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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

A new statistical model of upconversion in erbium doped fibers

Sergey V. Sergeyev

Published Jun 15, 2007• 0 citations
Publisher

Abstract

Unlike mean-field approach that was used in previous statistical model, in this paper we use a new approximation to excitation back transfer accounting for variance in population of the first excited level. Based on the results, we find that for concentrations of erbium ions more than critical, upconversion rate calculations deviate substantially from the calculations based on simplified model.

DOI
10.1117/12.751980

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Unlike mean-field approach that was used in previous statistical model, in this paper we use a new approximation to excitation back transfer accounting for variance in population of the first excited level. Based on the results, we find that for concentrations of erbium ions more than critical, upconversion rate calculations deviate substantially from the calculations based on simplified model.
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 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.
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.
Applying a nonlinear spectroscopic technique, we accurately monitor the dynamics of the homogeneous upconversion (HUC) in Er-doped fibers. We provide the first experimental confirmation, to our knowledge, of the earlier theoretical predictions that, for low erbium concentrations, a decay of HUC-influenced excitation probability of Er ions can be well approximated by the formula describing the static HUC. By correlating the experimentally obtained HUC dynamics with the results of our analytical model in a wide range of Er concentrations, we accurately estimate energy-transfer parameters for Er-doped silica glass and experimentally assess the validity of the model.
Erbium-doped fiber amplifier(EDFA)efficiency strongly depends on erbium concentration.Highly doped erbium devices show degraded performance when compared with low concentration ones.The mechanism of upconversion is studied and the effect of it on the performance of an EDFA is analyzed numerically,by means of a set of rate equations model.Approximate analytical solutions,for the rate equations,which include the effect of the upconversion,are presented,when the amplified spontaneous emission can be neglected,compared to the pump and signal powers.Results show that the pump and signal powers all bear degradation due to upconversion.,and the effect can't be neglected when the Er3+ concentration is larger than 2.95×1025 m-3.