Fig. 1 Energy diagram of Yb:YAG. λ_f, λ_P, and λ_L represent the mean fluorescence wavelength, the wavelength of pump and laser photon, respectively.

Fig. 2 (a) Measurement (circles) and fitting (solid curve) of the laser cooling efficiency η_c of the Yb:YAG disk at room temperature. The blue-shaded area represents the cooling regime. (b) Absorption ${\alpha }_0\left(\lambda \right)$ (dotted curve) and $\alpha \left(\lambda \right)=-\gamma (\lambda , I_P=20 kW/c{m}^2,I_L=0)$ (solid curve) spectra of 5% Yb:YAG. The small signal gain spectrum is calculated with 20 kW/cm² incident pump intensity at 1030 nm. The yellow-shaded area represents the regime with optical gain.

Fig. 3 Schematic of the intracavity-pumped radiation balanced disk laser setup. On the right, the mounting of the Yb:YAG disk is shown where it is glued onto two bare fibers, which are in turn supported by a glass slide to reduce the heat load.

Fig. 4 Side-scattered fluorescence spectrum from the Yb:YAG disk laser. The zero-crossing wavelength at 1021 nm along with the scattered VECSEL pump at 1030 nm and the laser line at 1050 nm are also shown. Inset is the measured beam profile at the RBL condition.

Fig. 5 (a) and (b) are the thermal images of the mounted gain disk at room temperature and radiation balancing condition after 30 minutes, with darker shades representing lower temperatures. The red lines in (a) represent the outline of the disk. (c) The line-integrated time-evolution of the temperature change along the vertical white dash line in (a) after the VECSEL cavity is unblocked at t = 1 minute. The black dashed lines represent the pump beam position. The estimated Gaussian profiles of the pump (green) and laser (red) beams are depicted on the right.

Fig. 6 The five data points represent the measured intracavity Yb:YAG disk laser powers at λ_L = 1050 nm versus the intracavity VECSEL pump power at λ_P = 1030 nm. Open-squares are in the self-cooling regime (H<0), solid-square is in the heating regime (H>0) and the solid-circle is the RBL point (H∼0). The theoretical curves given by Eqs. (6) and (7) show an excellent agreement with the data; indicating the RBL point at the crossing of the two curves. For comparison, the RBL condition for plane-waves (or top-hat beams) as given by Eq. (5), is also shown.