## 1 Introduction and History of Cryogenic Lasers
### The Modern Era
Measurements of the thermal diffusivity, specific heat at constant pressure, thermal conductivity, thermal expansion coefficient, optical path length thermo-optic coefficient, and the thermo-optic coefficient \(\mathrm{d}n/\mathrm{d}T\) were presented. This article also reported measurements of the thermal diffusivity and thermal conductivity for Yb doped samples of Y\({}_{3}\)Al\({}_{5}\)O\({}_{12}\), YAlO\({}_{3}\), and LiYF\({}_{4}\) as well, and identified the doping density as an important parameter to consider in the design of cryogenic lasers. Further materials properties measurements by this group have appeared in subsequent publications. In [3], additional thermo-optic measurements are provided for ceramic and single-crystal YAG, GGG, GdVO\({}_{4}\), and Y\({}_{2}\)O\({}_{3}\). Spectroscopic data are also presented for Yb:YAG and Yb:YLF. A third publication [30] provides thermo-optic data for the sesquioxide ceramic laser materials Y\({}_{2}\)O\({}_{3}\), Lu\({}_{2}\)O\({}_{3}\), Sc\({}_{2}\)O\({}_{3}\), as well as for YLF, YSO, GSAG, and YVO\({}_{4}\). The modern cryogenic laser period began with the publications of the first experimental cryogenic Yb:YAG laser [1], and a significantly performance-enhanced Ti:Al\({}_{2}\)O\({}_{3}\) laser [11], both in 1991. Subsequent theoretical and experimental work in the years 1995-1998 confirmed that not only can enhanced laser properties be obtained by cryogenic-cooling, but that dramatic reductions in thermo-optic distortion and enhanced mechanical properties can be realized as well. Thermo-optic properties were not emphasized in the historical era, where the focus was mainly on laser physics, kinetics, and spectroscopy. Thus in our opinion, what is new is that that in the modern era, laser physicists, designers, and engineers have for the first time fully appreciated that the entire set of physical crystal properties (optical, laser kinetics, thermal, thermo-optic, and elastic) must be taken into account to effect successful laser outcomes. Apreciation of this reality has and will continue to drive the demonstration of much higher average power lasers, as well as HAPP lasers, in the future. The concurrent work of our group and that at the MIT Lincoln Laboratory has solved the longest standing problem in the development of solid-state lasers: the near-elimination of deleterious thermal effects. This point cannot be emphasized enough. The manipulation of the thermo-optic properties of solid-state laser hosts through the use of cryogenic-cooling has been proven capable of providing both high average power and near-vanishing thermally-induced aberrations. This results in output beams whose divergence and transverse beam size are virtually constant, without the use of any external beam correction. Beam-parameter independent lasers are highly desirable for harmonic generation, as well as for many other scientific, commercial, and military applications. In addition to the development of other oxide lasers, and in particular the development of Yb based lasers, cryogenic-cooling has advanced the performance of Ti:Al\({}_{2}\)O\({}_{3}\) ultrafast laser technology as well. Unlike Yb materials like Yb:YAG, Yb:LuAG, Yb:Lu\({}_{2}\)O\({}_{3}\), Yb:YLF, and others which all have small quantum defects and thus minimal heat loads, for Ti:Al\({}_{2}\)O\({}_{3}\) lasers, where optical-pumping usually takes place near 532 nm, the quantum defect for lasing near the peak of the gain profile near 790 nm is about 33%, a value \(>\) 3-5 times that of typical Yb based materials. The large heat load of Ti:Al\({}_{2}\)O\({}_{3}\) however can be largely be mitigated by cooling the sapphire-based material to 77 K where the thermal conductivity is dramatically larger, and by the substantial reductions in the thermal expansion and thermo-optic coefficients [11].