Analytical model for the intensity dependence of 1500 nm to 980 nm upconversion in Er3+: A new tool for material characterization

Abstract

We propose a simplified rate-equation model for the 1500 nm to 980 nm upconversion in Er 3+ . The simplifications, based on typical experimental conditions as well as on conclusions based on previously published more advanced models, enable an analytical solution of the rate equations, which reproduces known properties of upconversion. We have compared the model predictions with intensity-dependent measurements on four samples with different optical properties, such as upconversion-luminescence yield and the characteristic lifetime of the 4 I 13/2 state. The saturation of the upconversion is in all cases well-described by the model over several orders of magnitude in excitation intensities. Finally, the model provides a new measure for the quality of upconverter systems based on Er 3+ -the saturation intensity. This parameter provides valuable information on upconversion parameters such as the rates of energy-transfer upconversion and cross-relaxation. In the present investigation, we used the saturation intensity to conclude that the differences in upconversion performance of the investigated samples are mainly due to differences in the nonradiative relaxation rates. * brianj@phys.au.dk 1 N. Bloembergen, Phys. Rev. Lett. 2, 84 (1959). 2 F. Auzel, J. Lumin. 31-32, 759 (1984).

Improving the efficiency of upconversion by light concentration using nanoparticle design

“…Such a model was, for example, developed by S. Fischer, et al [17], where a heroic attempt was made to either measure directly or fit indirectly every parameter in a rate-equation model, which then had to be solved numerically for modeling the upconversion process. More recently, we developed an analytical model, which involved a number of approximations and reached a set of simple expressions that describes the upconversion process well [18]. In the present subsection, the main equations of this analytical modeling will be stated together with a discussion of the results and their relation to an efficient upconversion device.…”

Strongly enhanced upconversion in trivalent erbium ions by tailored gold nanostructures: Toward high-efficient silicon-based photovoltaics

“…Second, together with the ζ-parameter the concentration factor can be interpreted as a lowering of the saturation intensity by the factor ζ/C ns , and as a result, the saturation intensity approaching the ideal excitation condition of I ≈ 10I sat , suggested in Ref. [19]. Nevertheless, the impressive C ns -factor reported in this article is still not enough for a working solar-cell device with currently available erbium-based upconverters.…”

“…This excitation intensity is roughly four orders of magnitude lower than the desired excitation regime for a TiO 2 :Er upconverter. Even if we had chosen the more efficient upconverter system of NaYF 4 :Er, with a significantly lower saturation intensity [19], we are still between one and two orders of magnitude short in concentration factor. This estimate is even assuming that we could achieve similar photonic concentration in the NaYF 4 , which is highly unlikely due to the smaller refractive index limiting the waveguiding efficiencies [31].…”

“…For two-photon upconversion, the upconversionintensity dependence will saturate from a quadratic depen-dence in the low-excitation limit toward a linear dependence in the high-excitation limit [18]. In a recent paper [19], we have shown that for a bare upconverting film the intensity dependence of the UCL yield, Y UCL , is given by…”

Experimental validation of a modeling framework for upconversion enhancement in 1D-photonic crystals

“…A detailed overview can be found in the Supplementary Tables 1-4. Also detailed understanding of plasmonic enhancement effects are of major interest in various areas of application [47][48][49] . However, the theoretical understanding of how photonic effects influence UC and its implementation in simulation models is mostly lacking.…”