Dynamic Simulation of the Thermal Lensing in a Titanium:Sapphire Laser Crystal*

Thermal lensing is a phenomenon caused by the temperature gradients present in optically pumped laser crystals. The crystal acts as a lens that affects the propagation of the laser mode in the resonator. Therefore, to design a stable resonator, the thermal lens' focal length must be calculated or experimentally measured. We present a dynamic simulation created with Wolfram Mathematica, that allows a user to calculate the temperature gradient in a Titanium:Sapphire laser crystal, which is the first step in determining the thermal lens' and focal length. Several parameters can be varied – the dimensions of the laser rod, the pumping intensity, the pumping geometry, and the temperature of active cooling. The results are visualized with contour plots and plots of the temperature in longitudinal and transverse cross-sections. Next, we will add the calculation of the thermal lens' focal length. The simulation will be submitted to the Wolfram Demonstration Project and available for use from their website https://demonstrations.wolfram.com/.