Microscopic theory of a radiation-balanced solar laser

Abstract

We develop a microscopic open-quantum-system theory for a radiation-balanced solar laser (RBSL) based on ytterbium-doped yttrium aluminum garnet (Yb:YAG), in which optical gain, thermal redistribution among sublevels of the electronic ground and excited manifolds, and lattice-temperature dynamics are treated within a unified framework. Starting from a Lindblad master equation for a multilevel gain medium coupled to a cavity mode, we include incoherent solar pumping, spontaneous emission, cavity loss, and phonon-assisted intra-manifold relaxation obeying detailed balance. In the regime of fast thermalization within each electronic manifold, a compact temperature-dependent two-level model is derived, in which the gain, inversion, and lasing threshold are controlled by Boltzmann occupation factors and partition functions of the electronic sublevels. This microscopic reduction is then coupled self-consistently to a thermal balance equation accounting for anti-Stokes fluorescence cooling, quantum-defect heating, parasitic absorption, and heat exchange with the environment. The theory predicts several operating regimes, including pure cooling, lasing with net cooling, and lasing with net heating, as well as dynamical effects such as delayed lasing onset induced by self-cooling into threshold. In contrast to earlier radiation-balanced laser (RBL) models based mainly on macroscopic rate equations and thermodynamic balance arguments, the present approach provides a microscopic description of the feedback between quantum optical dynamics and temperature redistribution. It therefore offers a physically transparent framework for analyzing RBSLs and for identifying design strategies that exploit level structure, thermalization, and photonic-environment engineering to stabilize laser operation while minimizing internal heat load.