Determination of reverse cross-relaxation process constant in Tm-doped glass by ^3H_4 fluorescence decay tail fitting

Abstract

International audienceIn this paper, we numerically investigate the fluorescence decay of Tm-doped tellurite glasses with different dopant concentrations. The aim is to find a set of data that allows the prediction of material performance over a wide range of doping concentrations. Among the available data, a deep investigation of the reverse cross-relaxation process (3 F 4 , 3 F 4 ,→ 3 H 6 , 3 H 4) was not yet available. The numerical simulation indicates that the reverse cross-relaxation process parameter can be calculated by fitting the slow decaying 3 H 4 fluorescence tails emitted when the pump level is almost depopulated. We also show that the floor of the 3 H 4 decay curve is indeed related to a second exponential constant, half the 3 F 4 lifetime, kicking in once the 3 H 4 level depopulates. By properly fitting the whole set of decay curves for all samples, the proposed value for the reverse cross-relaxation process is 0.03 times the cross-relaxation parameter. We also comment on the measurement accuracy and best setup. Excellent agreement was found between the simulated and experimental data, indicating the validity of the approach. This paper therefore proposes a set of parameters validated by fitting experimental fluorescence decay curves of both the 3 H 4 and 3 F 4 levels. To the best of our knowledge, this is the first time a numerical simulation has been able to predict the fluorescence behavior of glasses with doping levels ranging from 0.36 mol% to 10 mol%. We also show that appropriate calculations of the reverse cross-relaxation parameter may have a significant effect on the simulation of laser and amplifier devices

Analytical modelling of Tm-doped tellurite glass including cross-relaxation process

“…For this reason in this paper, we present a new analytical model able for the first time, to the best of our knowledge, to consider the direct cross relaxation process. To evaluate the validity of this model we compare it with a set of experimental data and a full numerical model, including the reverse cross-relaxation process [18]. We show that our analytical model is able to fit the first part of the fluorescence decay signal but, as expected, fails when the reverse cross-relaxation process becomes important.…”

“…describe the energy transfer processes: P41 ( 3 H4, 3 H6→ 3 F4, 3 F4) is the cross relaxation constant, which is proportional to doping level [15] The above set of equation is similar to the one used in Ref. [18], without the reverse cross-relaxation phenomenon ( 3 F4, 3 F4→ 3 H6, 3 H4) taken into account, we will assess its impact in section 4.…”

“…The experimental data were reported in details in Ref. [15,18]. Numerical values use in the simulations are listed in Table 1 for the four samples presented, with a doping level ranging from 0.36 mol% to 7 mol%.…”

“…The pump cross section at 790 nm is taken from Ref [15] while the emission cross-section is calculated using Ref [22]. To simulate the pumping condition with non-instantaneous pump power decay, the pump intensity was set to 1.3*10 3 W/cm 2 , assuring a low excitation regime, and pump power decreasing is simulated by using an exponential decay curve with a 2 s time constant [18]. !…”

“…Despite the abundant evidences relating to lifetimes and cross-sections, the parameters associated with ion-ion interactions (i.e., cross-relaxation and the reverse transfer process) [6,[13][14][15][16][17] are more difficult to obtain or cannot be identified in a straightforward manner. For this reason in previous paper we carefully study a set of Tmdoped glass samples [15] with doping level ranging from 0.36 mol% to 10% mol (corresponding to doping levels ranging from 0.82 to 22*10 20 ion/cm -3 ) [6], and calculate the direct [6] and, recently, the reverse cross-relaxation parameters [18] with the results of being able to fit the whole set of samples and to show the impact on pumping efficiency [18]. While numerical modelling is a powerful approach, analytic modelling may lead to better understanding of the system and allow for find for example, intensity noise suppression guidelines allowing effective circuit design or modelling of chaotic behaviour, as done for Er-doped systems [19,20].…”