Fig. 1. Numerical calculation of the normalized pump intensity within a Yb:YAG crystal in comparison to the Lambert–Beer and saturated absorption models.

Fig. 2. A slice through the pumped Yb:YAG model in COMSOL.

Fig. 3. Pump profile (a) and thermal image (b) of the end-pumped and water-cooled $\text{Yb:CaF}_{2}$.

Fig. 4. Comparison of measured (solid) and simulated (dashed) thermal profiles. The measured temperature profiles for (a) Yb:YAG and (b) $\text{Yb:CaF}_{2}$ on both the front and back surfaces were compared to the simulated temperature profiles averaged over the pump cycle. (c) The front and back Yb:FP15 profiles are displayed for times 0 (directly before the 1.4 ms pump pulse), 0.1, 1, 2.5, and 5 s within the pump cycle (repetition rate 0.2 Hz).

Fig. 5. Schematic of the 3D pumping configuration of the Yb:FP15-based (perimeter in blue) A4 multi-pass amplifier at POLARIS with thermal images of an example of a single pump spot (top left) and the full pump profile (top right).

Fig. 6. Comparison of measured (solid) and simulated (dashed) thermal profiles of the pumped and thermalized Yb:FP15 within the A4 amplifier. A slice through the pumped Yb:FP15 model in COMSOL is shown in (a). The front and back Yb:FP15 profiles are displayed in (b) for times 0 (directly before the 2.7 ms pump pulse), 0.1, 5, 10, 25, and 50 s within the pump cycle (repetition rate 0.02 Hz). The temperature on the front and back centers of the Yb:FP15 material is plotted in (c) throughout the pump cycle.

Fig. 7. Comparison of the measured (solid) and simulated (dashed) front, back, and middle thermal profiles of the pumped Yb:FP15 within the A4 amplifier.

Table 1. Relevant optical and thermal properties of the considered active materials.