## 1 Introduction and History of Cryogenic Lasers
### The Modern Era
During 1998 Fan _et al._[24] presented the first experimental confirmation, using a 940 nm diode-pumped Yb:YAG crystal, that cooling the Yb:YAG crystal to 77 K resulted in a large reduction in thermo-optic effects, as well as a CW power output of 40 W. Further confirmation of the large reduction in thermal effects, in Nd:YAG, was provided in 2004 by Glur _et al._[25]. In 2005 we published an article further confirming the trends discussed in the aforementioned [2]. To provide confirmation that the same general behavior of the thermal conductivity, thermal expansion coefficient, and \(\mathrm{d}n/\mathrm{d}T\) could be expected in other crystals, we showed additional literature data. For the thermal conductivity, we showed data for LiF, MgO, Al\({}_{2}\)O\({}_{3}\), C, YbAG, LuAG, and YAG, all of which displayed significant increases at temperatures were lowered to 77 K and below. As expected, the behavior of the thermal conductivities for undoped crystals is dominated by the specific heat \(C_{\
u}\), which theoretically increases as approximately the inverse of the absolute temperature between 300 and 77 K. It is not surprising that fluoride and oxide hosts display the same general trend. For the thermal expansion data, we plotted data for seven different crystals, including the recently published data of the MIT Lincoln Lab group [23; 26], all of which could be seen converging towards a value close to zero at low temperatures. For the thermo-optic coefficient \(\mathrm{d}n/\mathrm{d}T\), we used the MIT data as well as literature data found for both axes of Al\({}_{2}\)O\({}_{3}\), ZnSe, Ge, and Si. In all cases substantial decreases in \(\mathrm{d}n/\mathrm{d}T\) were found as temperature is lowered. These results showed conclusively that the same trends for the thermal conductivity, thermal expansion coefficient, and \(\mathrm{d}n/\mathrm{d}T\) were apparent across a wide sampling of crystals. In addition to examining critical laser materials parameters, our paper also presented for preliminary cryogenic absorption cross-section data for Yb:YAG, measured between 300 and 77 K, and later presented in a more detailed publication [27]. Previously, absorption coefficients for Yb:YAG at 300 and 77 K were presented in [24]. A significant finding of that work was that at 77 K the 940 nm pump band doubled in intensity and narrowed, but remained broad enough for pumping with conventional diode pump sources. For quasi-three-level Yb materials like Yb:YAG that display finite ground-state laser absorption at room temperature, cryogenic-cooling also results in 4-level performance at 77 K, reducing the pump density needed to achieve transparency from a significant value to almost zero. We point out here that the large increase in the stimulated-emission cross-section from a value of about 1.8 \(\times\) 10\({}^{-20}\) cm\({}^{2}\) at room temperature [1] to 1.1 \(\times\) 10\({}^{-19}\) cm\({}^{2}\) at 80 K [3] by approximately a factor of 6 reduces the saturation fluence and intensity by the same factor, thus positively affecting the extraction and overall efficiencies that may be achieved. To achieve good amplifier extraction efficiency the incident amplifier fluence must take a value of at least 2 times the saturation fluence, and for Gaussian beams must be even higher [28]. A much smaller saturation fluence enhances the likelihood of being able to operate below the damage threshold fluence while at the same time achieving efficient extraction efficiency. Also in 2005, an impressive paper that for the first time measured the detailed thermo-optic properties of a large sampling of laser crystals from 300 to 80 K (Y\({}_{3}\)Al\({}_{5}\)O\({}_{12}\) (YAG), Lu\({}_{3}\)Al\({}_{5}\)O\({}_{12}\) (LuAG), YAlO\({}_{3}\) (YALO), LiYF\({}_{4}\) (YLF), LiLuF\({}_{4}\) (LuLF), BaY\({}_{2}\)F\({}_{8}\) (BYF), KGd(WO\({}_{4}\))\({}_{2}\) (KGW), and KY(WO\({}_{4}\))\({}_{2}\) (KYW)) was published by the MIT Lincoln Laboratory group [29].