# Saturation, Allowed Transitions and Quantum Interference in Laser Cooling of Solids
## 4 Discussion  
Laser cooling efficiencies in 10% Yb:YLF, measured with the DLT and TLS methods at various intensities and wavelengths, were in satisfactory mutual agreement. Absorption saturation of the background impurity was observed at high pump intensity, leading to a significantly higher cooling efficiency, as predicted by the differential absorption saturation theory. A method for measuring the saturation intensity of background impurities was devised based on identifying the cross-over point in the intensity-dependent cooling efficiency plot. Our experiments were in close agreement with analysis incorporating saturation effects, revealing that because background absorption can be reduced at high pump intensity, higher pump power reduced parasitic heating and enhanced cooling efficiency. This finding may allow the attainment of lower minimum temperatures and will promote the use of cooling materials that are not well developed and suffer from higher background impurity levels, such as KYW [24]. In addition, this result should enable laser refrigeration of some impure materials that could not be cooled previously at all. The method used to determine the saturation intensity of background absorption consisted of systematic measurements of laser cooling efficiency by Differential Luminescence Thermometry (DLT) and Thermal Lens Spectroscopy (TLS) versus wavelength and incident intensity. The slope of cooling efficiency versus wavelength exhibited an intensity dependence with a common intersection point at \(\lambda=1000\) nm in the 10% Yb\({}^{3+}\):YLF sample, indicating that at this wavelength, the saturation intensities of the coolant ions and background impurities had the same value (\(\sim\)2.6 \(\times\) 10\({}^{4}\) W/cm\({}^{2}\)). For wavelengths longer than 1000 nm, higher pump intensities improved the cooling efficiency significantly, agreeing well with the differential saturation model using the measured saturation intensities. Although major efforts have been made to improve crystal purity in hosts such as YLF to reach low temperatures by conventional ASF, the present results on improved cooling  
Figure 17: Plot of theoretical cooling efficiency versus pump wavelength of Ce\({}^{3+}\) ions in LiCaAlF\({}_{6}\) obtained from Equation (10) Cooling curves are shown for three different values of external quantum efficiency, assuming a background impurity absorption coefficient of \(\alpha_{b}=1\times 10^{-5}\) cm\({}^{-1}\). Peak cooling efficiency occurs at 305 nm but extends from 293–310 nm for unity quantum efficiency. efficiency through optical saturation establish a new route for lowering the minimum achievable temperatures below those previously possible at a given background absorption level. However, it should be noted that room temperature measurements are insufficient to predict outcomes at cryogenic temperatures. The absorption coefficients of coolant ions and background impurities decrease with temperature [39], resulting in temperature-dependent saturation intensities. It is only in the case when the background absorption saturates first, at an intensity lower than the coolant ions, that lower minimum temperatures can be realized by increasing pump intensity. The intensity dependence of the cooling efficiency observed in this work is surprising because the saturation intensity of the background impurity absorption is unexpectedly low. This result must stem from a dominant impurity of particular valence and site symmetry. Iron is thought to be the main source of background absorption in Yb:YLF crystals [40]. This impurity is likely a substituent at the trivalent sites (Y\({}^{3+}\)) in YLF, which would render it predominantly trivalent. It is therefore of possible interest to note that trivalent iron in a material such as Fe:YAG has a low-energy excited state transition from \({}^{6}\)A\({}_{\text{lg}}\) to \({}^{4}\)T\({}_{\text{lg}}\), which is forbidden by both spin and parity selection rules [41].