Model of laser cooling in the Yb3+-doped fluorozirconate glass ZBLAN

A quantitative description of optical refrigeration in Yb3+-doped ZBLAN glass in the presence of transition-metal and OH impurities is presented. The model includes the competition of radiative processes with energy migration, energy transfer to transition-metal ions, and multiphonon relaxation. Molecular dynamics calculations of pure ZBLAN and ZBLAN doped with transition-metal ions provide the structural information that, when combined with spectroscopic data, allows for the calculation of electric-dipole energy-transfer rates in the framework of the Dexter theory. The structural data is further used to extend the traditional energy-gap law to multiphonon relaxation via vibrational impurities. The cooling efficiency is sensitive to the presence of both 3d metal ions with absorption in the near infrared and high-frequency vibrational impurities such as OH. The calculation establishes maximum impurity concentrations for different operating temperatures and finds Cu2+, Fe2+, Co2+, Ni2+, and OH to be the most problematic species. Cu2+ in particular has to be reduced to < 2 ppb, and Fe2+, Co2+, Ni2+, and OH have to be reduced to 10-100 ppb for a practical ZBLAN:Yb3+ optical cryocooler to operate at 100-150 K.