Focal length of the thermal lens for unequal diameters of the heating and probing beams

We present a way to assign a focal length to a thermal lens that explicitly separates the material heating from the resulting lensing effect, enabling accurate modeling in the common scenarios of unequal heating (pump) and probing (signal) beam diameters, and a single astigmatic beam. The utility of this expression is demonstrated by applying it in two exemplary situations, representing these scenarios. In both cases, we find improved agreement of predicted beam parameters with experimental data when our formula is applied instead of the commonly used expression. We can accurately predict the output beam parameter of a solid-state laser resonator containing a thermal lens, while the conventional expression produces worse predictions than neglecting the thermal effect entirely in several configurations of our system. We describe our model and its limits in detail, offering a practical tool for the design of high-power lasers.