## 2 Review of Cryogenic-Cooling Benefits
### Spectroscopic, Lasing, Linear and Nonlinear Optical Parameters
#### 2.7.2 Linear and Nonlinear Optical Parameters
Table 3 below shows reported values of \(n_{0}\), \(n_{2}\) and \(\gamma_{N}\) for a number of optical and laser materials of interest. All reported values are at or near room temperature. In some publications the value of \(n_{2}\) was measured, and in others \(\gamma_{N}\); Equation (74) was used to provide missing values of either in Table 4. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Crystal** & **Crystal** & **E Field** & **Wavelength** & \(n_{0}\) & \(n_{2}\) **(esu)** & \(\gamma_{N}\) **(cm\({}^{2}\)/W)** \\
**Type** & **Crystal** & **Orientation** & **(nm)** & **\(n_{0}\)** & \(10^{-13}\) & \(10^{-16}\) & **Reference** \\ \hline SC & Al\({}_{2}\)O\({}_{3}\) & E! | C & 1064 & 1.76 & 1.30 & 3.09 & [68] \\ SC & Al\({}_{2}\)O\({}_{3}\) & E! | C & 532 & 1.78 & 1.40 & 3.30 & [68] \\ SC & Al\({}_{2}\)O\({}_{3}\) & E! | C & 355 & 1.80 & 1.60 & 3.72 & [68] \\ SC & Al\({}_{2}\)O\({}_{3}\) & E! | C & 266 & 1.82 & 2.60 & 5.98 & [68] \\ SC & Al\({}_{2}\)O\({}_{3}\) & E! | C & 650 & 1.77 & 1.36 & 3.21 & [69] \\ SC & Al\({}_{2}\)O\({}_{3}\) & E! | C & 700 & 1.77 & 1.33 & 3.17 & [69] \\ SC & Al\({}_{2}\)O\({}_{3}\) & E! | C & 750 & 1.76 & 1.32 & 3.14 & [69] \\ SC & Al\({}_{2}\)O\({}_{3}\) & E! | C & 800 & 1.76 & 1.31 & 3.11 & [69] \\ SC & Al\({}_{2}\)O\({}_{3}\) & E! | C & 850 & 1.76 & 1.30 & 3.09 & [69] \\ SC & Al\({}_{2}\)O\({}_{3}\) & E! | C & 900 & 1.76 & 1.29 & 3.06 & [69] \\ SC & Al\({}_{2}\)O\({}_{3}\) & E! | C & 950 & 1.76 & 1.28 & 3.04 & [69] \\ SC & Al\({}_{2}\)O\({}_{3}\) & E! | C & 1000 & 1.76 & 1.26 & 3.01 & [69] \\ SC & Al\({}_{2}\)O\({}_{3}\) & E! | C & 1050 & 1.76 & 1.26 & 2.99 & [69] \\ SC & Al\({}_{2}\)O\({}_{3}\) & E! | C & 1100 & 1.75 & 1.24 & 2.97 & [69] \\ SC & LiSar & Unspecified & 850 & 1.39 & 1.10 & 3.30 & [70] \\ SC & LiCAF & Unspecified & 850 & 1.38 & 1.22 & 3.70 & [70] \\ SC & LiSGAF & Unspecified & 850 & 1.39 & 1.10 & 3.30 & [70] \\ SC & Mg\({}_{2}\)SiO\({}_{4}\) & Unspecified & 1240 & 1.64 & 0.78 & 2.00 & [70] \\ GM & SiO\({}_{2}\) & I & 1064 & 1.45 & 0.95 & 2.74 & [71] \\ GM & SiO\({}_{2}\) & I & 527 & 1.46 & 1.05 & 3.00 & [71] \\ GM & SiO\({}_{2}\) & I & 351 & 1.48 & 1.27 & 3.60 & [71] \\ GM & BK-7 & I & 1064 & 1.52 & 1.46 & 4.00 & [68] \\ SC & YAG & I & 1064 & 1.82 & 2.51 & 5.78 & [72] \\ SC & YAG & I & 1064 & 1.82 & 2.70 & 6.21 & [73] \\ CER & YAG & I & 1064 & 1.82 & 2.49 & 5.73 & [72] \\ SC & YALO & E! | C & 1064 & 1.91 & 3.33 & 7.30 & [52] \\ SC & YLF & Unoriented & 1.46 (o) & 0.60 & 1.72 & [74] \\ SC & LuAG & I & 1064 & 2.14 & 5.50 & 10.77 & [73] \\ SC & Y\({}_{2}\)O\({}_{3}\) & I & 1064 & 1.78 & 5.33 & 12.54 & [73] \\ CER & Y\({}_{2}\)O\({}_{3}\) & I & 1064 & 1.78 & 5.79 & 13.63 & [72] \\ CER & Sc\({}_{2}\)O\({}_{3}\) & I & 1064 & 1.85 & 5.32 & 12.05 & [72] \\ CER & Lu\({}_{2}\)O\({}_{3}\) & I & 1064 & 1.83 & 3.96 & 9.06 & [72] \\ SC & MgO & I & 1064 & 1.74 & 1.61 & 3.88 & [73] \\ SC & MgAl\({}_{2}\)O\({}_{4}\) & I & 1064 & 1.72 & 1.50 & 3.65 & [73] \\ SC & CaF\({}_{2}\) & I & 1064 & 1.43 & 0.43 & 1.26 & [73] \\ SC & YVO\({}_{4}\) & E! | C & 1080 & 2.25 & 8.06 & 15.00 & [75] \\ SC & YVO\({}_{4}\) & E! | A & 1080 & 1.96 & 8.89 & 19.00 & [75] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Reported room temperature values of the linear index, nonlinear index and nonlinear coefficient for a number of important laser crystals and optical materials. Also shown are the crystal type (SC-Single Crystal, GM-glassy material, or CER-Ceramic), the E-field orientation (Parallel to specified crystal axis, unspecified, and I-Isotropic), and the measurement wavelength. Al2O3, LiSAF, LiCAF, LiSGAF, Mg2 SiO4, SiO2, YLF, MgO, MgAl2O4, and CaF2 all exhibit rather small nonlinear index values in the spectral region 800-1100 nm. YAG, YALO, and LuAG display somewhat larger values, while the sesquioxides Y2O3, Sc2O3, and Lu2O3 show a substantial increase, followed by the vanadates YVO4 and GdVO4 and the tungstates KGW and KYW which display the largest nonlinear index values.