Intrinsic Thermo-Optical Feedback as a Fundamental Nonlinear Interaction in Rare-Earth-Doped Systems

Intrinsic heating is generally regarded as a secondary consequence of optical excitation in rare-earth (RE³⁺)-doped materials. Here, we demonstrate that intrinsic thermo-optical feedback can drive the transient dynamics of optically excited RE³⁺ systems. To isolate this mechanism, we develop a minimal coupled population-temperature model that describes the interplay among optical excitation, temperature-dependent non-radiative relaxation, heat generation, and thermal dissipation. The model predicts the emergence of a threshold excitation power associated with intrinsic thermo-optical feedback, giving rise to pronounced slowing down of the transient dynamics, non-monotonic evolution of the characteristic transient time, population overshoot, and accelerated relaxation above threshold. These phenomena originate from the progressive establishment of a positive feedback loop linking temperature, non-radiative relaxation, quantum efficiency, and heat generation. Our results demonstrate that temperature should no longer be regarded merely as a passive external parameter, but rather as an active dynamical variable capable of continuously reshaping the relaxation pathways of the system. More broadly, this work establishes intrinsic thermo-optical feedback as a general framework for understanding nonlinear transient phenomena in optically excited RE³⁺ materials and provides a complementary perspective for interpreting threshold-like optical responses beyond conventional photon-avalanche mechanisms.