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Journal of the Optical Society of America B

Homogeneous upconversion in Er-doped fibers under steady state excitation: analytical model and its Monte Carlo verification

Dmitry Khoptyar, Sergey V. Sergeyev, B. Jaskorzyńska

Published Mar 1, 2005• 25 citations
Publisher

Abstract

We present an extension to our earlier proposed statistical model [Phys. Rev. B 62, 15628 (2002)] for studying migration-assisted homogeneous upconversion in erbium-doped fibers. The extension takes into account minimum proximity distance between erbium ions randomly distributed in the host material and the nonuniformity of the excitation distribution among them. We derive a transcendental equation for the population inversion and find the dependence of the upconversion rate on the population inversion and the pump power for the entire range of feasible Er concentrations. We verify the validity and accuracy of the model by means of time-resolved Monte Carlo simulations.

DOI
10.1364/josab.22.000582

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We present an extension to our earlier proposed statistical model [Phys. Rev. B 62, 15628 (2002)] for studying migration-assisted homogeneous upconversion in erbium-doped fibers. The extension takes into account minimum proximity distance between erbium ions randomly distributed in the host material and the nonuniformity of the excitation distribution among them. We derive a transcendental equation for the population inversion and find the dependence of the upconversion rate on the population inversion and the pump power for the entire range of feasible Er concentrations. We verify the validity and accuracy of the model by means of time-resolved Monte Carlo simulations.
We report a new analytical method to evaluate the accuracy of a statistical model of the migration assisted upconversion in Er-doped fibres. Unlike the mean-field approach to the excitation back transfer which was used in a previous statistical model, we use a new approximation accounting for the variance of population of the first excited level. Such an approach presents more realistic physical description of the excitation – emission processes in heavily-doped Er-based fibres. Implementing these results, we find that the accuracy of upconversion rate calculations is within 13% if the concentration of erbium ions is smaller than the critical one.
We investigate homogeneous upconversion (HUC) assisted decay of the population inversion in Er-doped silica after delta-pulse excitations by means of Monte Carlo simulations. We derive an analytic expression for this decay when energy migration among Er is negligible and show that it is essentially an extension of the Fo/spl uml/rster-type donor-acceptor quenching decay for the case when donor and acceptor ions are the same species. We compare HUC during the decay to HUC while pumping CW and show that they considerably differ at the low and moderate Er concentrations. Based on Monte Carlo (MC) simulations, we construct a heuristic approximation to the HUC assisted decay, which makes our MC results readily available for the future experimental and theoretical studies and provides simple means for determination of HUC parameters by fitting to experimental data.
From careful studies of the 1530-nm fluorescence decay, we obtain the rate of energy transfer upconversion as a function of the inverted population for a series of nine highly Er-doped silica fibers (with concentrations from 0.3 to 8.6/spl middot/10/sup 25/ Er/sup 3+/-ions per m/sup 3/). The results demonstrate that the slow component (microsecond to millisecond scale) of the upconversion, usually referred to as the homogeneous upconversion, is clearly nonquadratic in its dependence on the inverted population, contrary to previous assumptions in the literature. In a second part, we present a new detailed model for energy transfer upconversion, permitting-to our knowledge for the first time-calculation of the rate of migration accelerated upconversion for any given spatial distribution of Er/sup 3+/-ions. We demonstrate that the results from the decay measurements may be explained with this model. Next, we review the results from a CW green fluorescence detection experiment for the determination of the degree of clustering, which was previously performed on five of the nine fibers. We find accordance between these results and our model, with parameters consistent with those needed to fit the results of the decay experiment, and we arrive at a new conclusion about the nature of clustering.