Rise kinetics of up-conversion luminescence under pulsed excitation. Probabilistic model and experiment

A probabilistic model describing the luminescence kinetics in systems of interacting rare-earth ions is proposed. The basic position of the model is that any mechanism of energy transfer between ions can be represented as a sequence of elementary processes. The duration of each elementary process of energy transfer is a random variable. An analytical expression is found for the time dependence of the radiant flux spectral density of ions for any pump modulation and its special case when the durations of elementary processes have exponential distribution laws and the excitation modulation is a rectangular or short pulse. It is shown that the initial stage of this dependence is a power function. The process of energy transfer from the pump radiation to the emitting ion consists of a number of elementary successive stages which determine the exponent. Mechanisms of up-conversion energy transfer under pulsed excitation are considered in systems consisting of ions of two types: donors interacting with pump radiation and acceptors receiving energy from donors. The number of successive elementary processes, of which these mechanisms are composed, is determined. A regression analysis of the rise kinetics of up-conversion luminescence of the Y0.8Yb0.2F3: Tm3+ (1 at%) crystal is made using the proposed probabilistic model. The kinetics was obtained under rectangular pulsed excitation by IR radiation of a lambda(P) = 933 nm semiconductor laser diode. The most important mechanisms of energy transfer from Yb3+ ions to the Tm3+ ions responsible for transitions between the ground H-3(6) term and excited F-3(4), H-3(4) , (1)G(4) , D-1(2) , I-1(6) terms of the Tm3+ ions are established. The durations of these energy transfer processes are determined.