applied to any materials with cylindrical geometry employing a stable laser cavity design.