Upconversion Power Dependence

The energy- and time-dependence of an upconversion process are extremely useful for identification of the upconversion mechanism. A third variable parameter that has received relatively little attention is the excitation power. It is often stated in the literature that two-photon excitation processes such as upconversion must follow a quadratic power dependence, or more generally. 

To understand the origin of such behavior, we consider the power dependence of the rate equations presented in Eq. (10) [26-28]. Since the 100% sample in Fig. 8 c shows pure GSA/ETU behavior, we consider the power dependence of 

under low-power excitation conditions, the GSA/ETU intensity has the quadratic power dependence commonly discussed in the Hterature. 

As the excitation power is increased, the upconversion rate WetuI increases much more rapidly than does kiNi, and above a certain power the high-power limiting condition of kiNi 2 WetuI i be reached. At this power, upconver- 

under high-power excitation conditions the GSA/ETU intensity no longer shows a quadratic power dependence, but rather increases with a linear dependence on power. The intermediate level population increases as the square root of the power. Note that although this behavior resembles a saturation effect, it does not derive from depletion of the ground-state population due to high exci- 

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Two regimes in the upconversion power dependence, with an extremely nonlinear intensity jump when pump powers rise above a certain critical threshold... 

Thus, whereas GSA/ESA upconversion luminescence under low-power conditions shows the anticipated quadratic power dependence, that observed under high-power excitation conditions is expected to show only a linear dependence on pump power, exactly as in the GSA/ETU case (Eqs. 15 and 18). The intermediate-level population in a GSA/ESA system, however, remarkably becomes independent of changes in power at high powers when 2 = 2a (Eq. 21), in contrast with the high-power P behavior of the intermediate-level population in the GSA/ETU mechanism (Eq. 17). When ki = 25 GSA/ESA process the high... 

An extremely unusual power dependence has been observed in the cooperative upconversion luminescence of Yb -doped Cs3Lu2Br9 and related systems [57-61]. As illustrated by the 7.5 K power-dependence data in Fig. 14a, b, increasing the excitation power from the low-power excitation limit results in a sharp jump in both VIS and NIR luminescence intensities at a certain critical power. Reversing the direction of the power sweep also results in a sharp jump on the return path, but this jump occurs at a lower power than the forward jump, resulting in a hysteresis behavior with a distinct region of bistability. Monitoring the transmission of the laser beam shows that the absorption of the sample also increases and decreases at these same critical powers (Fig. 14a, inset) [62]. The properties of this jump are clearly dependent upon temperature, with smaller jumps observed at lower excitation powers as the temperature is elevated (Fig. 14). 

The pump photons are therefore only required to be resonant with B D. One characteristic of PA is a power threshold above which the emission intensity increases by orders of magnitude. The Ln ion concentration needs to be sufficiently high for efficient ETU. Whereas many examples of the PA phenomenon exist in the hterature, only raie study has been made for elpasoUte systems, for Cs2NaGdCl6 Tm, where the upconverted emission is due to the G4 transition at 480 nm [135]. The situation is rather more complex than in Fig. 9 because several other processes can occur, which lead also to emission from D2. A quadratic emission G4 intensity-excitation power dependence was obtained at low excitation intensities for samples of Cs2NaGdCl6 doped between 6 and 15 mol % Tm ". However, a dramatic increase of the emission intensity appears above the excitation threshold value, 9 kW cm . The slope of the log /gm versus log P increases to 6 for the 10 mol% Tm -doped sample. The time dependence of the upconverted emission exhibits different behavior at different excitation powers. At the threshold excitation power, the upconversion emission has an almost linear risetime which is followed by a further slower rise over several seconds. At high excitation powers, the establishment of the stationary state is quicker, and the F4 —> G4 ESA decreases the transmitted laser light by several percent. 

Pollnau M, Gamelin DR, Liithi SR, Giidel HU (2000) Power dependence of upconversion luminescence in lanthanide and transition metal systems. Phys Rev B 61 3337-3346... 

The demonstration of linear incident power dependence for upconversion process using both coherent and noncoherent light sources ... 

To determine fully the kinetic parameters governing upconversion using Eq. (10) it is imperative to know the laser-induced excitation densities, Nj and N2, in steady state, or Mi(0) and 2(0) in time-dependent studies. These parameters may be determined from careful measurement of the physical properties of the sample, the excitation configuration, and the experimentally absorbed power. These numbers are not easily reliably determined, however, and they are therefore more commonly estimated or taken as experimental unknowns in the use of these equations for simulations. The difficulty with which absolute excitation densities are determined is one of the practical limitations of this rate equation model. 

Frequency upconversion of 800 nm ultrashort 175 fs optical pulses by two-photon absorption in a stilbenoid compound-doped polymer (PMMA) optical fiber was reported [28]. By the intensity-dependent transmission method, the two-photon absorption cross section was deduced. The combination of a well-designed organic chromophore incorporated into a fiber geometry is appealing for the development of an upconversion blue polymer laser. Upconversion fluorescence and optical power limiting effects based on the two- and three-photon absorption process of a frans-4,4 bis(pyrrolidinyl)stilbene were investigated [29]. The molecular TPA cross section three-photon absorption (3PA) cross section g3 at 720-1000 nm were measured. The 3PA-induced optical power-limiting properties were also illustrated at 980 nm. 

A clear example of three-body upconversion is the Do Fj Eu " emission in Y2O3 rEu ", Yb upon 970 nm laser diode excitation into the %/2 multipletof Yb [145]. The schematic energy level diagram is shown in Fig. 13a, where the lowest F5/2 and Di energies are (in cm ) 10,225 and 18,937, respectively. The two-photon namre of the process is confirmed by the emission intensity-laser power plot in Fig. 13b. It is observed that the Eu " emission intensity increases considerably with temperature in the range from 10 K up to room temperature (Fig. 13c) and this was accounted for by two simulations. One of these simulations was based upon the thermalization of the Fi levels of Eu ", whereas the alternative simulation focused on the dependence of upconversion rate upon temperature [145]. 

Fig. 13 (a) Schematic diagram of Yb -Eu cooperative upconversion mechanism (b) log-log dependence of Dq — p2 transition intensity upon excitation power (c) temperature dependence... 

Yang Y, Tu LP, Zhao JW, Sun YJ, Kong XG, Zhang H (2009) Upconversion luminescence of beta-NaYp4 Yb, Er beta NaYp4 core-shell nanoparticles excitation power, density and surface dependence. J Phys Chem C 113 7164-7169... 

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