A theoretical study of intrinsic optical bistability dynamics in Tm ³⁺/Yb³⁺ codoped systems with an upconversion avalanche mechanism

This paper presents theoretical investigations on the dynamics of intrinsic optical bistability (IOB) in Tm³⁺/Yb³⁺ codoped systems with an upconversion avalanche mechanism. Numerical simulations based on the rate equation model demonstrate distinct IOB hysteresis and critical slowing dynamics around the avalanche thresholds. Moreover, the unusual IOB characteristics are well interpreted by developing a simplified analytic model which gives the formulations of two critical thresholds and the necessary condition for IOB to occur. The simplified model shows that such IOB phenomena may occur only if the total quantum yields of the dipole-dipole energy transfer processes are much higher than that of the inherent decay losses involved in an upconversion avalanche. The analytic model developed in the paper may be useful for the prediction of new rare-earth-doped materials giving rise to IOB.