Thermal modeling of continuous-wave end-pumped solid-state lasers

In order to estimate deleterious effects caused by heating in continuous-wave end-pumped solid-state lasers, the heat equation has been solved for an axially heated cylinder with a thermally conductive boundary at the periphery. Steady-state thermal profiles are developed using both a full numerical solution and an analytic approximation which assumes only radial heat flow. The analytic solution, which is in good agreement with the numerical solution, is utilized to obtain an expression for the thermal focusing due to temperature-induced refractive index changes. For Nd:YAG, 1 W of pump power deposited as heat is predicted to cause a thermal focusing length comparable to the cavity length of a typical diode end-pumped laser.