Iterative 3D modeling of thermal effects in end-pumped continuous-wave HO$^{3+}$:YAG lasers

We present a highly accurate model for end-pumped continuous-wave Ho$^{3+}$:YAG laser resonators, based on a vectorial beam propagation method (BPM) algorithm. Thermal effects in the laser crystal like thermal lensing and stress birefringence are taken into consideration. The implementation of these effects is based on an iterative method, which updates the temperature and displacement in the crystal at specific roundtrip intervals. An experimental Ho$^{3+}$:YAG resonator cavity in continuous wave operation is used to validate the model. At higher pump powers, the resonator reaches its stability limit and shows beam distortions, which is well replicated with the presented model.