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IEEE Journal of Quantum Electronics

Upconversion assisted decay of population inversion in Er-doped silica after delta-pulse excitation

Dmitry Khoptyar, Sergey V. Sergeyev, B. Jaskorzyńska

Published Jan 24, 2005• 7 citations
Publisher

Abstract

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.

DOI
10.1109/jqe.2004.839684

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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.
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.
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.
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.
Based on an approach for averaging solution of rate equations over possible ensemble configurations, we derive integral equation for population inversion taking into account nonlinear homogeneous upconversion and migration in Er3+{\mathrm{Er}}^{3+}Er3+-doped silica waveguides for the case of 1480-nm CW excitation switch-off (CWES) regime. Because of pump for CWES is off, only migration tends to refill the holes in excitation distribution caused by upconversion. Thus the upconversion is weaker than that for the CW operation, except for t=0t=0t=0 and $\stackrel{\ensuremath{\rightarrow}}{t}\ensuremath{\infty},$ upconversion.
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.
Measurements of time evolution of amplified spontaneous emission for square-wave modulated pump were made on a highly erbium-doped silica photonic crystal fiber and fitted to theoretical results calculated using different formalisms to describe theEr3+{\rm Er}^{3+}Er3+-ion migration-assisted co-operative upconversion mechanism in the population densities rate equations. The determined characterization parameters are the constant homogeneous upconversion coefficient, 3.0×10−24 m3/s\times 10^{-24}~{\rm m}^{3}/{\rm s}×10−24 m3/s, the critical radii for upconversion and migration, 10.5 and 14Å, respectively, and the rate of clustered ions, 14%. These parameters are analysed and compared to those obtained with continuous-wave pump characterization techniques. Although similar values are obtainable for many parameters using steady-state and dynamic characterization techniques, if a careful enough modelling is carried out, dynamic techniques are preferable to assess the presence of pair-induced quenching.