Transient analysis of thermal effects in non-symmetrically pumped laser slabs

Abstract

The analytic solution to the problem of time-dependent non-homogeneous heat equation is derived for a temporally pulsed and spatially non-homogeneous source term. For pulsed pumping with an inverse repetition rate much less than system thermal relaxation time, the problem of heat flow in a laser medium is typically studied within the approximation of time-independent heat equation. When the condition fails, due for instance to a short relaxation time or to a low repetition rate, transient analysis of thermal effects becomes necessary. Moreover the time-independent formalism fails in predicting both the focusing properties of the active material and any beam bending inside the resonator, while the transient analysis of thermal effects allows to finely predict the temperature distribution and to still apply, locally, the matrix formalism. In the paper we apply the formalism to a double side pumped Er:Yb glass slab laser with a non symmetric cooling scheme at several repetition rates. By evaluating the temporal evolution of the local temperature in the slab cross section, the difference with the stationary spatial temperature distribution turns out to be not negligible at repetition rates below 10 Hz. We observe that the lack of symmetry in the temperature profile reduces thermal focusing effects, but leads to a dynamic drift of mode laser axis which can make unstable the resonator cavity. We validated the model by comparing the theoretical values of slab focal length and of modal axis drift with experimental measurements at several repetition rates, proving also that the thermal focusing becomes a secondary effect in comparison with modal axis drift at increasing repetition rates.