Resolving the size–efficiency–power trade-off in solid-state optical refrigerators via temperature-dependent geometry optimization

Solid-state optical refrigeration offers a vibration-free route to cryogenic cooling for quantum and space technologies. However, its power has been bottlenecked by an unquantified trade-off: larger crystals enhance pump absorption but aggravate fluorescence reabsorption. This work resolves this trade-off by establishing a universal, temperature-dependent optimization framework. Using Yb3+:Y3Al5O12 (YAG), the scaling of key cooling parameters with crystal size is first experimentally mapped. Integration with a multi-pass cavity model then reveals a pivotal design principle: the optimal crystal size for maximum cooling power increases as the operating temperature decreases. Furthermore, a scaling law is extracted, showing the efficiency penalty scales with n2, thus quantifying the interdependence between material properties and geometry. To mitigate reabsorption, an 80° corner-cut crystal geometry is proposed and validated, extending the benefits of size scaling. The generality of these laws is confirmed through cross-validation with Yb3+:LuLiF4 (LLF). Collectively, this work provides a predictive design framework that transforms optical cryocooler development from an empirical art into a predictive, model-driven engineering discipline.