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 <2ppb , and Fe²⁺ , Co²⁺ , Ni²⁺ , and OH have to be reduced to 10-100ppb for a practical ZBLAN:Yb³⁺ optical cryocooler to operate at 100-150K .