## 2 Review of Cryogenic-Cooling Benefits
### Spectroscopic, Lasing, Linear and Nonlinear Optical Parameters
#### 2.7.4 Spectral and Laser Properties of Traditional and New Laser Materials  
The design and performance of ultrafast lasers is critically dependent upon the spectral and laser properties of the amplifier materials used. We have already, in the aforementioned, discussed the important nonlinear parameters and the dispersion parameters needed to optimize the performance of ultrafast lasers. Here, we review the spectral properties of a number of important laser materials, including a number of legacy ultrafast materials as well as some newer laser materials, all based upon the Yb\({}^{3+}\) lasing ion. A more complete compilation of properties for most Yb based laser materials will be presented elsewhere [100]; here we show only Yb materials for which both room and cryogenic temperature data are available. Table 6 shows the laser material, the crystal classification (anaxial (A) and uniaxial (U)), the absorption span \(\delta\lambda_{abs}\) (FWHM) and wavelength of peak absorption \(\lambda_{abs}^{P}\), the absorption bandwidth \(\Delta\lambda_{abs}\) (FWHM), peak absorption cross-section \(\sigma_{abs}^{P}\), the wavelength of the peak stimulated-emission cross-section \(\lambda_{em}^{P}\), the emission bandwidth \(\Delta\lambda_{em}\) (FWHM), the value of the peak stimulated-emission cross-section \(\sigma_{em}^{P}\), the upper level (\({}^{2}\)F\({}_{5/2}\)) fluorescence lifetime \(\tau_{F}\), the absolute temperature, and the references from whence the data were taken [3; 6; 30; 101; 102; 103; 104; 105; 106; 107; 108; 109; 110]. The three legacy laser materials shown, Ti:Al\({}_{2}\)O\({}_{3}\), Cr:LiSAF, and Cr:LiCAF, are uniaxial and we show data for the cases E\(\mid\)|c and E\(\mid\)|a, and at room temperature. While Ti:Al\({}_{2}\)O\({}_{3}\) is often cooled to near 77 K to reduce thermal aberrations [31; 33; 34; 35], little data is available in the literature regarding the spectral properties at that temperature. For Cr:LiSAF and Cr:LiCAF, we were not able to find any cryogenic data available in the literature. The bandwidths for these materials indicate that for transform-limited Gaussian pulses, pulsewidths of as short as 4, 6, and 7 fs can be achieved, in the absence of gain-narrowing. For the Yb materials Yb:CaF\({}_{2}\), Yb:LuAG, Yb:YAG, and Yb:YLF, complete sets of spectral parameters are available at room temperature and near 77 K, and both are shown in Table 6. We have also included the recently developed sesquioxide laser materials Yb:Lu\({}_{2}\)O\({}_{3}\), Yb:Sc\({}_{2}\)O\({}_{3}\), and Yb:Y\({}_{2}\)O\({}_{3}\), but complete data sets are available at present only at 300 K. The first Yb laser material to be investigated at cryogenic temperature was Yb:YAG [1], but the emission bandwidth is narrow and only capable of producing Gaussian transform-limited pulses of about 1 ps at 80 K, due to the narrower gain bandwidth [3]. The material Yb:LuAG, very similar to Yb:YAG, is capable of producing 1.4 ps pulses. The first Yb:YLF laser operated at cryogenic temperatures was reported in [109]. Yb:YLF is an interesting ultrafast cryogenic laser material, due to the wide emission bandwidths for both \(\pi\) and \(\sigma\) polarizations. For E\(\mid\)|c and E\(\mid\)|a at 300 K, the shortest transform-limited Gaussian pulsewidths that can be obtained are about 43 and 57 fs at 300 K, and 191 and 55 fs at 79 K. The material is robust and has relatively high thermal and stress figures of merit (Table 3). The first demonstration of combining two Yb laser materials together (Yb:YAG and Yb:GSAG) to broaden the gain bandwidth, produced recompressed shorter pulses of ~1.6 ps duration [110]. Not all of the spectral properties of Yb:GSAG are known, particularly at room temperature, but we have included the known properties in Table 6.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Crystal**} & \multirow{2}{*}{**Crystal Type**} & \( \begin{array}{c}\delta_{\text{Abs}}\;\lambda_{\text{An}}^{P}\\ \textbf{(FWHM) (nm)}\end{array}