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IEEE Lasers and Electro-Optics Society Annual Meeting (LEOS)

Concentration dependence of up-conversion quenching rate in Er-doped glass fiber

Н. В. Никоноров, Alexander K. Przhevuskii

Published Nov 22, 2002• 3 citations
Publisher

Abstract

For creation of planar and fiber amplifiers, the up-conversion processes in Er-doped glasses should be taken into account. We consider the up-conversion transition in a pair of Er/sup 3+/ions, when in initial state both the ions are at the /sup 4/I/sub 13/2/level, and in final state one ion is at the /sup 4/I/sub 15/2/ ground level and other at the /sup 4/I/sub 9/2/ level.

DOI
10.1109/leos.1997.645439

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Journal of the Optical Society of America B•Mar 1, 2005•25 citations
For creation of planar and fiber amplifiers, the up-conversion processes in Er-doped glasses should be taken into account. We consider the up-conversion transition in a pair of Er/sup 3+/ions, when in initial state both the ions are at the /sup 4/I/sub 13/2/level, and in final state one ion is at the /sup 4/I/sub 15/2/ ground level and other at the /sup 4/I/sub 9/2/ level.
The dependence of erbium-doped fiber amplifier (EDFA) performance on the erbium ion concentration is studied experimentally and theoretically. The quantum efficiency of the amplifier is found to he strongly dependent on the erbium ion concentration, the signal wavelength, and the relative propagation direction of the pump and signal beams. This dependence is fully explained by the presence of an upconversion mechanism between ions residing in pairs or larger clusters and suggests that other sources of amplifier performance degradation (back-ground loss, excited state absorption, homogenous upconversion) are negligible. The experimental data show that in the present EDFA designs with over 80% quantum/conversion efficiency, the aluminum co-doped fibers with erbium ion concentration less than 20/spl times/10/sup 24/ m/sup -3/ (900 molar ppm Er/sup 3+/) are most suitable.
The effect of homogeneous upconversion on the performance of an erbium-doped fiber amplifier (EDFA) is analyzed numerically, by means of a set of rate equations model. In particular, the influence of pump power, signal power, and Er/sup 3+/ concentration on the degradation, due to upconversion, is examined. Forward pumping is considered and amplified spontaneous emission, as well as scattering loss are taken into account. In addition, approximate analytical solutions, for the rate equations, which include the effect of the cooperative upconversion, are presented. It is shown that under the considered conditions, these analytical solutions provide a good approximation to the exact numerical solution and thus may be used for the design of such amplifiers.
Strong interest in heavily doped erbium-doped waveguides1 and in the applications of heavily doped erbium-doped fibers (EDFs) in lasers has resulted in several recent studies of collective processes in erbium ions. Rapid cross relaxation within a fraction of clustered ions, called pair-induced quenching (PIQ), has been identified as the main cause of EDF performance degradation.2-4 To date, studies on the dependence of EDF performance on ion concentration have been focused on pair/cluster-induced nonsaturable absorption of EDFs,2 which leads to the reduced quantum efficiency (QE) of EDF lasers.4 Recently, detailed theoretical analysis of the effect of PIQ on the performance of erbium-doped fiber amplifiers (EDFAs) has also been reported.4
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.
A study of the complex atomic susceptibility of erbium-doped fiber amplifiers operating near the 1.53- mu m transition (/sup 4/I/sub 13/2/-/sup 4/I/sub 15/2/) developed from a semiclassical theoretical description is presented. Expressions for the emission cross section sigma /sub e/( lambda ) and absorption cross section sigma /sub a/( lambda ) of erbium:glass as a quasi-three-level laser system with Stark-split sublevel manifolds are derived. The results are used to calculate the cross sections of aluminosilicate erbium-doped fibers at low temperatures (T=4.2, 77 K) and at room temperature. It is demonstrated that an expression for the gain coefficient of the fiber amplifier can be derived from the expression of the susceptibility. Using Kramers-Kronig relations, an expression for the refractive index change in the fiber is derived. The theoretical spectral gain profile of the fiber amplifier and concurrent refractive index changes are analyzed for different pumping regimes.>
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.