Longitudinal temperature distribution in an end-pumped solid-state amplifier medium: application to a high average power diode pumped Yb:YAG thin disk amplifier

We propose a simple analytical derivation making it possible to compute a one-dimensional temperature variation in an end-pumped solid-state laser. This derivation takes into account the pump intensity variation along the crystal, the doping concentration, and temperature dependence of the thermal conductivity. We then compare this simulation with the one usually used, which does not take into account any of these dependences. The results show that, at room temperature, the two methods are in good agreement, but at a cryogenic temperature where the thermal conductivity varies fast with temperature, a large discrepancy is found, and the conventional computations underestimate both the average temperature and the longitudinal gradient.