能量传递制冷机制中激光制冷的最佳泵浦频率和最大制冷效率

The Best Pump Frequency and the Most Cooling Efficiency in Laser Cooling with Energy Transfer Mechanism

在能量传递型激光制冷中，对于非均匀线宽比较窄的情况，引起最大制冷效率的激发光频率不随温度的变化而变化；最大制冷效率与温度呈三次暴的关系。对于非均匀线宽比较宽的情况。随着温度的降低，最佳激发光频率与非均匀线形的中心频率差越来越大，并在较低的温度下迅速拉大它们间的距离。由能量传递机制所引起的荧光制冷最大效率也随着温度的降低而越来越低，并在最后趋于零。它们随温度的降低而降低的规律与实验中得到的结论相符合。

In our earlier papers on theoretical analysis of fluorescent cooling, it is pointed out that there are two kinds of basic physical mechanism- anti - Stokes fluorescent cooling in single center (ASFCSC ) and anti- Stokes fluorescent cooling by energy transfer(ASFCET). Doubtless, ASFCSC is an important process and dominants in fluorescent cooling of solid, but ASFCET can exist at the same time. Actually, the excitation transfers of rare-earth ions have been studied a lot even for ytterbium ions in fluoride glasses. Many experiment Phenomena show it is possible for ASFCET to realize. In this paper, we discussed the most cooling efficiency in ASFCET, which is a fluorescent cooling mechanism based on energy transfer among the centers within the inhomogeneously broadened spectral profile. A model was developed to evaluate the fluorescent cooling under the mechanism. We discussed it in two situations: two-phonon-assisted energy transfer process with small energy mismatch and one-phonon-assisted energy transfer process with large energy mismatch. The dependence of the most cooling efficiency on excitation photon energy and temperature was given. When the inhomogeneous line width is narrow, the best pump light frequency does not change with temperature and the most cooling efficiency is proportional to the cube of temperature. When the inhomogeneous line width is wide, the difference between the best pump light frequency and the center frequency of the inhomogeneous line gets wider as the temperature goes lower. The difference changes rapidly at low temperature. The most fluorescent cooling efficiency produced by energy transfer tends to lower with temperature decreasing, and trends to zero finally. The regularities by which fluorescent cooling efficiency lower with temperature are correspond to the results obtained in experiments.