## 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
\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**} & \(\begin{array}{c}\delta\lambda_{\text{det}},\lambda^{D}_{\text{det}}\\ \textbf{(FWHM)}\textbf{(mm)}\end{array}\) & \(\Delta\lambda_{\text{det}}\textbf{(FWHM)}\) & \(\boldsymbol{\alpha^{D}_{\text{det}}}\textbf{(cm^{2})}\textbf{(10}^{-23})\) & \(\boldsymbol{\lambda^{D}_{\text{det}}}\textbf{(mm)}\) & \(\Delta\lambda_{\text{det}}\textbf{(FWHM)}\) & \(\boldsymbol{\alpha^{D}_{\text{det}}}\textbf{(cm^{2})}\) & \(\boldsymbol{\gamma_{\text{f}}}\textbf{(sin)}\) & **Temp (G)** & **Refs** \\ \cline{3-10} Yb3+YAG & A & 909 & 2.8 (300) & 3.28 & 1029 & 8.5 & 2.3 & 951 & 300 & [3,27] \\  & & 941 & 18.3 (300) & 1.22 & 1029 & 8.5 & 2.3 & 951 & 300 & [3,27] \\ \hline Yb3+YAG & A & 909 & 0.6 (80) & 37.0 & 1029 & 1.5 & 11.0 & 951 & 75-80 & [3,27] \\ \hline Yb3+YLF & U & 960 & 10.0 & 1.1 & & & & & & & \\ E1 (c/g) & U & 992 & 8.0 & 0.4 & 1020 & 36.0 & 0.8 & 2080 & 300 & [3,108] \\ \hline Yb3+YLF & \multirow{3}{*}{U} & 929-953 & 25.0 & 0.3 & & & & & & & & \\ E1 (a/e) & & 900 & 6.0 & 0.4 & 1020 & 27.0 & 0.7 & 2080 & 300 & [3,108] \\  & & 971 & 12.0 & 0.3 & & & & & & & \\ \hline Yb3+YLF & \multirow{3}{*}{U} & 960 & \(<\)1 & 6.8 & & & & & & & & \\ E1 (c/g) & U & 971 & \(<\)0.5 & 1.4 & 1020 & 8.0 & 1.8 & 1990 & 79 & [3,108] \\ \hline Yb3+YLF & \multirow{3}{*}{U} & 930-950 & 21.0 & 0.8 & & & & & & & & \\ E1 (a/e) & & 900 & \(<\)2 & 2.4 & 1020 & 28.0 & 1.0 & 1990 & 79 & [109] \\ \hline Yb3+GSAG & A & 971 & \(<\)1 & 2.8 & & & & & & & & \\ \hline Yb3+GSAG & A & 928-950 & 22 & - & - & - & - & - & - & 300 & [30,110] \\  & & 946 & & & & & & & & & \\ \hline Yb3+GSAG & A & 930-947 & 17 & - & 1080 & 2.4 & 5.6 & - & 77 & [30,110] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _Cont._Yb:CaF\({}_{2}\) has come to the fore recently because of its broad emission bandwidth, resulting in <100 fs pulsewidths from a mode-locked laser recently [111]. From Table 6, we see that it has a wide emission bandwidth, particularly at 77 K. The Gaussian transform-limited pulsewidths expected are 59 fs and 37 fs at 300 and 77 K respectively. As we have seen previously in Section 2.6, however, this laser material has the lowest thermal and stress figures-of-merit (Table 3), potentially limiting its usefulness as a material for high average power ultrafast systems. As shown in Figure 15, even for modest Yb doping levels of a few at. %, the thermal conductivity of Yb:CaF\({}_{2}\) can be less than the undoped value at 300 K at temperatures of both 300 and 80 K. As a consequence, the figures of merit are even worse for Yb-doped CaF\({}_{2}\) crystals. Recall that the figures-of-merit shown in Table 3 are for undoped crystals only. An attractive feature of this material for systems applications is that it has a very low nonlinear index (Table 4), although such a low value makes Kerr-lens mode-locking much more difficult. For the sesquioxide laser materials at room temperature, the expected Gaussian transform-limited pulsewidths are calculated to be 119, 119, and 109 fs for Yb:Lu\({}_{2}\)O\({}_{3}\), Yb:Sc\({}_{2}\)O\({}_{3}\), and Yb:Y\({}_{2}\)O\({}_{3}\) respectively. All have relatively good thermal and stress figures-of-merit (Table 3).