Migration-Accelerated Quenching of Luminescence in Glasses Activated by Rare-Earth Ions

Monte Carlo simulations of homogeneous upconversion in erbium-doped silica glasses

“…The equivalent average quenching rate experienced by an Er ion in the manifold is . The quadratic model can be shown theoretically, if migration is assumed sufficiently strong (the kinetic limit) [21] and the model has been supported by some experimental results [4], [23]. Other authors have suggested a cubic model [2], [24].…”

“…For an arbitrary Er ion the probability of being quenched by upconversion with another Er ion will vanish as . At sufficiently low population inversions, the single-ion excitation probabilities will, therefore, remain unperturbed by upconversion: (17) 3 Equation (16) lacks a factor of two compared with [21], because P uc = R 6 uc =( rad R 6 ) in the present text has been defined to be the total probability per time unit of two excited Er 3+ ions performing an upconversion process with either of the two ions as the donor. The second-order joint probabilities will, however, not all be equal to since the negative correlation effect will be present at arbitrarily low population inversion.…”

“…By inserting (13) into (6), a general expression for the number of upconversion processes occurring per time and volume unit in the kinetic limit is reached: (14) From (14), it is seen that in the kinetic limit upconversion depends quadratically on the population inversion for any ion distribution and any radial dependance of the upconversion probability . If furthermore we use the assumption of dipole-dipole interaction, (14) can be rewritten as (15) By finally averaging (15) over the assumed random ion distribution, we find the expression (16) which corresponds 3 to the expression for the kinetic limit in the classical quenching theory [21]. The applicability of the classical quenching theory in the kinetic limit is expectable, since the strong migration erases the special features of selfquenching.…”

“…This assumption is frequently used within quenching theory [19]- [21], [25] and corresponds to regarding the glass host as a totally disordered material [21]. According to [5], 0.35 nm should be applied as the minimum Er -ion separation in Erdoped silica glasses (0.35 nm is the shortest distance between two Er ions in crystalline Er O .…”

“…A detailed theory exists-including work by Dexter [17], Eisenthal and Siegel [19], Bȗrshtein [20], Gapontsev and Platonov [21], etc.-describing quenching of a system of excited donors by energy-transfer to a system of acceptors. In discussions on upconversion between Er ions, references are often made to this theory.…”