Temporal dynamics of IR-to-visible up-conversion in LiNbO 3 : Er 3 + / Yb 3 + : a path to phosphors with tunable chromaticity

In this work, a study of the temporal dynamical behavior of IRvisible up-conversion in the LiNbO3: Er/Yb system under modulated IR excitation at 980 nm is presented. It is shown that modulation characteristics, including the relative green-to-red emission ratio (GRR), can be quantitatively explained by using the rate equations formalism. The relevant spectroscopic magnitudes are identified and this provides a general framework to explore the properties of other Er/Yb doped up-converting phosphors. ©2012 Optical Society of America OCIS codes: (160.2540) Fluorescent and luminescent materials; (160.3730) Lithium niobate; (160.5690) Rare-earth-doped materials; (300.6280) Spectroscopy, fluorescence and luminescence; (250.5230) Photoluminescence. References and links 1. N. Tansu, J. Y. Yeh, and L. J. Mawst, “Extremely-low threshold-current-density InGaAs quantum well lasers with emission wavelength of 1215-1233 nm,” Appl. Phys. Lett. 82(23), 4038–4040 (2003). 2. T. Takeuchi, Y.-L. Chang, A. 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In addition, the availability of such high performance IR diode lasers for pumping rareearth doped materials has also driven renewed interest in the preparation of new materials and novel applications which include displays, lasers and amplifiers, optical temperature sensors, biological markers and multiphotonic microscopy [15][16][17][18][19][20][21][22][23].Particularly interesting at the moment is the development of materials with multiple emissions, suitable as biological markers and the control of their chromaticity [16,18,24,25].
Er 3+ /Yb 3+ co-doped materials have attracted particular attention in these applications because of the high absorption cross section of Ytterbium ions at 980 nm, a wavelength readily available with commercial semiconductor diode lasers, together with the efficient Yb 3+ → Er 3+ resonant energy transfer and the subsequent up-conversion processes leading to visible emissions [26][27][28].
Generally, there is the possibility of chromaticity modification through the choice of host and of dopant concentrations, that is, through the synthesis of different phosphors [29][30][31][32].Also, there is an additional possibility of chromaticity tuning within a given phosphor with its given host and concentration of dopants, which relies on the dynamical dependence of the upconversion processes on the duration of the excitation.This idea of tunable phosphors, which may be traced back to the early times of semiconductor design [33], has been revisited recently in other Yb 3+ activated materials [34,35].Nevertheless, the description of this phenomenon is so far mostly qualitative, lacking a quantitative treatment based on the dynamics of the luminescence and energy-transfer processes involved therein.
In order to understand the origin and the relevance of the different parameters involved in this phenomenon, here we present a study of the dynamics of the LiNbO 3 : Er 3+ /Yb 3+ system under 980 nm modulated pumping.The advantage of this material, in addition to its applications in optoelectronic and integrated optics devices, lies in its well-known spectroscopic parameters [26,[36][37][38][39][40], allowing a detailed analysis of the up-conversion dynamics.

Experimental system
Monocrystalline LiNbO 3 : Er 3+ /Yb 3+ was grown by the Czochralski method with automatic diameter control by a crucible weighting system.The starting materials were congruent LiNbO 3 ([Li]/[Nb] = 0.945) and Erbium and Ytterbium oxides with a purity grade of 99.99%.The Er 3+ and Yb 3+ concentrations in the crystal (determined by an X-Ray Fluorescence Technique) were found to be 0.7 and 2.7 mol%, respectively (further details can be obtained from the supplementary information attached to Fig. 1 (Media 1)).Z-cut slices of 1 mm width were cut and polished up to optical grade.
Photoluminescence experiments were performed by using a 980 nm laser diode (LIMO FQ-A0063), allowing the generation of symmetric square pulses.The luminescence signal was dispersed by a SpectraPro 500-i monocromator and detected by a Thorn Emi photomultiplier, QB9558 model.The signal was averaged by using a Keithley 6514 system electrometer and/or a TEKTRONIX TDS 420 oscilloscope.

Emission spectroscopy
It is well known that the 980 nm pumping scheme in Er 3+ /Yb 3+ codoped materials gives rise to two intense visible emission bands in the green and red spectral ranges, associated to the 2 H 11/2 : 4 S 3/2 → 4 I 15/2 and 4 F 9/2 → 4 I 15/2 Er 3+ transitions respectively [15].Figure 1 shows the upconverted emission spectra (normalized to the red emission band) measured in the Er 3+ /Yb 3+ co-doped LiNbO 3 sample, after 980 nm pumping, for two symmetric square pulses of different width (1 ms, dotted black line; 60 ms, continuous red line).As can be seen, the relative intensity of green and red emissions depends on the frequency used to modulate the excitation beam, similarly to previous reports for other Er 3+ /Yb 3+ co-doped materials [34].The inset of Fig. 1 shows the power dependence of the green and red up-converted emissions (in double-logarithmic scale).It is well known [41] that the intensity of upconverted luminescence I UC depends on pump power P as I UC ∝ P n , where n represents the number of photons absorbed in the process.It can be observed that, within the experimental error, both emissions exhibit a quadratic dependence (slope value close to n ≈2) indicating that the IR-to visible energy conversion operates by two-photon processes.
The dependences of green and red emissions on excitation modulation are presented in Fig. 2, where the overall intensities (measured as the area under the emission band) are represented as function of the excitation pulse width.It can be observed that both emissions increase monotonously for short modulation periods, reaching a plateau when the excitation window is sufficiently long.A closer look reveals a faster growth of the green emission, which reaches the saturation plateau before (i.e., at shorter widths than) the red emission.This is a clear indication that the dynamics of up-conversion processes leading to the green and red emissions are different, as shall next be examined in detail.

Population dynamics
The effect of the excitation modulation on the up-conversion properties can be examined considering the different population paths involved in the generation of green and red emissions.
The different lifetimes of the intermediate levels involved in those excitations are responsible for the different modulation-dependent up-conversion properties.
In order to further quantify the up-conversion temporal dynamics, we shall describe it by using the rate equations formalism [15,26,42] incorporating all the above mentioned processes.The temporal evolution of the population densities in the different manifolds is given by the following rate equations: ( )  ( ) where (N i with i = 1, 2, …, 7) represents the population densities in the corresponding levels, as indicated also in Fig. 3.
represent the radiative and non-radiative transition probabilities respectively, associated to the i → j transition, τ i being the experimental lifetime of the i-th level.C ij are the macroscopic energy transfer coefficients.N Er and N Yb are total concentrations of erbium and ytterbium ions and, finally, the R mn represents the pumping rates associated to the m → n transitions which are related to the corresponding absorption cross sections (σ mn ) by: where I exc stands for the excitation intensity.In Eqs. ( 1)- (7), energy transfer processes between Er 3+ ions have not been included, given that their efficiencies are negligible compared to Yb 3+ -Er 3+ ion interactions [36].All the spectroscopic parameters used in the model have been previously reported in the literature, and they are summarized in Table 1.
The population dynamics has been studied by integrating Eqs. ( 1)- (7) assuming that the excitation is modulated in the form of a square shaped pulse of constant amplitude and variable width, Λ (period Τ = 2Λ).Figure 4 represents the temporal evolution of the different population densities (N i ), calculated using a 4th-order Runge-Kutta algorithm, for three different pulse widths: Λ = 300 μs, Λ = 3 ms and Λ = 30 ms.
Figure 4(a) corresponds to the fastest modulation frequency or shortest pulse width: Λ = 300 μs.In this case the pulse width is shorter than the longest-lived Er 3+ excited state, the metastable 4 I 13/2 manifold (Λ = 300 μs << τ 4 ≈ 3 ms), but comparable to or even longer than the natural lifetime of the other relevant Er 3+ or Yb 3+ excited states (see Table 1).Then, the excited states populations are driven by pump modulation which causes the levels to begin to fill up but stopping short of reaching their steady state populations.Also, when the excitation is removed, the system starts to decay, but only partially before a new pump cycle reinitiates the population increase.The fluctuations of these populations are clearly visible in the figure for all the excited states with the only exception of the metastable 4 I 13/2 manifold, due to its much longer characteristic response time.Its population (N 4 ) grows almost steadily towards the saturation (steady state) value with much smaller fluctuations (barely visible in the figure).
Figure 4(c) corresponds to the opposite limit when modulating periods are much longer than the lifetimes of all manifolds, including the metastable one ( 4 I 13/2 ).In this case, the excitation period is long enough to allow all excited states to increase their population reaching the steady state (compare those values with the corresponding values of Fig. 4(a)).Also during the "dark period" the excited manifolds are given enough time to decay, losing practically all their population.The more interesting case, Fig. 4(b), appears in between these two limits, when the excitation time is comparable with the longest lifetime of the system (Λ = 3 ms ≈τ 4 ).In this temporal range, pump modulation results in a dissimilar behavior of long lived or short lived excited Er 3+ levels.For instance, the 2 H 11/2 : 4 S 3/2 manifolds, with a low lifetime value, have enough time to reach the steady state and therefore a constant population before the excitation turn-off occurs.In contrast, the 4 I 13/2 and 4 F 9/2 levels, whose temporal behavior is coupled via the non-resonant energy transfer mechanism 2 F 5/2 → 2 F 7/2 (Yb 3+ ): 4 I 13/2 → 4 F 9/2 (Er 3+ ), cannot achieve constant populations during the excitation window.Therefore, green and red Er 3+ emissions, that originate from the 2 H 11/2 : 4 S 3/2 and 4 F 9/2 manifolds respectively, behave differently under modulated excitation and their intensity ratio can be controlled by changing the excitation pulse width.These differences can be experimentally verified, measuring luminescence intensities under modulated excitation.Figure 5 presents the temporal evolution of green and red emissions, normalized to their maximum value, obtained for two different pulse widths: (a) Λ = 3 ms and (b) Λ = 20 ms.These two ranges correspond to similar situations to these sketched in Figs.4(b) and 4(c) and confirm that in the last case both emitting levels reach their saturation value, while in the former case this happens only for the green emitting levels ( 2 H 11/2 : 4 S 3/2 ) but not for the red emitting manifold ( 4 F 9/2 ), and therefore the relative intensities change with time.The figure includes also (solid lines) the theoretical prediction obtained by integration of Eqs. ( 1)-( 7), using the spectroscopic parameters listed in Table 1 with C 26 as fitting parameter.The best fit was obtained for C 26 ≈0.2 × C 27 , a value of the same order of magnitude but higher than that reported in the literature [40].This value is consistent with the expected concentration dependence of this transfer coefficient [40] and, in fact, the sensitivity of the fitting of the temporal evolution (Fig. 5) indicates that this is a good method for C 26 quantification.It should be noted that the calculation reproduces as well the luminescence decay times of both emissions, as shown in the inset of Fig. 5(b

"Green to Red Ratio"
As indicated above, the relative intensities of green and red emissions under modulated excitation depend on the excitation period.This can be quantified with the ratio between green and red emissions (GRR), which is presented in Fig. 6 as function of modulation frequency (f = 1/2Λ).The red symbols correspond to the experimental data for excitation pulses of between 1 ms and 100 ms width while the solid line represents the calculated values obtained by the rate equations model developed above.In the figure, for comparison purposes, the experimental and the calculated data were normalized to the GRR ratio for CW excitation (infinite pulse width).For low modulation frequencies both green and red emitting levels reach their steady state population values and the luminescence behaves similarly to CW excitation, as expected.But increasing the modulation frequency, as indicated above, the intensity of the red emission starts to decrease, so that the relative green-to-red value increases.The dependence of GRR with modulation frequency (Fig. 6) presents a sigmoid shape (in semilogarithmic scale), reaching a saturation value when the pulse width approaches the longest lifetime of the system (a few milliseconds).It can be observed that the rate equations model correctly reproduces the experimentally observed modulation frequency dependence.This makes it possible to determine that the modulation frequency range where GRR can be modulated corresponds to frequencies slightly below the natural frequency of the longest-lived Er 3+ level, that is, the metastable 4 I 13/2 multiplet, which in LiNbO 3 corresponds to approximately 300 kHz.Fig. 6. Green to red ratio (GRR) as a function of the excitation pulse width.
The GRR value can be increased by a factor 1.4 in LiNbO 3 under modulation, although this figure is obviously dependent on the luminescence properties and spectroscopic characteristics of the material.In the case of LiNbO 3 where the green luminescence is dominant, such increase in GRR implies only a limited change in the chromaticity of the material which remains always within the 'green' region of the chromatic diagram.It seems plausible that in other hosts with stronger Erbium red emission, the increase of GRR with modulation might provide wider color tunability.

Conclusions
We may therefore conclude that LiNbO 3 : Er 3+ /Yb 3+ system, emitting in green and red under Yb 3+ pumping (around 980 nm), shows color-tunability under excitation modulation.This tunability arises from the different temporal response of the up-conversion processes that populate the green ( 2 H 11/2 : 4 S 3/2 ) and red ( 4 F 9/2 ) emitting levels.It is shown that modulation characteristics, including the GRR values, can be quantitatively explained by using the rate equations formalism.This formalism is adequate for any Er 3+ /Yb 3+ activated up-conversion phosphors and should be easily extended to other hosts, provided that the spectroscopic magnitudes that govern the emission dynamics are known.We have also identified the magnitudes needed in the rate equations model, and highlighted the fact that the modulation frequency range is governed by the natural lifetime of the metastable 4 I 13/2 Erbium level to a high extent.
Although the color modulation achievable in LiNbO 3 : Er 3+ /Yb 3+ is limited (being in fact smaller than in other reported systems [34]), it is plausible to suppose that other hosts, with stronger red emission under CW pumping, could provide a wider modulation dependent color tunability.There are a number of Er 3+ /Yb 3+ doped materials where such intense red emission has been reported [45][46][47][48] and are therefore potential candidates for wide color tunability by excitation modulation.

Fig. 1 .
Fig. 1.A comparison of two emission spectra measured using symmetric square pulses of different width: 1 ms (black dotted line) and 60 ms (red solid line) width.The inset shows the power dependence of both emission bands, presented in double logarithmic representation (Media 1).

Fig. 3 .
Fig. 3. Schematic diagram showing the processes involved in the population of the upper Er 3+ manifolds responsible of the green (a) and red (b) emissions, after Yb 3+ excitation at 980 nm.

Fig. 5 .
Fig. 5. Temporal evolution of the green and red luminescence, measured (symbols) and calculated (solid lines) for pulses of 3 ms and 20 ms width, (a) and (b) respectively.