Model of laser-induced temperature changes in solid-state optical refrigerators

We present an efficient and numerically stable method to calculate time-dependent, laser-induced temperature distributions in solids and provide a detailed description of the computational procedure and its implementation. This study combines the two-dimensional heat equation with laser-induced heat generation and temperature-dependent luminescence. The time-dependent optical response of a system is obtained numerically by the Crank–Nicolson method. This general model is applied to the specific case of optical refrigeration in ytterbium (Yb3+) doped fluorozirconate glass (ZBLAN). The laser-induced temperature change upon optical pumping and the respective transient luminescence response are calculated and compared to experimental data. The model successfully predicts the zero-crossing temperature, the net quantum efficiency, and the functional shape of the transients. We find that the laser-cooling transients have a fast and a slow component that are determined by the excited-state lifetime of the lumines...