From the up-converting multimodal luminescent thermometer to ratiometric visual power density meter based on Er³⁺,Yb³⁺ emission

Abstract

This study demonstrates that thermally induced variations in the spectroscopic properties of Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ can be effectively harnessed for multimodal remote temperature sensing. As shown, Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ supports multiple ratiometric sensing modes based on the intensity ratios of (i) ²H_11/2 → ⁴I_15/2 and ⁴S_3/2 → ⁴I_15/2; (ii) ²H_9/2 → ⁴I_13/2 and ⁴S_3/2 → ⁴I_15/2; and (iii) green-to-red emission intensity ratio, achieving maximum relative sensitivities of 2.8% K⁻¹, 3% K⁻¹, and 1.8% K⁻¹, respectively. The synergy between thermal changes observed in the green-to-red emission intensity ratio of Er³⁺ ions, combined with the efficient optical heating of Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ at elevated Yb³⁺ concentrations enables the development of a visual optical power density sensor, exhibiting relative sensitivities of S_Rx = 1.0% W⁻¹ cm² and S_Ry = 0.9% W⁻¹ cm² at 15 W cm⁻² when quantified using CIE 1931 chromaticity coordinates. To the best of our knowledge, this is the first report of a visual luminescent optical power density sensor. Furthermore, it was demonstrated that Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ can be successfully applied for two-dimensional imaging of optical power density, thereby enabling spatial visualization of power distribution within an illuminated field.

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New concepts

In this work, we present not only the exceptional thermometric capabilities of the up-converting Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ phosphor, enabling multi-modal and complementary temperature sensing but, more importantly, we introduce a novel application of these thermal properties for optical power density sensing. By leveraging the synergy between optically induced heating and the resulting thermally driven color changes in the emitted luminescence, we have developed the first visual optical power density sensor based on up-conversion phosphors reported to date. Crucially, this approach enables spatial imaging of optical power density using a standard digital camera, without the need for additional optical filters or complex instrumentation. This simplicity, combined with the high sensitivity and visual nature of the response, marks a significant advancement in the field of luminescent sensing. We believe that the strategy presented here not only expands the functional versatility of up-converting materials but also opens new avenues for their application in optical diagnostics, beam profiling, and remote sensing technologies.

Introduction

Up-converting phosphors co-doped with Er³⁺ and Yb³⁺ ions have garnered significant attention in recent years, primarily due to their potential applications in remote temperature sensing.^1–10 This capability arises from the thermal coupling between the ²H_11/2 and ⁴S_3/2 energy levels of Er³⁺ ions.^11,12 According to the Boltzmann distribution, an increase in temperature enhances the relative population of the ²H_11/2 level compared to the ⁴S_3/2 level.^11,13 The resulting temperature-dependent luminescence intensity ratio (LIR) between emissions from these levels offers a theoretically predictable thermometric parameter, representing a key advantage for quantitative temperature readout. However, the close spectral overlap of the ²H_11/2 → ⁴I_15/2 and ⁴S_3/2 → ⁴I_15/2 transitions necessitates the use of bandpass filters for effective thermal imaging.

In this study, we present results for Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺, a material in which, alongside the typical Er³⁺-related ²H_11/2 → ⁴I_15/2, ⁴S_3/2 → ⁴I_15/2, and ⁴F_3/2 → ⁴I_15/2 emission bands, additional luminescence corresponding to the ²H_9/2 → ⁴I_13/2 transition was detected. This emission results from a three-photon excitation process, enabling population of the ²H_9/2 state. The unique population dynamics in Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ support three distinct temperature readout strategies – LIR between: (i) ²H_11/2 → ⁴I_15/2 and ⁴S_3/2 → ⁴I_15/2; (ii) ²H_9/2 → ⁴I_13/2 and ⁴S_3/2 → ⁴I_15/2; and (iii) green-to-red emission intensity ratio. These approaches provide application-specific flexibility in thermometric performance. Notably, the third method enables direct visual temperature indication, as increasing temperature enhances green up-conversion emission with respect to red one, producing a perceptible thermal color shift in the emitted light. Furthermore, the 980 nm excitation light absorbed by Yb³⁺ ions induces optical heating of the Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ material, with efficiency increasing with sensitizer (Yb³⁺) concentration.

As demonstrated in previous studies, the combination of optical heating with luminescence thermometry enables the development of luminescence-based sensors for excitation power density. Earlier approaches have primarily exploited either Er³⁺ (luminescence intensity ratio of emission bands corresponding to the ²H_9/2 → ⁴I_15/2 to ²H_9/2 → ⁴I_13/2 or ²H_11/2 → ⁴I_15/2 to ⁴S_3/2 → ⁴I_15/2 electronic transitions)^14,15 ions or the thermal coupling between ²E_g and ⁴T_2g levels of Cr³⁺ ions.^16,17 In both cases, ratiometric readout of the optical excitation power density was achieved by monitoring thermally induced variations in a suitably defined luminescence intensity ratio (LIR). However, a major limitation of these earlier strategies lies in the close spectral proximity of the emission bands employed for LIR determination. This necessitates either measurement of the full emission spectrum or the use of specialized optical luminometers to access the optical power density, which significantly complicates two-dimensional imaging of its spatial distribution.

In this work, we propose a different approach, based on modifying the up-conversion ratio of green and red luminescence bands emitted by Er³⁺ ions. While the use of the green-to-red emission ratio of Er³⁺ for luminescence thermometry has been reported for a variety of host materials,^18–25 here we demonstrate how the synergy between optical heating and the pronounced difference in the up-conversion orders for the green (²H_9/2 → ⁴I_13/2, ²H_11/2 → ⁴I_15/2 and ⁴S_3/2 → ⁴I_15/2) and red (⁴F_9/2 → ⁴I_15/2 electronic transition) emissions in Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ enables direct color tuning of the emitted light as a function of excitation power density. This phenomenon provides the basis for the development of a visual luminescence-based optical power density sensor for 980 nm excitation, offering not only quantitative sensing but, importantly, also two-dimensional imaging of the optical power density distribution. As demonstrated, a standard digital camera and analysis of green and red channel signals, enables visualization of the spatial distribution of 980 nm beam intensity without additional optical filters, providing a simple, rapid and filter-free approach to optical power density mapping.

Experimental section

Synthesis

Powder samples of Na₃Sc₂(PO₄)₃:Er,0.5%,x%Yb³⁺, (where x = 5, 10, 15, 30) were synthesized using a conventional high-temperature solid-state reaction technique (exact amount of precursors used in the synthesis of phosphors are given in Table S1). Na₂CO₃ (99.9% of purity, Alfa Aesar), Sc₂O₃ (99.9% of purity, Alfa Aesar), NH₄H₂PO₄ (99.9% of purity, POL-AURA), Er₂O₃ (99.999% of purity, Stanford Materials Corporation) and Yb₂O₃ (99.999% of purity, Stanford Materials Corporation) were used as starting materials. The stoichiometric amounts of reagents were finely ground in an agate mortar with a few drops of hexane and then annealed in the alumina crucibles at 1573 K for 5 h (heating rate of 10 K min⁻¹) in air. The final powders were allowed to cool naturally to room temperature and then ground again to obtain powder samples for structural and optical characterization.

Characterization

The obtained materials were examined using powder X-ray diffraction. Powder diffraction data were obtained in Bragg-Brentano geometry using a PANalytical X’Pert Pro diffractometer using Ni-filtered Cu Kα radiation (V = 40 kV, I = 30 mA).

Differential scanning calorimetric (DSC) measurements were performed using a PerkinElmer DSC 8000 calorimeter equipped with controlled liquid nitrogen accessory LN2 with a heating/cooling rate of 20 K min⁻¹. The sample was sealed in an aluminum pan. Measurements were performed for the powder sample in the 100–800 K temperature range. The excitation spectra were obtained using the FLS1000 fluorescence spectrometer from Edinburgh instruments equipped with a 450 W Xenon lamp and R928 photomultiplier tube from Hamamatsu as a detector. Emission spectra were measured using the same system with 980 nm laser diodes as the excitation source. During the temperature-dependent emission measurements, the temperature of the sample was controlled using a THMS600 heating–cooling stage from Linkam (0.1 K temperature stability and 0.1 K set point resolution). Luminescence decay profiles were also recorded using the FLS1000 equipped with 150 W μFlash lamp.

To obtain the images, photographs were taken using a Canon EOS 400D camera equipped with an EFS 60 mm macro lens and a 750 nm short-pass optical filter (Thorlabs). Luminescence images were acquired under 980 nm laser excitation. The temperature of the samples was determined using a FLIR T540 thermographic camera, providing a measurement accuracy of ±0.5 K. The red and green channels (RGB) were extracted from the photographs using IrfanView 64 4.51 software, and the R and G intensity maps were subsequently processed and divided using ImageJ 1.8.0_172 software.

Results and discussion

Na₃Sc₂(PO₄)₃ – a member of the NASICON (sodium superionic conductor) family of compounds – is reported to exist in three different crystallographic structures.^26–30 The specific structure in which Na₃Sc₂(PO₄)₃ crystallizes depends on synthesis conditions, ionic substitution schemes, and external stimuli such as temperature.^26–36 In general, temperature-induced reversible phase transitions have been widely reported: upon heating, the monoclinic α-phase with space group Bb transforms into the β phase at approximately 320 K, and subsequently into the γ phase at around 440 K, both of which adopt a trigonal structure with space group R3̄c (Fig. 1).^28,30 This behavior was confirmed by differential scanning calorimetry (DSC) analysis performed for Na₃Sc₂(PO₄)₃ sample co-doped with 5%Yb³⁺ and 0.5%Er³⁺ ions (Fig. S1), where a reversible phase transition was observed at approximately 340 K. However, one important factor influencing the structure of Na₃Sc₂(PO₄)₃ is ionic substitution. This phenomenon has been demonstrated in the case of Na₃Sc₂(PO₄)₃ host ions substitution by lanthanide ions.^28,29,35 For instance, it has been shown that increasing concentrations of Eu²⁺ and Eu³⁺ ions induce a transition from a monoclinic to a trigonal structure.³⁵ A similar effect is observed in the present study for Yb³⁺ and Er³⁺ co-doping, as evidenced by the XRD patterns measured (results of Rietveld refinement of the XRD patterns are shown in Fig. S2–S4). For Yb³⁺ concentrations of 5% and 10% (with constant Er³⁺ concentration of 0.5%), a monoclinic phase at room temperature was obtained, while at 15%, a gradual transition toward a trigonal phase occurred, resulting in a mixed monoclinic-trigonal phase composition. In contrast, the sample with 30% Yb³⁺ at room temperature is dominated by the trigonal phase. Furthermore, the XRD measurements confirmed that the incorporation of up to 30% Yb³⁺ does not lead to the formation of impurity phases or structural defects. Additionally, no evidence of this phase transition was observed for this sample in the DSC analysis (Fig. S6). The difference in the ionic radii between Yb³⁺ (R ≈ 0.868 Å) and Er³⁺ (R ≈ 0.89 Å) replacing Sc³⁺ (R ≈ 0.745 Å),³⁷ lead to a contraction of the unit cell with an increase in the Yb³⁺ concentration as reflected in the shift of the diffraction reflections toward larger 2theta angles.

Fig. 1 Visualization of the structure of the monoclinic and trigonal phases of Na₃Sc₂(PO₄)₃ (a); the comparison of room temperature XRD patterns of Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ with different Yb³⁺ concentration (b).

The up-conversion properties of Er³⁺,Yb³⁺-doped systems have been extensively studied;^12,38–48 therefore, only a simplified description is provided here. In these systems, Yb³⁺ ions act as sensitizers by absorbing excitation radiation (λ_exc = 980 nm) and transferring energy to Er³⁺ ions, which serve as acceptors (Fig. 2a). Although the excitation energy matches the gap between the ⁴I_15/2 and ⁴I_11/2 states of Er³⁺, the larger absorption cross-section of Yb³⁺ and the longer lifetime of its ²F_5/2 state favor energy-transfer up-conversion. The initial transfer from Yb³⁺ to Er³⁺ is followed by a second one that populates the ⁴F_7/2 level, which relaxes nonradiatively to the ⁴S_3/2 and, via thermalization, to the ²H_11/2 level. While this is the mechanism most often reported, Berry and May⁴² showed that a subsequent transfer may promote electrons from ⁴S_3/2 to ²D_5/2, which relaxes to ²H_9/2, yielding emission bands near 410 nm (²H_9/2 → ⁴I_15/2) and 575 nm (²H_9/2 → ⁴I_13/2). Radiative relaxation from ⁴S_3/2 and ²H_11/2 produces emissions at 550 and 520 nm, respectively. Because these levels are thermally coupled, higher temperatures shift the population toward ²H_11/2, reducing the ⁴S_3/2 population and thereby decreasing ²H_11/2 luminescence.

Fig. 2 Schematic energy levels diagram of the Yb³⁺–Er³⁺ ions (a); comparison of room-temperature emission spectra (λ_exc = 980 nm, 20 W cm⁻²) of Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ with different Yb³⁺ concentrations (b); green-to-red emission intensity ratio (c); and CIE1931 chromaticity coordinates with corresponding photographs of up-conversion emission of Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ with different Yb³⁺ concentrations (d).

The ⁴F_9/2 level may be populated by multiphonon relaxation from ⁴S_3/2 or via nonradiative relaxation from ⁴I_11/2 to ⁴I_13/2 followed by photon absorption. The latter dominates in hosts with high phonon energy, weak Yb³⁺–Er³⁺ transfer (large interionic distance), or low excitation density. Both mechanisms may operate concurrently, with relative contributions depending on conditions. Radiative depopulation of ⁴F_9/2 gives the red emission (⁴F_9/2 → ⁴I_15/2) (Fig. 2b). Since transfer efficiency depends strongly on interionic distance, the spectroscopic properties of Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ were studied across samples with varying Yb³⁺ content (Fig. 2c). Room-temperature spectra consistently revealed four emission bands at ∼525, 550, 575, and 670 nm, consistent with the transitions above. The 575 nm (²H_9/2 → ⁴I_13/2) band confirms the three-photon process. Although the band positions remain constant with Yb³⁺ content, the green emission intensities increase relative to red with higher Yb³⁺ concentration, reflecting more efficient population of higher Er³⁺ levels. The green-to-red intensity ratio rises monotonically from ∼0.2 for 5% Yb³⁺ to ∼0.4 for 30% Yb³⁺, accompanied by a visible color change from orange (5% Yb³⁺) to greenish (30% Yb³⁺) (Fig. 2d).

To evaluate the influence of temperature on the up-conversion luminescence behavior of Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺, their temperature-dependent luminescence spectra were recorded over the range 83 K to 603 K. Representative spectra (Fig. 3a) for Na₃Sc₂(PO₄)₃:0.5%Er³⁺,5%Yb³⁺ reveal that at 83 K, the emission is predominantly composed of bands corresponding to the ⁴S_3/2 → ⁴I_15/2, and ⁴F_3/2 → ⁴I_15/2 transitions, with a weak signal also observed from the ²H_9/2 level (see also Fig. S7–S10). As the temperature increases, a general decrease in the intensity of all emission bands is noted; however, the most pronounced changes occur within the green spectral region (Fig. 3b). Notably, the ²H_9/2 → ⁴I_13/2 band shows a distinct thermal response, with its intensity increasing up to a maximum at approximately 250 K, followed by a progressive decline. Above ∼450 K, the intensity of this band becomes negligible. Interestingly, the temperature range over which the ²H_9/2 → ⁴I_13/2 band diminishes corresponds closely with the thermal activation of the ²H_11/2 → ⁴I_15/2 band. Concurrently, the intensity of the ⁴S_3/2 → ⁴I_15/2 band begins to decrease, reflecting thermal coupling between the ²H_11/2 and ⁴S_3/2 levels. Beyond 480 K, the emission band corresponding to the ²H_11/2 → ⁴I_15/2 electronic transition dominates the green region of the spectrum. To further assess these variations, the integral intensities of individual Er³⁺ emission bands were quantified as a function of temperature (Fig. 3c). For a sample doped with 5% Yb³⁺, the ⁴F_9/2 → ⁴I_15/2 band has stable intensity up to ∼350 K, after which it begins to decline. In contrast, the ⁴S_3/2 → ⁴I_15/2 and ²H_9/2 → ⁴I_13/2 bands exhibit thermal enhancement up to ∼350 K, followed by a decrease in emission with further temperature increase. The most significant enhancement is observed for the ²H_9/2 → ⁴I_13/2 band, whose intensity at 250 K is approximately five times higher than at 83 K. The emission intensity of the band corresponding to the ²H_11/2 → ⁴I_15/2 transition exhibits a sharp rise in intensity up to ∼300 K, after which it continues to increase, albeit at a reduced rate.

Fig. 3 Emission spectra of Na₃Sc₂(PO₄)₃:Er³⁺,5%Yb³⁺ measured as a function of temperature (λ_exc = 980 nm, 20 W cm⁻²) (a); and the corresponding thermal map of normalized emission spectrum (each spectrum normalized to its maximal intensity value) shown in the 500–580 nm spectral range (b); and the influence of the temperature on the normalized (normalization to the value of the emission intensity obtained at 83 K) integrated emission intensities of Na₃Sc₂(PO₄)₃:Er³⁺,5%Yb³⁺ for different emission bands of Er³⁺ ions (c).

Power-dependent studies of up-conversion emission intensity provide critical insights into the population mechanisms of the excited states of Eu³⁺ ions involved in the up-conversion process. According to the methodology proposed by Pollnau et al.,³⁸ within the low optical excitation power density regime, the luminescence intensity (I) follows a power-law relationship with the excitation power density (P):

I ∼ P^N (1)

where, N refers to the process order and denotes the number of photons involved in populating the emitting state. It is essential to perform such analyses under low power density conditions, as higher excitation densities can lead to saturation effects that artificially lower the observed process order. To investigate these dynamics, the dependence of up-conversion luminescence intensity on optical power density was measured for Na₃Sc₂(PO₄)₃:0.5%Er³⁺,5%Yb³⁺ and Na₃Sc₂(PO₄)₃:0.5%Er³⁺,30%Yb³⁺ (Fig. 4a, see also Fig. S11 and S12). The results clearly show an increase in emission intensity with rising power density. Notably, the green emission bands exhibit a steeper increase than the ⁴F_9/2 → ⁴I_15/2 emission band. For instance, the integrated intensity of the ⁴S_3/2 → ⁴I_15/2 band for a sample containing 5% Yb³⁺ yields a process order N = 2.95, with a decline observed beyond ∼50 W cm⁻², indicating saturation (Fig. 4b). When the Yb³⁺ concentration is increased to 30%, N for the same band decreases to 2.3, suggesting enhanced energy transfer efficiency due to reduced interionic distances. Similarly high process order values are obtained for the ²H_9/2 → ⁴I_13/2 emission band, where N ≈ 3, confirming its three-photon excitation origin, consistent with the high energy of this excited level (Fig. 4c). While the ⁴S_3/2 level is generally associated with two-photon excitation as reported in the literature,^12,39–41 the present results indicate an unusual three-photon process under low Yb³⁺ concentrations.⁴² However, a higher concentration of Yb³⁺ ions – for which the interionic distance between sensitizer and activator is shortened – facilitates the Yb³⁺ → Er³⁺ energy transfer, transitioning the population scheme to a conventional two-photon mechanism. In contrast, the ⁴F_9/2 level displays an N value close to 2 across all concentrations, suggesting a consistent two-photon excitation mechanism, largely independent of sensitizer ion concentration (Fig. 4d). These findings collectively elucidate the nuanced dependence of up-conversion dynamics on dopant concentration and excitation conditions. It is worth noting that the difference in up-conversion order between the emission bands in the green spectral region and red one becomes particularly evident above approximately 50 W cm⁻² (N = 1.07 for the ⁴S_3/2 level and N = 0.49 for the ⁴F_9/2 level for 30% Yb³⁺). This disparity is even more pronounced across the entire range of optical power densities analyzed for the ²H_9/2 → ⁴I_15/2 band, clearly indicating a stronger increase in luminescence intensity within the green spectral region compared to the red. When considering the total luminescence intensity from all green emission bands (Fig. S13), it can be shown that above 50 W cm⁻² the green emission intensity for 30% Yb³⁺ increases at approximately twice the rate of the red emission, as the excitation density rises. This distinct difference in the growth rates of green and red luminescence, stemming from the population mechanisms of the emitting levels in Na₃Sc₂(PO₄)₃:0.Er³⁺,Yb³⁺, provides a robust basis for the development of a luminescence-based optical power density meter, as will be discussed further.

Fig. 4 Room temperature emission spectra of Na₃Sc₂(PO₄)₃:Er³⁺,30%Yb³⁺ measured as a function of power densities of λ_exc = 980 nm (a); the log–log plots of emission intensities as a function of excitation density for emission bands corresponding to the ⁴S_3/2 → ⁴I_15/2 (b); ²H_9/2 → ⁴I_13/2 (c) and ⁴F_9/2 → ⁴I_15/2 (d), electronic transitions of Er³⁺ ions for Na₃Sc₂(PO₄)₃:Er³⁺,5%Yb³⁺ (green points) and Na₃Sc₂(PO₄)₃:Er³⁺,30%Yb³⁺ (orange points).

In ratiometric luminescence thermometry, achieving high temperature sensitivity relies on selecting emission bands that exhibit opposite thermal monotonicity. The analysis of the temperature dependence of the individual Er³⁺ emission bands, as presented in Fig. 3c, reveals several such band pairs. Among them, the emission bands associated with the depopulation of the well-established thermally coupled ²H_11/2 and ⁴S_3/2 levels are particularly notable.^10,11 The thermal evolution of their emission intensities, shown in Fig. 5a and b, demonstrates that the ²H_11/2 → ⁴I_15/2 band intensity increases monotonically with temperature across the entire studied range. Notably, this increase is most pronounced at low Yb³⁺ concentrations and approximately a 40-fold enhancement of its emission intensity for 5% Yb³⁺ was observed compared to a 20-fold increase at 30% Yb³⁺. A minor deviation from the general trend of these curves is observed around 330 K, which likely corresponds to a structural phase transition discussed earlier. In contrast, the ⁴S_3/2 → ⁴I_15/2 band displays a non-monotonic trend (Fig. 5b). At low Yb³⁺ concentrations, its intensity initially increases with temperature up to ∼250 K, followed by a gradual decrease. This thermally activated enhancement diminishes with increasing Yb³⁺ concentration, and at 15% Yb³⁺, a monotonic decline in emission intensity is observed throughout the temperature range. These findings indicate that at low Yb³⁺ doping levels, both levels are highly responsive to temperature fluctuations. The initial enhancement of the intensity of the ⁴S_3/2 → ⁴I_15/2 emission suggests the involvement of thermally activated (likely phonon-assisted) processes in its population. The probability of phonon-assisted processes increases with temperature. However, above 250 K, some decrease in the emission intensity with further temperature increase can be observed for phosphors with low Yb³⁺ concentration. The observation that the magnitude of this thermally induced luminescence enhancement below 250 K decreases with increasing Yb³⁺ concentration indicates that the effect is related to energy transfer between Er³⁺ and Yb³⁺ ions. At higher Yb³⁺ concentrations, the average distance between interacting ions is reduced, leading energy diffusion between Yb³⁺–Yb³⁺ to dominate over phonon-assisted processes. A very similar effect of thermally and Yb³⁺ concentration dependent interplay between interionic energy transfers in Yb³⁺, has recently been reported for Na₃Sc₂(PO₄)₃:0.1%Yb³⁺.⁴³ This interpretation is further supported by the observed reduction in the power dependence parameter N for the ⁴S_3/2 → ⁴I_15/2 band at elevated Yb³⁺ ions concentration. The ratio of the emission intensities from the ²H_11/2 → ⁴I_15/2 and ⁴S_3/2 → ⁴I_15/2 levels (LIR₁) is defined as:

If these levels remain thermally coupled, the ratio should follow a Boltzmann-type dependence.¹¹ Indeed, as shown in Fig. 5c, the natural logarithm of LIR₁ exhibits a linear relationship with the inverse of temperature (1/T) in the range 0.002 to 0.010 K⁻¹. Remarkably, the slope of this linear relationship remains nearly constant across all Yb³⁺ ions concentrations, confirming that thermal coupling is preserved and the energy separation between the two levels remains unaffected by doping concentration. This consistency implies that the observed differences in temperature dependence are attributed primarily to variations in the population mechanisms of the levels, rather than to alternative depopulation pathways or energy transfer processes. The performance of this thermometric approach is quantified by the relative sensitivity, defined as:

The calculated values of S_R1 are similar across all Yb³⁺ concentrations, with sensitivities decreasing from approximately 2.8% K⁻¹ at 200 K to 0.8% K⁻¹ at 300 K, and further to 0.4% K⁻¹ at 550 K (Fig. 5d, corresponding thermal dependence of absolute sensitivity is shown in Fig. S14). These results highlight the reliability and robustness of the ratiometric approach based on ²H_11/2 → ⁴I_15/2 to ⁴S_3/2 → ⁴I_15/2 bands in Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ for temperature sensing applications over a broad temperature range and various sensitizer concentrations.

Fig. 5 Thermal dependence of normalized (normalization to the value of the emission intensity obtained at 83 K) integral emission intensities of emission bands (λ_exc = 980 nm, 20 W cm⁻²) corresponding to the ²H_11/2 → ⁴I_15/2 (a), and ⁴S_3/2 → ⁴I_15/2 (b), electronic transitions of Er³⁺ ions for different dopant concentration of Yb³⁺ ions; LIR₁ as a function of 1/T (c); and corresponding thermal dependence of S_R1 (d).

As previously demonstrated, the intensity of the ²H_9/2 → ⁴I_13/2 emission band also increases with rising temperature; however, this enhancement is observed only up to approximately 250 K. Beyond this point, further temperature increases result in a gradual decline in luminescence intensity. Similar to the behavior of the ²H_11/2 → ⁴I_15/2 band, the thermal enhancement of the ²H_9/2 → ⁴I_13/2 band decreases with increasing Yb³⁺ ion concentration, suggesting that this effect is closely linked to the mechanism of level population. Nevertheless, a comparative analysis of the thermal growth rates of the ²H_9/2 → ⁴I_13/2 (Fig. 6a) and ⁴S_3/2 → ⁴I_15/2 emission bands (Fig. 6b) reveals that their intensity ratio (LIR₂) can be employed for ratiometric temperature sensing:

As shown, LIR₂ exhibits a consistent thermal trend across all Yb³⁺ concentrations, rising with temperature up to ∼275 K, followed by a decline (Fig. 6c). Since reliable temperature readout in ratiometric luminescence thermometry requires monotonic variation of LIR, this inflection limits the applicable thermal range of LIR₂-based sensing to a maximum of ∼275 K. This behavior is further reflected in the thermal dependence of the relative sensitivity S_R2 (Fig. 6d, the corresponding thermal dependence of absolute sensitivity is shown in Fig. S15), which peaks at ∼3% K⁻¹ near 100 K and gradually decreases, becoming negative above ∼280 K. Although negative S_R values are not suitable for quantitative sensing, they are presented here to illustrate the loss of thermal monotonicity in LIR₂. Notably, due to the fact that the ²H_9/2 → ⁴I_13/2 emission band is observed at lower temperatures than the ²H_11/2 → ⁴I_15/2 band, LIR₂-based thermometry extends the operational range of the Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺-based luminescent thermometers down to sub-200 K temperatures, providing complementary thermometric capabilities to those based on LIR₁.

Fig. 6 Thermal dependence of normalized (normalization to the value of the emission intensity obtained at 83 K) integral emission intensities of emission bands (λ_exc = 980 nm, 20 W cm⁻²) corresponding to the ²H_9/2 → ⁴I_13/2 (a), and ⁴S_3/2 → ⁴I_15/2 (b), electronic transitions of Er³⁺ ions for different dopant concentration of Yb³⁺ ions; thermal dependence of LIR₂ (c); and corresponding thermal dependence of S_R2 (d).

A comprehensive analysis of the temperature-dependent intensity variations of Er³⁺ emission bands in Na₃Sc₂(PO₄)₃:0.5%Er³⁺,5%Yb³⁺ reveals a pronounced difference between the thermal behavior of bands located in the green spectral region and those in the red region. This distinction is particularly relevant for practical applications, as the green emission bands are spectrally well-separated from the ⁴F_9/2 → ⁴I_15/2 band, unlike LIR₁ and LIR₂. This spectral separation facilitates more accurate temperature readings and, more importantly, enables visual temperature sensing due to the resulting changes in emission color. To investigate this possibility, the temperature dependence of the total emission intensities of the ²H_11/2 → ⁴I_15/2, ⁴S_3/2 → ⁴I_15/2, and ²H_9/2 → ⁴I_13/2 bands was analyzed (Fig. 7a). All three bands exhibit thermal enhancement across the studied Yb³⁺ ion concentrations, although the rate of increase diminishes with higher dopant levels. In contrast, the ⁴F_9/2 → ⁴I_15/2 band displays only a slight intensity increase up to ∼400 K for 5% Yb³⁺, followed by thermal quenching (Fig. 7b). It can be clearly seen that for low Yb³⁺ concentrations an evident jump in the thermal dependence of both analyzed signals can be found at around 340 K. The thermal range at which this behavior is observed corresponds to the phase transition temperature described above. However, at higher dopant concentration this effect is not observed, most likely due to the stabilization of the high temperature phase of Na₃Sc₂(PO₄)₃. Additionally, for higher Yb³⁺ concentrations, no thermal enhancement is observed, only intensified thermal quenching.

Fig. 7 Thermal dependence of normalized (normalization to the value of the emission intensity obtained at 83 K) integral emission intensities (λ_exc = 980 nm, 20 W cm⁻²) of green emission – total emission intensities of emission bands corresponding to the ²H_9/2 → ⁴I_13/2 + ²H_11/2 → ⁴I_15/2 + ⁴S_3/2 → ⁴I_15/2 electronic transitions of Er³⁺ ions (a), and red emission – corresponding to the ⁴F_9/2 → ⁴I_15/2 electronic transitions of Er³⁺ ions (b), for different dopant concentration of Yb³⁺ ions; thermal dependence of LIR₃ (c), and the corresponding thermal dependence of S_R3 (d); thermal dependence of CIE 1931 chromatic coordinates (e), and the corresponding thermal dependence of chromatic coordinates (f).

These findings allowed the definition of a third luminescence intensity ratio (LIR₃) as follows:

which, as shown in Fig. 7c, increases by over 50-fold upon heating to 553 K. The relative sensitivity (S_R3) peaks at 1.6% K⁻¹ at 100 K for 10% Yb³⁺, indicating strong thermometric responsiveness (Fig. 7d, the corresponding thermal dependence of absolute sensitivity is shown in Fig. S16). This substantial variation in LIR₃ corresponds to a noticeable shift in the emission color, confirmed by the calculated CIE 1931 chromaticity coordinates (Fig. S17–S20). For example, with 5% Yb³⁺, the emission color changes from orange at 83 K to greenish-yellow at 553 K, while for 30% Yb³⁺, the transition spans from yellow to green over the same temperature range (Fig. 7e). Moreover, analysis of the temperature evolution of the x and y chromaticity coordinates shows an inflection for low Yb³⁺ concentrations, likely due to a structural phase transition, whereas 30% Yb³⁺ doping yields a smooth and predictable chromatic shift (Fig. 7f). These results highlight the viability of colorimetric thermometry using Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺, offering a practical and filter-free strategy for visual temperature sensing.

As demonstrated, the pronounced temperature-dependent color changes in the luminescence of Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ can be effectively utilized for visual temperature sensing. In addition to passive temperature variations, the sample temperature can also be actively modulated by adjusting the optical power density of the excitation source. This is due to the partial conversion of absorbed excitation energy into heat, rather than up-conversion emission. Consequently, the interplay between thermally induced luminescence color shifts, and optically induced heating can be harnessed to develop a visual optical power density sensor. Moreover, the difference in the rate of increase of luminescence intensity with rising optical power density, reflected in the distinct up-conversion orders of the emission bands in the green and red spectral ranges, further enhances the sensitivity of Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ to variations in optical power density. Given that the absorption efficiency of excitation light is proportional to the concentration of sensitizer ions, the emission color change under varying optical power densities was investigated for two extreme Yb³⁺ concentrations: 5% and 30%. Digital images reveal that for 5% Yb³⁺, the sample emits a weak orange glow at low excitation densities, which gradually shifts to yellow and finally to a greenish-yellow hue at 104 W cm⁻² (Fig. 8a, Fig. S21–S24). In contrast, the 30% Yb³⁺-doped sample exhibits significantly stronger luminescence across the same power density range, with a pronounced color shift from orange to bright green (Fig. 8b, Fig. S25–S28). Additionally, surface temperature measurements confirmed the enhanced optical heating efficiency in the sample with 30% Yb³⁺, reaching 534 K at 104 W cm⁻², compared to only 329 K for the 5% Yb³⁺ counterpart. These findings demonstrate the potential of Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ as a dual-function material for both luminescent temperature sensing and visual optical power density mapping. The variation in the color of light emitted by Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ in response to changes in excitation power density is clearly reflected in the shift of the corresponding CIE 1931 chromaticity coordinates (Fig. 8c). For the sample doped with 30% Yb³⁺, these coordinates transition from values characteristic of orange emission to those indicative of green emission across the analyzed power density range. A detailed analysis of these changes reveals substantially greater chromatic shifts for the 30% Yb³⁺ sample: the x coordinate varies from 0.56 to 0.36, and the y coordinate from 0.43 to 0.61 (Fig. 8d, exact values of CIE 1931 coordinates can be found in Table S2). In comparison, the 5% Yb³⁺ sample exhibits more modest changes, with x decreasing from 0.62 to 0.52 and y increasing from 0.38 to 0.47. The relative sensitivity values derived from chromatic coordinate variations, calculated analogously to thermal sensitivity but using power density (p) instead of temperature (T) (see eqn (S2) and (S3)), demonstrate that for Na₃Sc₂(PO₄)₃:Er³⁺,30%Yb³⁺, maximum sensitivities reach S_Rx = 1.0% W⁻¹ cm² and S_Ry = 0.9% W⁻¹ cm² at 15 W cm⁻² (Fig. 8e). These values decrease with increasing power density to 0.14% W⁻¹ cm² and 0.27% W⁻¹ cm², respectively, at 90 W cm⁻². In contrast, nearly two-fold lower sensitivities are observed for the 5% Yb³⁺ sample. These findings underscore that higher Yb³⁺ ion concentrations, which lead to more efficient absorption of excitation light and enhanced optically induced heating, are advantageous for the development of luminescent optical power density sensors.

Fig. 8 Photos of up-conversion emission of Na₃Sc₂(PO₄)₃:0.5%Er³⁺,5%Yb³⁺ (a), and Na₃Sc₂(PO₄)₃:0.5%Er³⁺,30%Yb³⁺ (b), captured under different excitation densities of λ_exc = 980 nm, and the picture from the thermovision camera of these samples obtained at 104 W cm⁻²; the influence of the power density on the CIE 1931 chromatic coordinates for 30% Yb³⁺ (c); the influence of the excitation density on the x and y chromatic coordinates for 5% Yb³⁺ and 30% Yb³⁺ (d), and corresponding relative sensitivities (e).

As demonstrated above, variations in the optical power density used to excite the up-conversion luminescence of Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ result in noticeable changes in the color of the emitted light. However, performing colorimetric analysis based on CIE 1931 chromaticity coordinates, requires full spectral acquisition and extensive post-processing, which is time-consuming and impractical, particularly for two-dimensional imaging applications. A more straightforward, cost-effective, and rapid alternative involves capturing luminescence images and analyzing the intensity values recorded in the red (R), green (G), and blue (B) channels of a standard digital camera. This method enables the generation of spatial distribution maps for each color channel, and by calculating the G/R intensity ratio, a corresponding map of the optical power density can be obtained. While this image-based approach has been utilized in luminescent thermometry^44,45 and thermal history sensing,⁴⁶ to the best of our knowledge, it has not yet been applied to optical power density mapping. In the case of Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺, this strategy is particularly advantageous because the relevant emission bands are spectrally resolved by the R channel (⁴F_9/2 → ⁴I_15/2) and G channel (²H_9/2 → ⁴I_13/2, ⁴S_3/2 → ⁴I_15/2, ²H_11/2 → ⁴I_15/2). To implement this method, a series of luminescence images of Na₃Sc₂(PO₄)₃:Er³⁺,30%Yb³⁺ were acquired under varying optical power densities (Fig. 9a). From each image, intensity maps for the G and R channels were extracted and used to compute G/R ratio maps. These data were used to construct a calibration curve relating G/R to optical power density, which followed an exponential trend up to 130 W cm⁻² (Fig. 9b):

To validate the effectiveness of this approach for spatially resolved measurements, a layer of Na₃Sc₂(PO₄)₃:Er³⁺,30%Yb³⁺ was illuminated with a 980 nm quasi-Gaussian laser beam (maximum intensity: 110 W cm⁻²), and luminescence images were captured. The resulting G/R ratio map revealed a clear radial gradient, with a peak intensity at the center (∼1.5 mm in diameter), decreasing outward (Fig. 9c). Using the calibration curve, the G/R ratio map was converted into a spatially resolved optical power density map (Fig. 9d). The obtained power distribution closely resembles the expected Gaussian profile, although minor deviations observed in the cross-sectional intensity profiles (Fig. 9e) reflect the inhomogeneity of the excitation beam itself. In conclusion, the results confirm the strong application potential of Na₃Sc₂(PO₄)₃:Er³⁺,30%Yb³⁺ as a luminescent material for real-time, visual two-dimensional imaging of optical power density distributions using a standard digital camera without the need for optical filters. It should be also noted here that the dominant process responsible for G/R ratio change is associated with optically induced temperature increases. This may indicate a lack of selectivity of the developed optical power density sensor and the possibility of cross-reading disturbances in the case of simultaneous changes in temperature and optical power density. However, the temperature rise induced by optical excitation produces a considerably greater change in the phosphor's temperature than any variations that might be expected from fluctuations in ambient atmospheric conditions. This effect is inherent to all luminescent optical power density sensors reported in the literature to date. Additionally, the same limitation applies to conventional electro-optical detector heads used in spectroscopic laboratories, where temperature variations likewise influence the generated photocurrent. Consequently, to accurately determine the power density when using such devices, it is necessary to record and account for the ambient temperature during measurements. Since operation of this optical density sensor requires absorption of the excitation photons, its spectral operating range is inherently restricted, primarily to the absorption band of Yb³⁺ ions corresponding to the ²F_7/2 → ²F_5/2 electronic transition (920–1000 nm). While this represents a limitation of the sensor, it is important to note that the 980 nm excitation wavelength is among the most extensively employed in the literature, owing to the widespread use of up-conversion processes and the vast body of research devoted to them. Consequently, the development of a luminescent optical power density sensor specifically designed for 980 nm excitation is of substantial practical relevance. Considering that the sensitivity of Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ to variations in optical power density arises from the synergistic interplay between differences in the order of the up-conversion process and optical heating, it is reasonable to ask which of these mechanisms plays the dominant role. Analysis of the calibration curve shown in Fig. 9b reveals that it maintains the same monotonic trend across the entire investigated range of optical power densities. In contrast, power dependence studies conducted above 50 W cm⁻² show a distinct reduction in the rate of emission intensity growth for both green and red emission bands (Fig. 4). The absence of this trend in the calibration curve suggests that, at least at higher excitation power densities (above 50 W cm⁻²), optically induced heating is the predominant factor. However, below this threshold, differences in the population mechanisms of the individual energy levels of Er³⁺ ions may significantly influence the dynamics of the green-to-red emission ratio with changing excitation power density. To verify the reproducibility of the optical density readout based on Na₃Sc₂(PO₄)₃:Er³⁺,30%Yb³⁺, an additional experiment using four different combinations of optical beam power and spot size was adjusted to yield a comparable optical power density of approximately 70 W cm⁻² (Table S3). Subsequently, the CIE 1931 chromaticity coordinates were determined. The results of this experiment demonstrate a high degree of reproducibility.

Fig. 9 The G/R maps for Na₃Sc₂(PO₄)₃:Er³⁺,30%Yb³⁺ determined from photos of up-conversion emission captured at different excitation densities (a); the calibration curve of power density vs. G/R ratio (b); the 2D G/R maps of the Na₃Sc₂(PO₄)₃:Er³⁺,30%Yb³⁺ luminescence obtained upon λ_exc = 980 nm of 120 W cm⁻² excitation density (c), and the corresponding 3D distribution of power density (d); power density cross section profiles along x and y lines marked in (c), (e).

Several studies in the literature report the use of luminescence for sensing optical power density, primarily based on phosphors doped with Cr³⁺,^17,47–48 or Er³⁺,Yb³⁺ ions.^14–15 In both cases, the sensing mechanism relies on changes in the emission intensity ratio of two thermally coupled energy levels, which are influenced by optically induced heating of the material. However, in all cases reported to date, the parameter employed for sensing is the luminescence intensity ratio, which complicates two-dimensional imaging of the optical power density distribution. For previously described sensors based on Er³⁺ emission,^14,15 the close spectral proximity of the bands used in sensing prevents a distinct change in the color of the emitted light. In this context, the capabilities offered by Na₃Sc₂(PO₄)₃:Er³⁺,30%Yb³⁺ as the first visual luminescent optical power density sensor, present a highly attractive alternative from an application standpoint.

Conclusions

In summary, this study investigated the influence of temperature on the up-conversion emission behavior of Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺. The analysis revealed that, in addition to the characteristic emission bands of Er³⁺ ions associated with the ²H_11/2 → ⁴I_15/2, ⁴S_3/2 → ⁴I_15/2, and ⁴F_9/2 → ⁴I_15/2 electronic transitions, an additional emission band around 575 nm was observed, which corresponds to the ²H_9/2 → ⁴I_13/2 transition. Significant temperature-dependent changes in the spectroscopic properties of Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ enabled the implementation of three distinct temperature-sensing modes based on various luminescence intensity ratios: (i) ²H_11/2 → ⁴I_15/2 and ⁴S_3/2 → ⁴I_15/2; (ii) ²H_9/2 → ⁴I_13/2 and ⁴S_3/2 → ⁴I_15/2; and (iii) green-to-red emission intensity ratio. As demonstrated, in the first mode, the concentration of Yb³⁺ ions had negligible influence on the relative sensitivity, with the maximum S_R1max = 2.8% K⁻¹ observed at 200 K. Since the ²H_11/2 → ⁴I_15/2 band becomes thermally activated above 200 K, the operational temperature range for this mode spans from 200 to 553 K. The ²H_9/2 → ⁴I_13/2 band, on the other hand, is already detectable at 83 K, and its opposite thermal monotonicity compared to the ⁴S_3/2 → ⁴I_15/2 band allowed for the development of an alternative temperature-sensing approach. This mode yielded a maximum sensitivity of S_R2max = 3% K⁻¹ at 100 K. As this mechanism remains functional below 200 K, combining both LIR₁ and LIR₂ approaches extends the overall thermal operating range of the Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺-based thermometer. Moreover, a thermally induced variation in the red-to-green emission intensity ratio was observed, contributing to a noticeable color change in the emitted light from Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺. This phenomenon, when combined with the efficient optical heating of Na₃Sc₂(PO₄)₃:Er³⁺,Yb³⁺ by the excitation beam, enabled the development of the first visual optical power density sensor.

Given that the temperature rise due to optical absorption is proportional to the sensitizer ion concentration, a visible color shift of the emitted light was recorded from orange at 7.28 W cm⁻² to green at 104 W cm⁻². Maximum relative sensitivities based on the chromaticity coordinates were S_Rx = 1.0% W⁻¹ cm² and S_Ry = 0.9% W⁻¹ cm² at 15 W cm⁻², respectively. To further simplify the optical power density readout, the ratio of intensity distribution maps recorded in the green and red channels of a standard camera was analyzed. This method enabled fast, low-cost, and two-dimensional imaging of optical power density distribution, validated by the analysis of the excitation beam profile. Altogether, the presented approach demonstrates strong potential for advancing research in the field of luminescence-based visual imaging of optical power density.

Conflicts of interest

There are no conflicts to declare.

Data availability

The datasets supporting this article have been uploaded as part of the SI. See DOI: https://doi.org/10.1039/d5mh01369k.

Acknowledgements

This work was supported by the National Science Center (NCN) Poland under project no. UMO-2020/37/B/ST5/00164. Maja Szymczak gratefully acknowledges the support of the Foundation for Polish Science through the START program.

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