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

Abstract

Abstract-Quenching of Er3+ ions by homogeneous energytransfer upconversion in high-concentration erbium-doped silica glasses has been theoretically investigated. The results indicate that at Er 3+ concentrations of 1.0-2.0110 26 m 03 or below, the kinetic limit of strong migration is not reached, and hence the widely accepted quadratic upconversion model is not generally valid. Nevertheless, the results offer an explanation of the experimental observations of quadratic upconversion. Furthermore, it has been shown that at a given population inversion, the quenching rate depends on the rate of exchange of the excited Er 3+ ions by emission and absorption.

Observation of strongly nonquadratic homogeneous upconversion in Er/sup 3+/-doped silica fibers and reevaluation of the degree of clustering

“…5 is that the upconversion rate experienced by the Er -ions in the manifold does not grow linearly with the population, i.e., the model predicting a quadratic dependence of the number of ETU processes on the excited state population, does not hold for our fibers. On the contrary, the curves all bend upwards, as would be expected for the case, where migration is too weak for the quadratic model to be valid [13]. At first sight, the tendency of bending upwards seems stronger for the curves representing the highest concentration fibers, but a closer inspection (comparison of the curves with the maximum upconversion rate normalized to 1) reveals that, apart from fibers #1 and #2, where the results are too noisy, all the curves have roughly the same shape.…”

“…In [13], we presented a detailed model for calculation of the macroscopic upconversion rate from an assumed microscopic spatial distribution of the Er -ions together with an assumed dependence of the upconversion and migration probabilities on the interionic distance. In a first version of the model, we used Monte Carlo simulations to generate the Er sites as well as to simulate the temporal behavior of the ions, whereas a second version described the temporal behavior via equations for the excitation probabilities for each ion together with the joint excitation probabilities for neighboring ions.…”

“…The homogeneous upconversion is slower and is usually modeled by a quadratic term in the rate equations [2], [11], [12], which corresponds to assuming that the macroscopic (i.e., averaged over all Er -ions) upconversion rate is proportional to the number of Er -ions per unit volume in the level: . However, we have recently presented modeling results demonstrating that the validity of this quadratic model for a random spatial ion distribution will depend strongly on the relative strength between migration and upconversion [13]. The main goal of this work was to investigate experimentally the validity of the quadratic model.…”

Lanthanide upconversion luminescence at the nanoscale: fundamentals and optical properties

“…This is a fairly coarse approximation for upconversion which generally requires a more nuanced and detailed understanding of random walks of excitation energy through the entire sensitizer-activator system. The physically most clear and intuitive understanding of upconversion in such systems is provided by a Markovian model which relates the rate of change of the probability that a single Ln 3+ ion site is excited to the various microscopic molecular transfer probabilities [101][102][103][104] . This stochastic approach considers the interactions in the Ln 3+ system of ions as a random-walk process where occupation probabilities execute a hopping motion across the different ionic sites.…”

Progress on erbium-doped waveguide components

“…An important class of methods is time-resolved spectroscopy including studies of the non-exponential component of the 1530 nm fluorescence decay [43,45, and studies of the decay of the 980 nm or 800 nm upconversion fluorescence [43,45,50-5 13, usually after cutoff of a steady-state pump. These techniques are suitable for examining ETU between homogeneously distributed ions [48,52] and (provided sufficient time resolution) for evaluating quenching times for clustered erbium ions [51], but not for estimating the fraction of clustered erbium ions, since only very few clustered ions will be in the upper laser level at pump cut-off. If, on the other hand, short, strong pump pulses are used, an even excitation of clustered and unclustered erbium ions may be assumed.…”