## 2 Review of Cryogenic-Cooling Benefits
### Spectroscopic, Lasing, Linear and Nonlinear Optical Parameters
#### 2.7.2 Linear and Nonlinear Optical Parameters
For a variation of the index in the third decimal place, the Sellmeier equation will change as well, and thus will all of the dispersion parameters. The same conclusion may be reached for most other crystals as well. It is then important going forward to obtain measurements of the indices of refraction as a function of wavelength at cryogenic temperatures. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Crystal** & **Wavelength (nm)** & \(n_{0}\) & \(\beta_{1}\) & \(\beta_{2}\) & \(\beta_{3}\) & \(\beta_{4}\) & \\  & & & **(fs/mm)** & **(fs2/mm)** & **(fs3/mm)** & **(fs4/mm)** & **Reference** \\ \hline Al\({}_{2}\)O\({}_{3}\)-(e) & & & & & & & \\ (HEM) & 800 & 1.7540 & 5928.1 & 49.9 & 48.3 & \(-\)30.0 & [79] \\ Al\({}_{2}\)O\({}_{3}\)-(o) & & & & & & \\ (HEM) & 800 & 1.7620 & 5960.6 & 42.2 & 48.7 & \(-\)36.7 & [79] \\ Al\({}_{2}\)O\({}_{3}\)-(e) & & & & & & \\ (HEM) & 1030 & 1.7477 & 5912.4 & 11.9 & 81.3 & \(-\)127.6 & [79] \\ Al\({}_{2}\)O\({}_{3}\)-(o) & 1030 & 1.7552 & 5946.7 & 7.0 & 87.9 & \(-\)146.4 & [79] \\ (HEM) & 850 & 1.4054 & 4709.2 & 7.9 & 15.7 & \(-\)15.0 & [82] \\ LiSAF-(o) & 850 & 1.4074 & 4720.0 & 9.5 & 28.4 & \(-\)1.2 & [82] \\ LiCAF-(e) & 760 & 1.3890 & 4654.6 & 23.6 & 13.6 & \(-\)3.3 & [83] \\ LiCAF-(o) & 760 & 1.3899 & 4659.5 & 23.1 & 13.7 & \(-\)3.9 & [83] \\ YAG & 1060 & 1.8243 & 6148.6 & 60.9 & 68.3 & \(-\)46.9 & [84] \\ YAG & 1030 & 1.8153 & 6211.7 & 66.6 & 66.7 & \(-\)41.6 & [84] \\ LuAG & 1060 & 1.8279 & 6136.5 & 74.6 & 45.7 & 7.3 & [85] \\ LuAG & 1030 & 1.8249 & 6151.8 & 64.4 & 66.1 & \(-\)39.3 & [85] \\ YALO-(a) & 1040 & 1.9341 & 6502.8 & 93.4 & 55.5 & 7.6 & [86] \\ YALO-(b) & 1040 & 1.9258 & 6473.2 & 90.3 & 53.5 & 7.2 & [86] \\ YALO-(c) & 1040 & 1.9140 & 6430.1 & 84.2 & 49.7 & 6.3 & [86] \\ YLF-(e) & 1020 & 1.4705 & 4927.6 & 21.7 & 24.2 & \(-\)18.7 & [87] \\ YLF-(o) & 1020 & 1.4483 & 4851.8 & 18.9 & 23.3 & \(-\)21.3 & [87] \\ YVO4-(e) & 1060 & 2.1661 & 5947.6 & 341.1 & 305.0 & 69.1 & [88] \\ YVO4-(o) & 1060 & 1.9579 & 6662.4 & 191.7 & 168.5 & 18.2 & [88] \\ KGW-(Np) & 1032 & 1.9829 & 6726.0 & 165.8 & 129.6 & 9.1 & [48] \\ KGW-(Nm) & 1027 & 2.0113 & 6828.7 & 178.7 & 139.5 & 12.6 & [48] \\ KGW-(Ng) & 1024 & 2.0625 & 7005.8 & 216.0 & 141.5 & 3.5 & [48] \\ KYW-(Np) & 1028 & 1.9690 & 6673.0 & 184.4 & 429.5 & 21.3 & [48] \\ KYW-(Nm) & 1028 & 2.0073 & 6814.0 & 207.2 & 495.1 & 26.0 & [48] \\ KYW-(Ng) & 1028 & 2.0514 & 6972.1 & 223.8 & 543.2 & 28.9 & [48] \\ KYbW-(Np) & 1040 & 1.9932 & 6772.2 & 130.5 & 106.2 & \(-\)29.9 & [48] \\ KYbW-(Nm) & 1026 & 2.0365 & 6897.3 & 173.2 & 421.5 & 56.3 & [48] \\ KYbW-(Ng) & 1024 & 2.0789 & 7074.3 & 179.6 & 307.7 & 20.9 & [48] \\ Y\({}_{2}\)O\({}_{3}\) & 1030 & 1.8889 & 6386.6 & 113.9 & 93.2 & \(-\)14.0 & [89] \\ Sc\({}_{2}\)O\({}_{3}\) & 1030 & 1.9654 & 6659.2 & 124.8 & 108.6 & \(-\)30.4 & [89] \\ Lu\({}_{2}\)O\({}_{3}\) & 1030 & 1.9102 & 5691.4 & 126.1 & 100.6 & \(-\)15.8 & [89] \\ CaF\({}_{2}\) & 1030 & 1.4287 & 4784.1 & 18.4 & 20.2 & \(-\)14.7 & [52] \\ BK-7, N-BK-7 & 800 & 1.5108 & 5088.8 & 44.6 & 32.0 & \(-\)10.0 & [52] \\ BK-7, N-BK-7 & 1030 & 1.5071 & 5070.2 & 25.1 & 44.7 & \(-\)49.8 & [52] \\ SF10 & 800 & 1.7112 & 5836.7 & 159.2 & 102.9 & 33.4 & [90] \\ SF10 & 1030 & 1.7030 & 5766.4 & 108.1 & 97.3 & \(-\)15.7 & [90] \\ SF11 & 800 & 1.7648 & 6036.4 & 189.4 & 124.1 & 48.3 & [52] \\ SF11 & 1030 & 1.7553 & 5952.9 & 128.9 & 113.0 & \(-\)7.3 & [52] \\ N-SF14 & 800 & 1.7429 & 5957.1 & 176.4 & 117.6 & 41.6 & [52] \\ N-SF14 & 1030 & 1.7337 & 5879.7 & 118.3 & 110.2 & \(-\)17.7 & [52] \\ Crystal SiO\({}_{2}\) (e) & 1030 & 1.5282 & 5189.3 & 0.4 & 98.8 & \(-\)193.5 & [91] \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Calculated room temperature values of the linear index and the first, second, third, and fourth order dispersion parameters for legacy and newer laser crystals of length 1 mm. Also shown are the operating laser wavelengths, as well as references to allow readers to know what Sellmeier or alternative index equation was used in the calculations.