Analysis of multi-pass pumped thin-disk laser performance with measured disk deformation

Predicting the steady-state performance of high-power thin-disk lasers requires not only pump-signal energy transfer but also how disk deformation contributes intra-cavity mode formation. In this work, we address the output-power reduction that occurs even when the laser remains in a single-mode regime with $\mathrm{M^2}$ around 1.1. We developed a numerical model in which the pump-induced inversion is initialized from a non-lasing multi-pass absorption model and then coupled to two-dimensional cavity-field propagation using measured disk optical path difference (OPD) maps. Applied to the Yb:YAG thin-disk laser, the model reproduces the residual pump fraction and predicts the signal power, beam diameter, and $\mathrm{M^2}$ with errors of 3.0$\%$, 1.7$\%$, and 0.05, respectively. To interpret the measured OPD, the disk surface is further analyzed by Zernike decomposition, and the defocus term is converted into an equivalent radius of curvature (eROC). The eROC-based simulation provides the defocus-only reference performance that is theoretically reachable in the absence of higher-order aberrations, whereas the measured-OPD simulation reproduces the experimentally observed power reduction at high pump intensity. The comparison quantitatively shows that higher-order aberrations beyond defocus reduce the overlap with the fundamental cavity mode and limit power scaling, even before strong $\mathrm{M^2}$ degradation appears. This result identifies aberration-induced modal loss as a key limitation in high-power single-mode thin-disk lasers.