# Recent Development of High-Energy Short-Pulse Lasers with Cryogenically Cooled Yb:YAG
## 2 Changes in Crystal Properties with Temperature
### Spectral Properties  
In addition to thermodynamic properties, spectral properties also change with temperature decrease. The researchers studied the absorption bandwidth, absorption cross-section, emission cross-section, fluorescence lifetime, and other properties of Yb:YAG crystals. Figures 2 and 3 show the comparison of the absorption cross-section of Yb:YAG crystals (0.24 mm thick and 9.8% doping concentration) at 300 K and 75 K, respectively [12]. The X-axis is the wavelength, and the Y-axis is the emission cross-section. It can be seen from the figure that, as the temperature decreases, the absorption bandwidth at 940 nm narrows slightly, from about 18 nm at 300 K to about 13 nm at 75 K, but it is still much higher than the absorption bandwidth of Nd:YAG at 808 nm of about 2 nm. The wide absorption bandwidth means fewer requirements for temperature control and wavelength stability of the pump source, which contributes to reducing costs. Additionally, then the absorption cross-section is greatly increased, about twice that at 300 K at 75 K, which is beneficial to improving the pump absorption efficiency, reducing heat generation, and mitigating the degradation of beam quality due to thermal effects. The emission cross-section of the Yb:YAG crystal also increases significantly with the decrease in temperature [10]. The measured emission cross-section of Yb:YAG crystal (2% doping concentration) at 80 K is about 1.1 \(\times\) 10\({}^{-19}\) cm\({}^{2}\). It is about 5 times that of room temperature, which greatly improves the laser gain, improves the energy extraction efficiency, and can reduce the demand for pump power, thereby reducing the possibility of thermal effects and crystal damage. However, at the same time, the emission spectrum width of the Yb:YAG crystal becomes narrow, due to the limitation of the time-bandwidth product, the narrowing of the spectral width results in a larger pulse width limit, which makes the pulse compression more difficult and limits the pulse width to the picosecond level [15]. The results of research on the fluorescence lifetime of Yb:YAG crystals show that with the decrease in temperature, the fluorescence lifetime of Yb:YAG crystals decreases slightly and remains at about 1 ms [15]. Although the fluorescence lifetime decreases with the increase in doping concentration, it does not have a significant effect on the energy storage capacity of the crystal for low doping concentration. Figure 2: Absorption cross–section of Yb:YAG crystal (0.24 mm thick and 9.8% doping concentration) as a function of wavelength for a crystal temperature of 300 K [12]. Reprinted/adapted with permission from Ref. [IEEE]. 2005, [PERSON]. In addition, Yb:YAG has a quasi-three-level structure, and there is a thermal particle number distribution of about 5.3% in the lower energy level at room temperature. Therefore, there is a serious self-absorption effect, resulting in a high pump threshold and a small effective emission cross-section. As shown in Figure 4, when the Yb:YAG crystal is cooled to 77 K, the proportion of particles in the lower energy level drops to the order of \(10^{-5}\), and the crystal transforms into a four-level structure, which effectively reduces the pumping threshold, increases the pumping efficiency, and increases the effective emission cross-section [8,9]. Figure 4: Thermal conductivity, thermo-optic coefficient, and thermal expansion coefficient of YAG crystal as a function of temperature. Figure 3: Absorption cross–section of Yb:YAG crystal (0.24 mm thick and 9.8% doping concentration) as a function of wavelength for a crystal temperature of 75 K [12]. Reprinted/adapted with permission from Ref. [IEEE]. 2005, [PERSON].