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Temperature-dependent radiative lifetime of Yb:YLF: refined cross sections and potential for laser cooling

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Abstract

We revisit the spectroscopic characterization of ytterbium-doped LiYF4 (Yb:YLF) for the application of laser cooling. Time-dependent fluorescence spectroscopy reveals a temperature dependence of the radiative lifetime which we explain by the Boltzmann distribution of excited ions in the upper Stark levels. The emission cross sections of Yb:YLF from 17 K to 440 K are revised using the temperature-dependent radiative lifetimes from fluorescence spectra. We provide fit equations for the peak values of important transitions as a function of temperature, which is also useful for the design of Yb:YLF laser oscillators and amplifiers operated at cryogenic temperatures. Based on our spectroscopic data, we show the prerequisite crystal purity to achieve laser cooling below liquid nitrogen temperatures.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Optically active materials can be cooled by optical excitation via anti-Stokes fluorescence, as proposed by Pringsheim in 1929 [1]. This technique is nowadays referred to as solid-state laser cooling, or optical refrigeration [2,3]. The first solid-state laser cooling was reported 66 years after Pringsheim’s initial work using an ytterbium (Yb)-doped fluorozirconate glass [4]. The advances in solid-state laser cooling, hereafter simply laser cooling, throughout the last two decades are remarkable. Cooling from room temperature down to below 100 K was realized [5,6]. In particular fluoride crystals exhibit a high quantum efficiency and thus an immense potential for laser cooling. Hence, Yb-doped LiYF4 (YLF) crystals have been the work-horse material for this technology so far [3,7]. Thulium (Tm) and holmium (Ho) doped fluoride crystals also exhibit a high potential as laser cooling materials [8,9], but the availability of high-power pump sources in the 1 µm region suited for the excitation of Yb3+ ions makes Yb-doped fluoride crystals the best choice for practical applications [10]. The technology of solid-state laser cooling is highly demanded for all-solid-state optical cryocoolers [10], which are attractive alternatives to liquefied-gas-based cooling. Optical cryocooler devices benefit from their compactness, simplicity, as well as the absence of any mechanical vibrations, and thus warrant a high ruggedness and reliability. This technology also offers the possibility of focal cooling suited for medical treatments [11]. Moreover, solid-state laser cooling is the underlying principle of the concept of ‘athermal lasers’, also known as ‘radiation-balanced lasers’ [12,13].

The spectroscopic properties of many Yb-doped crystals are well-known since they are state-of-the-art materials for high power solid-state lasers [1417]. Unfortunately, temperature-dependent spectroscopic data, including fluorescence lifetime as well as absorption and emission cross sections, are not readily available for most Yb-doped materials. However, such data are essential to reveal the potential of a material as a laser cooling medium. Moreover, they are also of high relevance for the application of Yb-doped gain media in cryogenically cooled laser oscillators and amplifiers [1724].

The accurate determination of the spectroscopic parameters of Yb-doped materials is not trivial. They exhibit a strong spectral overlap between the absorption and the emission causing significant reabsorption of emitted photons. As a result, emission cross sections can be inaccurate when calculated from fluorescence spectra which undergo reabsorption. In addition, multiple reabsorption and reemission results in fluorescence decay times longer than the intrinsic fluorescence lifetime, an effect often referred to as radiation trapping [25]. Thus, spectroscopy of reabsorbing materials needs to be performed very thoroughly to avoid these effects.

Various reports on the spectroscopic properties of Yb:YLF exist [14,17,32,33,23,24,2631]. However, these reports do not cover the full temperature range relevant for laser cooling applications. Moreover, high-temperature spectroscopic data are needed to evaluate the cooling efficiencies at elevated temperatures, e.g. for radiation-balanced lasers operating in this regime but such data have not been reported yet. Note that even lasers operated at ‘room temperature’ easily heat up by 100 K and their design might also benefit from these data. Further, many previous reports show a strong influence of reabsorption effects on the spectroscopic properties of Yb:YLF. In particular, the increase of the fluorescence lifetime with temperature is attributed to radiation trapping caused by a larger spectral overlap of absorption and emission [30,32], but on the other hand, a temperature-dependent radiative lifetime of Yb-doped materials has also been considered [34,35].

Here, we present a detailed spectroscopic characterization of Yb:YLF aiming to refine and extend the available spectroscopic data in particular with a focus on laser cooling applications. For this reason, we perform absorption and emission spectroscopy as well as fluorescence lifetime measurements in a wide range of temperatures from 17 K to 440 K. Reabsorption effects are carefully suppressed in the experiments. We determine the energetic positions of the Stark levels of Yb3+ ions in YLF and reveal an intrinsic temperature dependence of the radiative lifetime caused by the Boltzmann distribution in the upper Stark levels. With these refined spectroscopic data, we evaluate the cooling efficiency for different doping concentrations and purity levels, and find the minimum achievable temperatures to be below the liquid nitrogen temperature of 77 K for high purity Yb:YLF.

2. Determination of the energetic positions of Stark levels of Yb3+ in YLF

The accurate determination of the energetic positions of the Stark levels is essential to calculate their temperature dependent Boltzmann occupation and the cross sections by means of the reciprocity (or McCumber) relation [36]. We prepared two samples of different thickness from an Yb-doped YLF crystal grown at our institute by the Czochralski method [37]. YLF has a tetragonal crystal structure and possesses crystallographic a- and c-axes. Both samples were cut perpendicular to an a-axis. Inductively-coupled plasma optical emission spectroscopy (ICP-OES) revealed that 4.95 ± 0.05 at.% of Y ions in the YLF matrix are substituted by Yb ions, conventionally denoted as Yb(5 at.%):YLF. Spatially resolved X-ray fluorescence (XRF) (Bruker, TORNADO) measurements revealed homogeneously distributed Yb ions in these samples with a relative deviation of the concentration below ±0.5%. We identified the energetic positions of the Stark levels in the 2F7/2 and 2F5/2 multiplets of Yb3+ in YLF from the absorption and emission spectra recorded at 17 K using a high resolution monochromator (HORIBA, M1000) and a photomultiplier tube (Hamamatsu, R5108) as the detector. For both absorption and emission spectroscopy the spectral resolution was set to 0.08 nm to fully resolve the narrow zero-phonon line at 971.6 nm. The wavelength accuracy was evaluated to be better than 0.015 nm for the whole measurement range. The samples were cooled in a closed-cycle helium cryostat (Advanced Research Systems, DE204). In the absorption measurements, a broadband tungsten halogen lamp was used as the probe light, while a Ti:sapphire laser tunable from 700 to 1000 nm (M Squared, SolsTiS) was used as the excitation source in the emission spectroscopy. The wavelength dependent sensitivity of the entire measurement setup was characterized using a calibrated tungsten filament lamp (OSRAM, WI17G), and the recorded polarization-resolved fluorescence spectra were calibrated accordingly. Figure 1 shows the measured wavelength-dependent absorption coefficients (a) and fluorescence intensities (b) for σ (E ⊥ c) and π (E || c) polarization at 17 K. To measure the absorption coefficients for the entire spectral range with a good signal to noise ratio, a 180 µm thick sample was used to measure the strong absorption peaks above 955 nm, and another 4.5 mm thick sample was used to determine the weaker absorption features at wavelengths below 955 nm.

 figure: Fig. 1.

Fig. 1. Polarization-resolved (a) absorption coefficient and (b) fluorescence intensity spectra of the Yb(5 at.%):YLF samples recorded at 17 K. The absorption spectra left of the dashed line at 955 nm in (a) were taken with a sample of 4.5 mm thickness and are enhanced by a factor of 10 for clarity. The region above 955 nm was recorded with a 180 µm thick sample. In both figures the peaks assigned as the resonant transitions between the Stark levels are marked with black dots.

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For emission spectroscopy, again the 180 µm thick sample was used to minimize the influence of reabsorption at the zero-phonon line. The data obtained at 17 K enable us to determine the Stark-level positions of Yb3+ in YLF and compare it to existing data [27,28,33,3840]. In both absorption and emission spectra we find the zero-phonon line transition at 971.6 nm. We assign the strong absorption peak at 960.2 nm to the transition E1→E6. Among the numerous vibronic absorption peaks in the region below 995 nm, the peak at 947.9 nm is assigned to the transition E1→E7. This is further confirmed by the growth of an emission peak for the transition E7→E1 with increasing temperature (cf. Figure 6). Three emission peaks of notable strength at 992.4, 995.1, and 1019.7 nm are assigned to the transitions E5→E2, E5→E3, and E5→E4, respectively. We consider the emission peak at 1008 nm, previously assigned to be the transition E5→E3 [28], to be a vibronic transition due to its relatively low intensity. This assignment is further supported by a comparison with the Raman spectra [27]. Figure 2(a) illustrates the resulting energy diagram of Yb3+ in YLF with the respective absorption and emission lines. Our assignment is consistent with the result in [27], and the difference in the determined Stark level positions is smaller than 5 cm−1. Figure 2(b) illustrates the resulting calculated fractional occupancies of the three upper Stark levels.

 figure: Fig. 2.

Fig. 2. (a) Energy diagram of Yb3+ in the host material YLF with corresponding absorption and emission lines. (b) Fractional occupancy of the Stark levels in the 2F5/2 multiplet based on the Boltzmann distribution as a function of temperature calculated by Eq. (6).

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3. Temperature-dependent fluorescence lifetime

The determination of the fluorescence lifetime of Yb-doped materials is not trivial due to radiation trapping. Therefore, the pinhole method as described in [25] was applied to get access to the intrinsic fluorescence lifetime at room temperature. The experimental setup is identical to the layout illustrated in the reference. We used a series of pinholes with different diameters between 0.6 and 2.5 mm. Note that we used a sample thicker than 2.5 mm; otherwise, for too small diameters the excited volume does not have a cubic-relation with the pinhole diameter and the dependence of the lifetime on the pinhole diameter is not linear [25]. As an excitation source we used an optical parametric oscillator (GWU-Lasertechnik, versaScan) set to a wavelength of 960 nm and delivering 5-ns pulses at 10 Hz repetition rate. The detection setup was same as described in the previous section, and time-resolved fluorescence signals were recorded by an oscilloscope. We performed two measurements for each temperature with the detection set to 995 nm and 1020 nm, and confirmed unchanged measured fluorescence lifetimes by the detection wavelength. We observed a very good linear relation of the measured lifetime with the pinhole diameter as shown in Fig. 3(a), where the longest measured lifetime of 2.75 ms was 25% longer than the extrapolated fluorescence lifetime, unaffected by radiation trapping, determined to be 2.20 ± 0.03 ms (95% confidence interval). This clearly underlines the need to avoid radiation trapping during the determination of the fluorescence lifetime of Yb-doped materials to obtain reliable results. Multiphonon relaxation is strongly suppressed in Yb3+-doped materials, because the ground state 2F7/2 and the excited state 2F5/2 are typically separated by ≈104 cm−1, and thus an order of magnitude larger than the highest phonon energies in typical laser crystals. This allows for external quantum efficiencies well in excess of 99% [41]. For this reason, we interpret the extrapolated fluorescence lifetime of 2.20 ms as the radiative lifetime at room temperature.

 figure: Fig. 3.

Fig. 3. (a) Fluorescence lifetime measured with pinholes of different diameter. The intrinsic fluorescence lifetime is extrapolated to be 2.20 ± 0.03 ms. (b) Time-dependent fluorescence signal at 17 K and 440 K from a Yb(5 at.%):YLF sample of a 180 µm thickness suppressing radiation trapping. (c) Fluorescence lifetime versus temperature measured with a Yb(5 at.%):YLF sample of a 180 µm. Circular symbols represent the measured lifetime. Diamond symbols correspond to the fluorescence lifetime corrected for remaining radiation trapping by Eq. (5). Star symbol indicates the lifetime at room temperature determined by the pinhole method used as τ0 in Eq. (5). Dashed line is the result of fitting with Eq. (7) with the radiative lifetimes of each individual Stark level τi denoted in the figure.

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The temperature dependence of the fluorescence lifetime of Yb:YLF was examined with the 180 µm thick Yb:YLF sample. The measured room temperature lifetime of this sample was found to be 2.3 ms. This is only 4.5% longer than the lifetime obtained by the pinhole method, which shows the limited influence of radiation trapping for this sample geometry. A closed-cycle helium cryostat and a ceramic heater were employed to vary the temperature from 17 K to 300 K and 300 K to 440 K, respectively. Figure 3(b) shows the decay curves at 17 K and 440 K in which we clearly identify a temperature dependence of the fluorescence lifetime. Bensalah et al. reported the same lifetime of 1.94 ms at 12 K in Yb(0.5 at.%):YLF [27]. The fluorescence decay is single exponential for all the temperatures. The fast decay reported in Yb(25 at.%):YLF [32] is not observed in our Yb(5 at.%):YLF sample. The circular symbols in Fig. 3(c) show the measured fluorescence lifetime at different temperatures. We found a drop of the lifetime with decreasing temperature. This trend is consistent with previous reports on the fluorescence lifetime of Yb:YLF, where it was attributed to radiation trapping caused by a larger spectral overlap between the absorption and emission spectra at higher temperatures [30]. However, the room temperature lifetime of 2.3 ms measured with this very thin sample compared to the pinhole-lifetime of 2.20 ± 0.03 ms excludes radiation trapping as a single explanation for the observed much stronger temperature dependency. In order to evaluate the remaining radiation trapping at different temperatures T, we define the reabsorption factor for uniaxial crystals as

$${f_{\textrm{reabs}}}(T) = \frac{{\int {[{{\sigma_{\textrm{em},\pi }}(\lambda ,T){\sigma_{\textrm{abs},\pi }}(\lambda ,T) + 2{\sigma_{\textrm{em},\sigma }}(\lambda ,T){\sigma_{\textrm{abs},\sigma }}(\lambda ,T)} ]d\lambda } }}{{\int {[{\sigma_{\textrm{em},\pi }^2(\lambda ,T) + 2\sigma_{\textrm{em},\sigma }^2(\lambda ,T)} ]d\lambda } }}.$$

In the equation, λ is the wavelength, and σem and σabs are emission and absorption cross sections for π- and σ-polarization, respectively. This factor becomes unity when the absorption and emission spectra are identical, and would be zero if there is no overlap. The absorption cross section σabs can be expressed using the emission cross section σem by the reciprocity relation [36] given as

$$\begin{array}{l} {\sigma _{\textrm{em},\zeta }}(\lambda ,T) = {\sigma _{\textrm{abs},\zeta }}(\lambda ,T)\frac{{{Z_l}}}{{{Z_u}}}\textrm{exp} \left( { - \frac{{{{hc} / \lambda } - {E_{\textrm{ZPL}}}}}{{{k_B}T}}} \right),\\ \textrm{where }{Z_k} = \sum\limits_i {{g_i}\textrm{exp} \left( { - \frac{{{E_i}}}{{{k_B}T}}} \right)} . \end{array}$$

Here, h is Planck’s constant, kB is the Boltzmann constant, EZPL is the energy of the zero-phonon line transition at 10292 cm−1, Zk with i = 1, 2, 3, 4 and 5, 6, 7 is the partition function of the lower and upper multiplet Zl and Zu, respectively, and gi is the degeneracy of the respective Stark level. The emission cross section can be rewritten using the fluorescence intensity by the Füchtbauer-Ladenburg equation for uniaxial crystals [42] given as

$${\sigma _{\textrm{em},\zeta }}(\lambda ,T) = \frac{{{\lambda ^5}}}{{8\pi c{n_\zeta }(\lambda ){\tau _{\textrm{rad}}}}}\frac{{{I_\zeta }(\lambda ,T)}}{{\frac{1}{3}\int {[{\lambda {I_\pi }(\lambda ,T) + 2\lambda {I_\sigma }(\lambda ,T)} ]d\lambda } }},\cdot$$
where, c is the speed of light, Iζ is the fluorescence intensity in the polarization ζ (i.e. σ or π), nζ is the respective refractive index, and τrad is the radiative lifetime. Using Eq. (2) and (3), the reabsorption factor (Eq. (1)) can be simplified to
$${f_{\textrm{reabs}}}(T) = \frac{{{Z_u}(T)}}{{{Z_l}(T)}}\exp \left( { - \frac{{{E_{\textrm{ZPL}}}}}{{{k_B}T}}} \right)\frac{{\int {{\lambda ^{10}}[{I_\pi^2(\lambda ,T) + 2I_\sigma^2(\lambda ,T)} ]\textrm{exp} \left( {\frac{{{{hc} / \lambda }}}{{{k_B}T}}} \right)d\lambda } }}{{\int {{\lambda ^{10}}[{I_\pi^2(\lambda ,T) + 2I_\sigma^2(\lambda ,T)} ]d\lambda } }}.$$

Note that the resulting reabsorption factor is independent from the radiative lifetime and the actual cross sections, but only utilizes the shape of the fluorescence spectra Iζ(λ,T) and the energetic positions of the Stark levels. Instead of using the fluorescence spectra, the reabsorption factor can be also rewritten using the absorption spectra αζ(λ,T) in a very similar way.

Figure 4 shows the calculated reabsorption factor with respect to temperature using the fluorescence spectra (Eq. (4)) and the absorption spectra. The separately derived reabsorption factors are in a good agreement which indicates a limited influence of remaining reabsorption in the fluorescence spectra on freabs even at elevated temperatures. The reabsorption factor cannot drop to zero due to the remaining spectral overlap at the zero-phonon line. We corrected the remaining radiation trapping in the measured temperature-dependent fluorescence lifetime using the model presented in [43,44] but modified to consider temperature dependency. The measured fluorescence lifetime τmeas can thus be written as

$${\tau _{\textrm{meas}}}(T) = \frac{{{\tau _0}(T)}}{{1 - \beta {f_{\textrm{reabs}}}(T)}}.$$

Here, τ0 is the intrinsic fluorescence lifetime, and β is a temperature independent parameter accounting for the geometry of the sample and setup. Assuming the pinhole lifetime to be equal to the intrinsic fluorescence lifetime τ0, the parameter β is determined to be 0.11 for the 180 µm thick Yb:YLF sample from the ratio of the lifetimes measured with and without pinhole method. With this value, the intrinsic fluorescence lifetime τ0 can be calculated for all temperatures using the respective reabsorption factor. The temperature-dependent fluorescence lifetimes after the correction for the remaining radiation trapping are shown in Fig. 3(c). As clearly seen, the observed temperature dependency in fluorescence lifetime is still not solely explained by the radiation trapping. We thus conclude that the fluorescence lifetime of Yb:YLF, assumed to be identical with the radiative lifetime, is indeed temperature dependent.

 figure: Fig. 4.

Fig. 4. Reabsorption factor with respect to temperature calculated by Eq. (4) using the fluorescence spectra and using the absorption spectra.

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A temperature-dependent radiative lifetime of Yb-doped materials has already been considered [34,35] but corresponding experimental findings were previously explained by radiation trapping [30,32,45,46]. We attribute the observed temperature dependency to the distribution of population in the Stark levels of the upper 2F5/2 multiplet. A transition from one of the upper Stark levels Ei to one of the lower Stark levels Ej possesses a sub-level transition cross section σij [35]. Accordingly, each upper Stark level has an individual radiative lifetime. The fractional occupancy of each upper Stark level fi (i = 5, 6, and 7) based on the Boltzmann distribution, shown in Fig. 2(b), is given by

$${f_i}(T) = \frac{{\textrm{exp} \left( { - \frac{{{E_i} - {E_{\textrm{ZPL}}}}}{{{k_B}T}}} \right)}}{{\sum\limits_{k = 5}^7 {\textrm{exp} \left( { - \frac{{{E_k} - {E_{\textrm{ZPL}}}}}{{{k_B}T}}} \right)} }},$$
as a function of temperature T. The instantaneous rise and the single exponential decay of fluorescence at 17 K shown in Fig. 3(b) indicate that the thermalization in the Stark levels is much faster than the radiative decay process even at low temperatures. Thus, we can assume the three Stark levels to be in thermal equilibrium at all times. Therefore, the effective radiative lifetime of the upper multiplet τrad in the temperature range under investigation is given by
$${\tau _{\textrm{rad}}}(T) = {\left[ {\sum\limits_{i = 5}^7 {\frac{{{f_i}(T)}}{{{\tau_i}}}} } \right]^{ - 1}},$$
where τi is the radiative lifetime of each individual Stark level. We applied this model to fit the dependency of the measured fluorescence lifetimes (and thus the radiative lifetime) on the temperature. The corrected lifetime at 17 K of 1.93 ms was considered to be the lifetime τ5 of the level E5, since the fractional occupancy of E5 is practically unity below 30 K, as can be seen in Fig. 2(b). Figure 3(c) reveals an excellent agreement of the model with the measured lifetimes using τ6 = 3.2 ms and τ7 = 2.0 ms in Eq. (7). The effective radiative lifetimes τrad(T) resulting from the model are used to calculate the temperature-dependent emission cross sections by the Füchtbauer-Ladenburg equation in the following section. This approach is justified due to the thermal equilibrium of the Stark levels mentioned above.

We emphasize that this model can be applied for any Yb-doped material, and thus their radiative lifetime may also be a temperature-dependent parameter. This result motivates further investigations on the temperature-dependent lifetime of Yb3+ ions in other host materials.

4. Temperature-dependent spectra of Yb:YLF

We thoroughly characterized absorption and emission spectra of Yb:YLF at temperatures between 17 K and 440 K. The fluorescence measurements were carried out with the setup described in Section 2. To accurately evaluate the emission cross sections of Yb:YLF, we used the sample of 180 µm thickness, which had been proven to inhibit reabsorption. The spectral resolution of the measurements was optimized for each temperature to fully resolve the narrowest features, which in most cases were found at the zero-phonon line. Figure 5 shows the polarization-resolved absorption and emission cross section spectra at room temperature. The emission cross sections σem were derived by two different approaches: the reciprocity relation (Eq. (2)) and the Füchtbauer-Ladenburg equation (Eq. (3)). Since the temperature variation of refractive index dn/dT of Yb:YLF is only in the order of 10−6 K−1 [47], it is not taken into account in Eq. (3). Figure 5 also shows the emission cross sections calculated by the reciprocity relation using the absorption cross sections σabs which were obtained from absorption coefficients α calculated from transmission measurements and the Yb concentration cYb by a relation α = σabs·cYb. The identical shape of the emission cross section spectra independently obtained by both methods confirms that the reabsorption effect in the 180 µm thick sample is widely suppressed, and the use of the Füchtbauer-Ladenburg equation is reliable here. It is also a proof for the accurate intensity calibration of the measurement setup. The emission cross sections obtained by the Füchtbauer-Ladenburg equation are slightly lower than those from the reciprocity relation. The difference of ≈10% cannot be attributed to the much lower inaccuracy in the Yb concentration by ICP-OES. In addition, the absence of the ultraviolet absorption originating from Yb2+[42], confirmed by transmission measurements, ensures the determined Yb atomic concentration can be considered to be the Yb3+ concentration. In previous reports, the value stated for the room temperature emission cross section peak at 995 nm for π-polarization varies between 0.7·10−20 and 1.27·10−20 cm2, mainly because different radiative lifetimes are used in the Füchtbauer-Ladenburg equation [14,26,27,2931,33]. We evaluate the accuracy of our room temperature radiative lifetime of 2.2 ms to be better than ±5%. Therefore, non-reciprocity caused by vibronic transitions is suspected to play a role in the origin of this discrepancy [48].

 figure: Fig. 5.

Fig. 5. Polarization-resolved absorption and emission cross sections of Yb:YLF at 300 K. The emission cross sections drawn with solid lines are calculated by the Füchtbauer-Ladenburg (F-L) equation (Eq. (3)) using the radiative lifetime of 2.2 ms determined by the pinhole method. The emission cross sections shown with dashed lines are obtained using the reciprocity relation (Eq. (2)) from the absorption cross sections.

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We also recorded the fluorescence spectra of Yb:YLF for a wide range of temperatures from 17 K up to 440 K. Figure 6 shows the polarization-resolved emission cross sections calculated by the Füchtbauer-Ladenburg equation at selected temperatures in a logarithmic scale. The temperature-dependent effective radiative lifetimes given by Eq. (7), corresponding to the dashed line in Fig. 3(c), are used in Eq. (3). One clearly recognizes the correlation between the temperature-dependent emission cross sections and the population of the upper Stark levels shown in Fig. 2(b). For example, the intensity of the peaks at 960.2 nm (6→1 in Fig. 6) and at 947.9 nm (7→1 in Fig. 6) reflects the population of the corresponding Stark levels E6 and E7, respectively. The spectrum at 17 K confirms that the level E5 is the only populated Stark level at this temperature.

 figure: Fig. 6.

Fig. 6. Emission cross sections of Yb:YLF at selected temperatures between 17 K and 440 K. The cross section values were calculated from the fluorescence spectra by the Füchtbauer-Ladenburg equation using the temperature-dependent radiative lifetime model shown as dashed line in Fig. 3(c). The observed resonant transition peaks are labeled.

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Figure 7(a) shows the temperature dependency of the peak absorption cross section at the main laser pump wavelength of 960 nm for π-polarization. The data were derived from the emission cross sections in Fig. 6 using the reciprocity relation (Eq. (2)). This practice underestimates the absorption by ≈10%, which we confirmed by comparison with measured absorption data at room temperature (cf. Figure 5). In Fig. 7(b) and 7(c) the emission cross sections at the main laser wavelengths of 995 and 1020 nm for π-polarization are shown with respect to temperature. All data could be fitted with a sigmoidal Boltzmann function denoted in Figs. 7(a)-(c) with the respective fit parameters. Please note that the physical meaning of the fit parameters is limited because the change of the cross sections with temperature is only partially caused by a changing Boltzmann population and other relevant effects such as line-broadening with temperature are not considered. Demirbas et al. proposed polynomial fit equations for emission cross sections at representative wavelengths for the temperature range of 78–300 K [31]. Those at 995.1 and 1019.7 nm are shown with dashed lines in Fig. 7(b) and 7(c), respectively. Their emission cross section values are ≈10% larger around 300 K but in good agreement at 80 K as compared with our results, since they used a radiative lifetime of 2.0 ms for all temperatures. Our peak emission cross section values at 80 K are also consistent with another recent report [30].

 figure: Fig. 7.

Fig. 7. (a) Absorption cross section values at 960.2 nm and (b), (c) emission cross section values at 995.1, and 1019.7 nm for π-polarization with respect to temperature. Each data set is fitted by a sigmoidal Boltzmann function. The best fit parameters are shown in the respective figures. Dashed lines in (b) and (c) are the proposed fit equations in [31].

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5. Yb:YLF for laser cooling

A simple but useful model for laser cooling was first established by Hoyt et al. [49]. The model provides a temperature-dependent cooling efficiency ηc based on the external quantum efficiency ηext and a background absorption coefficient αb by

$${\eta _c}(\lambda ,T) = {\eta _{\textrm{ext}}}\cdot {\left[ {1 + \frac{{{\alpha_b}}}{{{\alpha_r}(\lambda ,T)}}} \right]^{ - 1}}\frac{\lambda }{{{\lambda _f}(T)}} - 1,$$
with the resonant absorption coefficient by the cooling ions αr, the pump wavelength λ and the mean fluorescence wavelength λf(T). The bracket term in the equation defines the absorption efficiency ηabs. Note that the external quantum efficiency and the background absorption coefficient are sample-specific parameters resulting from differences in crystal growth processes. This model enables to estimate the minimum achievable temperature (MAT) for a given excitation wavelength λ. The lowest MAT(λ) obtained at an optimum excitation wavelength λopt is so-called the global-MAT (MATg). The MAT in laser cooling depends strongly on the external quantum efficiency ηext and the absorption efficiency ηabs. A cooled medium reaches its MAT when cooling driven by anti-Stokes fluorescence balances with heating induced by impurities and non-radiative relaxation of the cooling ions. Recently, Volpi et al. revisited the model after they achieved cooling to temperatures below the MAT estimated from Eq. (8) using a YLF crystal doped with Yb and a small amount of Tm, and found a significant temperature dependence of the background absorption [6]. However, since the origin of the background absorption and its temperature dependency are not yet fully revealed, we treat the background absorption coefficient αb as a temperature-independent parameter. Instead, we calculate cooling efficiencies with a variety of background absorption coefficients αb.

One of the essential parameters for laser cooling based on anti-Stokes fluorescence is the mean fluorescence wavelength λf(T). This value is usually measured in the actual laser cooling setup because the detected fluorescence usually undergoes reabsorption and its influence depends on the pump and sample geometry. Thus, the calculated mean fluorescence wavelength λf for uniaxial crystals, defined as

$${\lambda _f}(T) = \frac{{\int {\lambda [{{I_{f,\pi }}(\lambda ,T) + 2{I_{f,\sigma }}(\lambda ,T)} ]} d\lambda }}{{\int {[{{I_{f,\pi }}(\lambda ,T) + 2{I_{f,\sigma }}(\lambda ,T)} ]d\lambda } }},$$
is usually longer than the value based on the intrinsic fluorescence spectra. Due to the strong spectral overlap between the emission and absorption on the shorter wavelength side, the mean fluorescence wavelength can be significantly red-shifted by reabsorption.

Figure 8 shows the temperature dependency of the mean fluorescence wavelength calculated from the fluorescence data with a 180 µm thick Yb:YLF sample. To intentionally show the influence of reabsorption, the mean fluorescence wavelength derived from data recorded with a 4.5 mm thick Yb:YLF sample is also presented in Fig. 8. For comparison, the linear fit equation presented in [7] is shown with the dashed line in the figure.

 figure: Fig. 8.

Fig. 8. Mean fluorescence wavelength λf from 17 to 440 K calculated from fluorescence spectra recorded with Yb:YLF samples of 180 µm and 4.5 mm thickness. A fitting with a sigmoidal Boltzmann function is applied to the values for the 180 µm sample above 50 K. The equation and the best fit parameters are also shown in the figure. Realignment and corresponding change of the reabsorption conditions with different temperature controllers above and below room temperature explains the minor discontinuity for the 4.5 mm sample. The dashed line is the linear fit equation presented in [7].

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As in Section 3 we confirmed that reabsorption effects in the fluorescence spectra are negligibly small for the 180 µm sample, its mean fluorescence wavelength can thus be considered to be the intrinsic mean fluorescence wavelength of Yb:YLF. To our knowledge this is the first report on the mean fluorescence wavelength not influenced by reabsorption. The data for the 180 µm sample are of particular relevance for laser cooling of micrometer-sized crystals [50], where the effect of reabsorption should be very limited. It is also reliable for thin samples with similar dimensions like the sample used here. Usual samples for laser cooling experiments have larger volume, so the amount of red shift in the mean fluorescence wavelength can be even larger than for the 4.5 mm sample. However, at temperatures below 50 K, the calculated mean fluorescence wavelengths for our two samples are very close, confirming that the influence of reabsorption on the mean fluorescence wavelength is very limited at these temperatures as seen in Fig. 4. This shows that the geometry of the sample becomes less relevant with decreasing temperature. It is also worth noting that the temperature dependency of the mean fluorescence wavelength can be considered to be linear when the fluorescence undergoes strong reabsorption [7].

The temperature-dependent resonant absorption coefficient αr(λ,T) is required for calculating the cooling efficiency according to Eq. (8). The corresponding values at 1020 nm, a typical pump wavelength for cooling Yb:YLF, easily become as low as 10−4 cm−1 at low temperatures. Such low values are not accessible by conventional absorption spectroscopy. Thus, the absorption spectra were again calculated using the reciprocity relation from the emission cross sections acquired with the 180 µm sample. The corresponding values for 20 K intervals in a temperature range between 50 K and 290 K for both polarizations are shown in Fig. 9.

 figure: Fig. 9.

Fig. 9. Temperature-dependent absorption cross sections of Yb:YLF calculated from the emission cross sections by the reciprocity relation (Eq. (2)). The temperature interval between each line is 20 K.

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With these data, we calculated the cooling efficiencies for Yb:YLF crystals of three different doping levels, 5 at.%, 10 at.%, and 20 at.%, using Eq. (8). Maximum cooling efficiencies ηc,max and optimum pump wavelengths λopt, defined as a wavelength to maximize cooling efficiency, with respect to temperature are plotted in Fig. 10. We calculated for various background absorptions αb, to account for different purity levels as well as a possible temperature dependence of the background absorption as reported in [6], and a fixed external quantum efficiency ηext of 99.5%. Note that we used the mean fluorescence wavelength obtained with the 180 µm sample. Figure 10 shows the cooling efficiencies in Yb:YLF also at elevated temperatures for the first time. The improved cooling efficiency here originates from the increasing population of the Stark levels E6 and E7 with temperature as shown in Fig. 2(b). This effect was recently experimentally confirmed with Yb:YAG [51]. Note that the longest pump wavelength in the calculation was 1070 nm as the absorption cross sections derived by the reciprocity relation above this wavelength are noisy since even the emission cross sections are fairly low above 1070 nm. Thus, for the data points with λopt = 1070 nm, even higher cooling efficiencies are obtainable at longer pump wavelengths. The calculations show that an Yb(20 at.%):YLF crystal with a reasonable background absorption of 4·10−4 cm−1 exhibits more than 6% cooling efficiency at 440 K. This corresponds to an enhancement of ≈30% in cooling efficiency compared to room temperature and may open a way to realize more efficient radiation-balanced lasers [12,13] operated at elevated temperatures.

 figure: Fig. 10.

Fig. 10. Optimum pump wavelengths λopt (top) and maximum cooling efficiencies (bottom) for (a) 5 at.%, (b) 10 at.%, and (c) 20 at.% Yb:YLF for π-polarization calculated for different background absorption coefficients. The external quantum efficiency was assumed to be 99.5% for all cases. Due to the lack of data for longer wavelengths, the optimum pump wavelength was restricted to a maximum value of 1070 nm. This underestimates the maximum cooling efficiency for the data points with λopt = 1070 nm.

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The zero-crossing temperature of each maximum cooling efficiency in Fig. 10 corresponds to the MATg. The MATg is always achieved at a pump wavelength of 1020 nm regardless of the doping concentration and the background absorption. Since the absorption at this wavelength corresponds to the resonant transition E4→E5, the population in the level E4 determines the absorption efficiency at low temperatures and accordingly the MATg. The calculated MATg for three external quantum efficiencies with respect to background absorption for five different Yb doping levels is shown in Fig. 11. It illustrates the significant decrease of the MAT with reduced background absorption.

 figure: Fig. 11.

Fig. 11. Global minimum achievable temperature (MATg) of 1 at.%, 2.5 at.%, 5 at.%, 10 at.%, and 20 at.% Yb:YLF for an external quantum efficiency ηext of (a) 98.5%, (b) 99.0%, and (c) 99.5% with respect to background absorption coefficient αb. The excitation is at 1020 nm for π-polarization to achieve the MATg for all cases.

Download Full Size | PPT Slide | PDF

As can be seen in Fig. 11(a) an external quantum efficiency of 98.5% is insufficient to cool down to the liquid nitrogen (LN) temperature of 77 K. The calculated results show the prospect to cool a highly pure Yb(20 at.%):YLF crystal down to ≈70 K assuming a background absorption in the order of 10−5 cm−1 and an external quantum efficiency higher than 99%. In a cooling setup, the mean fluorescence wavelength of bulk samples is longer than the presented intrinsic mean fluorescence wavelength due to reabsorption, but a MATg of ≈70 K would still be reasonable since at such low temperatures the impact of reabsorption becomes very small (cf. Figure 8). The investigations in [6] reveal a strong drop of the background absorption by an order of magnitude between 300 K and 110 K in an YLF crystal doped with Yb and co-doped with a small amount of Tm. In view of this result, it seems realistic to achieve cooling down to 70 K using crystals with room temperature background absorption in the order of 10−4 cm−1. Increasing the Yb concentration in YLF crystals without degrading the crystal quality and purity is thus considered to be the main challenge of crystal growth technology for the practical realization of cooling to such low temperatures.

6. Conclusion

We presented a detailed spectroscopic investigation of Yb:YLF for a wide range of temperatures between 17 K and 440 K. We were able to widely suppress radiation trapping by utilizing a very thin sample, and further corrected the measured fluorescence lifetimes by the temperature-dependent radiation trapping model with a reabsorption factor. The corrected data still exhibit a temperature dependence of the radiative lifetime originating from the Boltzmann distribution in the Stark levels of the 2F7/2 multiplet. To our knowledge, this is the first experimental proof directly showing such a temperature dependence of the radiative lifetime in Yb:YLF. This finding is also highly relevant for other host materials doped with Yb3+ since the precise radiative lifetime is important as the fluorescence lifetime at low temperatures was often erroneously taken as the radiative lifetime for all temperatures.

Further, we re-evaluated the emission cross sections in a wide temperature range by fully resolving all spectral features and strongly suppressing reabsorption effects. The derived sigmoidal Boltzmann fit equations for the temperature-dependent peak absorption and emission cross sections are also useful for the design of cryogenically operated laser oscillators and amplifiers based on Yb:YLF. These values also enabled to calculate the intrinsic mean fluorescence wavelength of Yb:YLF and to evaluate the influence of reabsorption on this parameter. Calculations of the MATg reveal that an external quantum efficiency higher than 99% and a background absorption in the order of 10−5 cm−1 are required to reach the LN temperature of 77 K or even lower values. Based on recent findings [6] we estimate that sufficiently low background absorption can be realized in crystals with a realistic value of 10−4 cm−1 at room temperature. Such crystals would furthermore provide significantly enhanced cooling efficiencies, thus increasing the efficiency limit of radiation-balanced lasers in particular when operated at elevated temperatures.

Acknowledgment

The authors thank Dr. Andrea Dittmar for determining the Yb concentration by ICP-OES, Dr. Steffen Ganschow for evaluating the homogeneity of the Yb concentration by XRF, and Albert Kwasniewski for orientating the Yb:YLF crystal by X-ray diffraction.

Disclosures

The authors declare no conflicts of interest.

References

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References

  • View by:

  1. P. Pringsheim, “Zwei Bemerkungen über den Unterschied von Lumineszenz- und Temperaturstrahlung,” Zeitschrift für Phys. 57(11-12), 739–746 (1929).
    [Crossref]
  2. M. Sheik-Bahae and R. I. Epstein, “Laser Cooling of Solids,” Laser Photonics Rev. 3, 67–84 (2009).
    [Crossref]
  3. D. V. Seletskiy, R. Epstein, and M. Sheik-Bahae, “Laser cooling in solids: Advances and prospects,” Rep. Prog. Phys. 79(9), 096401 (2016).
    [Crossref]
  4. R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnellt, and C. E. Mungant, “Fluorescent Cooling of a Solid,” Nature 377(6549), 500–503 (1995).
    [Crossref]
  5. S. D. Melgaard, A. R. Albrecht, M. P. Hehlen, and M. Sheik-Bahae, “Solid-state optical refrigeration to sub-100 Kelvin regime,” Sci. Rep. 6(1), 20380 (2016).
    [Crossref]
  6. A. Volpi, J. Meng, A. Gragossian, A. R. Albrecht, S. Rostami, A. Di Lieto, R. I. Epstein, M. Tonelli, M. P. Hehlen, and M. Sheik-Bahae, “Optical refrigeration: The role of parasitic absorption at cryogenic temperatures,” Opt. Express 27(21), 29710–29718 (2019).
    [Crossref]
  7. D. V. Seletskiy, M. P. Hehlen, R. I. Epstein, and M. Sheik-Bahae, “Cryogenic optical refrigeration,” Adv. Opt. Photonics 4(1), 78–107 (2012).
    [Crossref]
  8. S. Rostami, A. R. Albrecht, A. Volpi, M. P. Hehlen, M. Tonelli, and M. Sheik-Bahae, “Tm-doped crystals for mid-IR optical cryocoolers and radiation balanced lasers,” Opt. Lett. 44(6), 1419–1422 (2019).
    [Crossref]
  9. S. Rostami, A. R. Albrecht, A. Volpi, and M. Sheik-Bahae, “Observation of optical refrigeration in a holmium-doped crystal,” Photonics Res. 7(4), 445–451 (2019).
    [Crossref]
  10. M. P. Hehlen, J. Meng, A. R. Albrecht, E. R. Lee, A. Gragossian, S. P. Love, C. E. Hamilton, R. I. Epstein, and M. Sheik-Bahae, “First demonstration of an all-solid-state optical cryocooler,” Light: Sci. Appl. 7(1), 15 (2018).
    [Crossref]
  11. Q. Mermillod, J. Cazals, A. Glière, M. Dupoy, S. Chabardès, and N. Aubert, “Laser cooling of solids: towards biomedical applications,” in Photonic Heat Engines: Science and Applications, R. I. Epstein, D. V. Seletskiy, and M. Sheik-Bahae, eds. (SPIE, 2019), p. 21.
  12. S. R. Bowman, “Lasers without internal heat generation,” IEEE J. Quantum Electron. 35(1), 115–122 (1999).
    [Crossref]
  13. Z. Yang, J. Meng, A. R. Albrecht, and M. Sheik-Bahae, “Radiation-balanced Yb:YAG disk laser,” Opt. Express 27(2), 1392–1400 (2019).
    [Crossref]
  14. L. D. DeLoach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Evaluation of Absorption and Emission Properties of Yb3+ Doped Crystals for Laser Applications,” IEEE J. Quantum Electron. 29(4), 1179–1191 (1993).
    [Crossref]
  15. W. F. Krupke, “Ytterbium solid-state lasers - the first decade,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1287–1296 (2000).
    [Crossref]
  16. P.-H. Haumesser, R. Gaumé, B. Viana, and D. Vivien, “Determination of laser parameters of ytterbium-doped oxide crystalline materials,” J. Opt. Soc. Am. B 19(10), 2365–2375 (2002).
    [Crossref]
  17. T. Y. Fan, D. J. Ripin, R. L. Aggarwal, J. R. Ochoa, B. Chann, M. Tilleman, and J. Spitzberg, “Cryogenic Yb3+-doped solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 448–459 (2007).
    [Crossref]
  18. H. Cankaya, U. Demirbas, Y. Hua, M. Hemmer, L. E. Zapata, M. Pergament, and F. X. Kaertner, “190-mJ cryogenically-cooled Yb:YLF amplifier system at 1019.7 nm,” OSA Continuum 2(12), 3547–3553 (2019).
    [Crossref]
  19. U. Demirbas, H. Cankaya, Y. Hua, J. Thesinga, M. Pergament, and F. X. Kärtner, “20-mJ, sub-ps pulses at up to 70 W average power from a cryogenic Yb:YLF regenerative amplifier,” Opt. Express 28(2), 2466–2479 (2020).
    [Crossref]
  20. U. Demirbas, J. Thesinga, H. Cankaya, M. Kellert, F. X. Kärtner, and M. Pergament, “High-power passively mode-locked cryogenic Yb:YLF laser,” Opt. Lett. 45(7), 2050–2053 (2020).
    [Crossref]
  21. U. Demirbas, H. Cankaya, M. Pergament, and F. X. Kärtner, “Power and energy scaling of rod-type cryogenic Yb:YLF regenerative amplifiers,” J. Opt. Soc. Am. B 37(6), 1865–1877 (2020).
    [Crossref]
  22. Y. Liu, U. Demirbas, M. Kellert, J. Thesinga, H. Cankaya, Y. Hua, L. E. Zapata, M. Pergament, and F. X. Kärtner, “Eight-pass Yb:YLF cryogenic amplifier generating 305-mJ pulses,” OSA Continuum 3(10), 2722–2729 (2020).
    [Crossref]
  23. L. E. Zapata, D. J. Ripin, and T. Y. Fan, “Power scaling of cryogenic Yb:LiYF4 lasers,” Opt. Lett. 35(11), 1854–1856 (2010).
    [Crossref]
  24. N. Ter-Gabrielan, V. Fromzel, T. Sanamyan, and M. Dubinskii, “Highly-efficient Q-switched Yb:YLF laser at 995 nm with a second harmonic conversion,” Opt. Mater. Express 7(7), 2396–2403 (2017).
    [Crossref]
  25. H. Kühn, S. T. Fredrich-Thornton, C. Kränkel, R. Peters, and K. Petermann, “Model for the calculation of radiation trapping and description of the pinhole method,” Opt. Lett. 32(13), 1908–1910 (2007).
    [Crossref]
  26. J. Kawanaka, K. Yamakawa, H. Nishioka, and K. Ueda, “Improved high-field laser characteristics of a diode-pumped Yb:LiYF4 crystal at low temperature,” Opt. Express 10(10), 455–460 (2002).
    [Crossref]
  27. A. Bensalah, Y. Guyot, M. Ito, A. Brenier, H. Sato, T. Fukuda, and G. Boulon, “Growth of Yb3+-doped YLiF4 laser crystal by the Czochralski method. Attempt of Yb3+ energy level assignment and estimation of the laser potentiality,” Opt. Mater. (Amsterdam, Neth.) 26(4), 375–383 (2004).
    [Crossref]
  28. A. Sugiyama, M. Katsurayama, Y. Anzai, and T. Tsuboi, “Spectroscopic properties of Yb doped YLF grown by a vertical Bridgman method,” J. Alloys Compd. 408-412, 780–783 (2006).
    [Crossref]
  29. N. Coluccelli, G. Galzerano, L. Bonelli, A. Di Lieto, M. Tonelli, and P. Laporta, “Diode-pumped passively mode-locked Yb:YLF laser,” Opt. Express 16(5), 2922–2927 (2008).
    [Crossref]
  30. J. Körner, M. Krüger, J. Reiter, A. Münzer, J. Hein, and M. C. Kaluza, “Temperature dependent spectroscopic study of Yb3+-doped KG(WO4)2, KY(WO4)2, YAlO3 and YLiF4 for laser applications,” Opt. Mater. Express 10(10), 2425–2438 (2020).
    [Crossref]
  31. U. Demirbas, J. Thesinga, M. Kellert, F. X. Kärtner, and M. Pergament, “Detailed investigation of absorption, emission and gain in Yb:YLF in the 78–300 K range,” Opt. Mater. Express 11(2), 250–272 (2021).
    [Crossref]
  32. U. Demirbas, J. Thesinga, M. Kellert, M. Pergament, and F. X. Kärtner, “Temperature and doping dependence of fluorescence lifetime in Yb:YLF (role of impurities),” Opt. Mater. (Amsterdam, Neth.) 112, 110792 (2021).
    [Crossref]
  33. N. Uehara, K. Ueda, and Y. Kubota, “Spectroscopic Measurements of a High-Concentration Yb3+:LiYF4 Crystal,” Jpn. J. Appl. Phys. 35(Part 2, No. 4B), L499–L501 (1996).
    [Crossref]
  34. S. Dai, A. Sugiyama, L. Hu, Z. Liu, G. Huang, and Z. Jiang, “The spectrum and laser properties of ytterbium doped phosphate glass at low temperature,” J. Non-Cryst. Solids 311(2), 138–144 (2002).
    [Crossref]
  35. G. G. Demirkhanyan, “Intensities of inter-Stark transitions in YAG-Yb3+ crystals,” Laser Phys. 16(7), 1054–1057 (2006).
    [Crossref]
  36. D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136(4A), A954–A957 (1964).
    [Crossref]
  37. J. Czochralski, “Ein neues Verfahren zur Messung der Kristallisationsgeschwindigkeit der Metalle,” Z. Phys. Chem. 92U(1), 219–221 (1918).
    [Crossref]
  38. E. A. Brown, Harry Diamond Laboratories Reports TR-1932 (1980).
  39. J. E. Miller and E. J. Sharp, “Optical Properties and Energy Transfer in LiYF4:Nd 3+, Yb3+,” J. Appl. Phys. 41(11), 4718–4722 (1970).
    [Crossref]
  40. A. K. Kupchikov, B. Z. Malkin, A. L. Natadze, and A. I. Ryskin, “Raman study of the electron-phonon interaction in LiRF4 (RTb,Yb) crystals: Rare earth compounds: Tb, Dy, Ho, Er, Tm, Yb, Lu,” Sov. Phys.- Solid State 29, 3335–3346 (1987).
  41. S. Melgaard, D. Seletskiy, V. Polyak, Y. Asmerom, and M. Sheik-Bahae, “Identification of parasitic losses in Yb:YLF and prospects for optical refrigeration down to 80 K,” Opt. Express 22(7), 7756–7764 (2014).
    [Crossref]
  42. G. Huber, W. W. Krühler, W. Bludau, and H. G. Danielmeyer, “Anisotropy in the laser performance of NdP5O14,” J. Appl. Phys. 46(8), 3580–3584 (1975).
    [Crossref]
  43. J. B. Birks, “Energy Transfer in Organic Phosphors,” Phys. Rev. 94(6), 1567–1573 (1954).
    [Crossref]
  44. J. A. Caird, A. J. Ramponi, and P. R. Staver, “Quantum efficiency and excited-state relaxation dynamics in neodymium-doped phosphate laser glasses,” J. Opt. Soc. Am. B 8(7), 1391–1403 (1991).
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  45. D. S. Sumida and T. Y. Fan, “Emission Spectra and Fluorescence Lifetime Measurements of Yb:YAG as a Function of Temperature,” in Advanced Solid State Lasers (OSA, 2004), p. YL4.
  46. J. Dong, M. Bass, Y. Mao, P. Deng, and F. Gan, “Dependence of the Yb3+ emission cross section and lifetime on temperature and concentration in yttrium aluminum garnet,” J. Opt. Soc. Am. B 20(9), 1975–1979 (2003).
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  47. R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAlO3, LiYF4, LiLuF4, BaY2F8, KGd(WO4)2, and KY(WO4)2 laser crystals in the 80–300 K temperature range,” J. Appl. Phys. 98(10), 103514 (2005).
    [Crossref]
  48. B. Aull and H. Jenssen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. 18(5), 925–930 (1982).
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  49. C. W. Hoyt, M. P. Hasselbeck, M. Sheik-Bahae, R. I. Epstein, S. Greenfield, J. Thiede, J. Distel, and J. Valencia, “Advances in laser cooling of thulium-doped glass,” J. Opt. Soc. Am. B 20(5), 1066–1073 (2003).
    [Crossref]
  50. A. Pant, X. Xia, E. J. Davis, and P. J. Pauzauskie, “Solid-state laser refrigeration of a composite semiconductor Yb:YLiF4 optomechanical resonator,” Nat. Commun. 11(1), 3235 (2020).
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  51. Y. Nakayama, Y. Harada, and T. Kita, “Improving laser cooling efficiencies of Yb-doped yttrium aluminum garnet by utilizing non-resonant anti-Stokes emission at high temperatures,” Opt. Express 27(24), 34961–34973 (2019).
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2021 (2)

U. Demirbas, J. Thesinga, M. Kellert, F. X. Kärtner, and M. Pergament, “Detailed investigation of absorption, emission and gain in Yb:YLF in the 78–300 K range,” Opt. Mater. Express 11(2), 250–272 (2021).
[Crossref]

U. Demirbas, J. Thesinga, M. Kellert, M. Pergament, and F. X. Kärtner, “Temperature and doping dependence of fluorescence lifetime in Yb:YLF (role of impurities),” Opt. Mater. (Amsterdam, Neth.) 112, 110792 (2021).
[Crossref]

2020 (6)

2019 (6)

2018 (1)

M. P. Hehlen, J. Meng, A. R. Albrecht, E. R. Lee, A. Gragossian, S. P. Love, C. E. Hamilton, R. I. Epstein, and M. Sheik-Bahae, “First demonstration of an all-solid-state optical cryocooler,” Light: Sci. Appl. 7(1), 15 (2018).
[Crossref]

2017 (1)

2016 (2)

D. V. Seletskiy, R. Epstein, and M. Sheik-Bahae, “Laser cooling in solids: Advances and prospects,” Rep. Prog. Phys. 79(9), 096401 (2016).
[Crossref]

S. D. Melgaard, A. R. Albrecht, M. P. Hehlen, and M. Sheik-Bahae, “Solid-state optical refrigeration to sub-100 Kelvin regime,” Sci. Rep. 6(1), 20380 (2016).
[Crossref]

2014 (1)

2012 (1)

D. V. Seletskiy, M. P. Hehlen, R. I. Epstein, and M. Sheik-Bahae, “Cryogenic optical refrigeration,” Adv. Opt. Photonics 4(1), 78–107 (2012).
[Crossref]

2010 (1)

2009 (1)

M. Sheik-Bahae and R. I. Epstein, “Laser Cooling of Solids,” Laser Photonics Rev. 3, 67–84 (2009).
[Crossref]

2008 (1)

2007 (2)

H. Kühn, S. T. Fredrich-Thornton, C. Kränkel, R. Peters, and K. Petermann, “Model for the calculation of radiation trapping and description of the pinhole method,” Opt. Lett. 32(13), 1908–1910 (2007).
[Crossref]

T. Y. Fan, D. J. Ripin, R. L. Aggarwal, J. R. Ochoa, B. Chann, M. Tilleman, and J. Spitzberg, “Cryogenic Yb3+-doped solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 448–459 (2007).
[Crossref]

2006 (2)

A. Sugiyama, M. Katsurayama, Y. Anzai, and T. Tsuboi, “Spectroscopic properties of Yb doped YLF grown by a vertical Bridgman method,” J. Alloys Compd. 408-412, 780–783 (2006).
[Crossref]

G. G. Demirkhanyan, “Intensities of inter-Stark transitions in YAG-Yb3+ crystals,” Laser Phys. 16(7), 1054–1057 (2006).
[Crossref]

2005 (1)

R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAlO3, LiYF4, LiLuF4, BaY2F8, KGd(WO4)2, and KY(WO4)2 laser crystals in the 80–300 K temperature range,” J. Appl. Phys. 98(10), 103514 (2005).
[Crossref]

2004 (1)

A. Bensalah, Y. Guyot, M. Ito, A. Brenier, H. Sato, T. Fukuda, and G. Boulon, “Growth of Yb3+-doped YLiF4 laser crystal by the Czochralski method. Attempt of Yb3+ energy level assignment and estimation of the laser potentiality,” Opt. Mater. (Amsterdam, Neth.) 26(4), 375–383 (2004).
[Crossref]

2003 (2)

2002 (3)

2000 (1)

W. F. Krupke, “Ytterbium solid-state lasers - the first decade,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1287–1296 (2000).
[Crossref]

1999 (1)

S. R. Bowman, “Lasers without internal heat generation,” IEEE J. Quantum Electron. 35(1), 115–122 (1999).
[Crossref]

1996 (1)

N. Uehara, K. Ueda, and Y. Kubota, “Spectroscopic Measurements of a High-Concentration Yb3+:LiYF4 Crystal,” Jpn. J. Appl. Phys. 35(Part 2, No. 4B), L499–L501 (1996).
[Crossref]

1995 (1)

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnellt, and C. E. Mungant, “Fluorescent Cooling of a Solid,” Nature 377(6549), 500–503 (1995).
[Crossref]

1993 (1)

L. D. DeLoach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Evaluation of Absorption and Emission Properties of Yb3+ Doped Crystals for Laser Applications,” IEEE J. Quantum Electron. 29(4), 1179–1191 (1993).
[Crossref]

1991 (1)

1987 (1)

A. K. Kupchikov, B. Z. Malkin, A. L. Natadze, and A. I. Ryskin, “Raman study of the electron-phonon interaction in LiRF4 (RTb,Yb) crystals: Rare earth compounds: Tb, Dy, Ho, Er, Tm, Yb, Lu,” Sov. Phys.- Solid State 29, 3335–3346 (1987).

1982 (1)

B. Aull and H. Jenssen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. 18(5), 925–930 (1982).
[Crossref]

1975 (1)

G. Huber, W. W. Krühler, W. Bludau, and H. G. Danielmeyer, “Anisotropy in the laser performance of NdP5O14,” J. Appl. Phys. 46(8), 3580–3584 (1975).
[Crossref]

1970 (1)

J. E. Miller and E. J. Sharp, “Optical Properties and Energy Transfer in LiYF4:Nd 3+, Yb3+,” J. Appl. Phys. 41(11), 4718–4722 (1970).
[Crossref]

1964 (1)

D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136(4A), A954–A957 (1964).
[Crossref]

1954 (1)

J. B. Birks, “Energy Transfer in Organic Phosphors,” Phys. Rev. 94(6), 1567–1573 (1954).
[Crossref]

1929 (1)

P. Pringsheim, “Zwei Bemerkungen über den Unterschied von Lumineszenz- und Temperaturstrahlung,” Zeitschrift für Phys. 57(11-12), 739–746 (1929).
[Crossref]

1918 (1)

J. Czochralski, “Ein neues Verfahren zur Messung der Kristallisationsgeschwindigkeit der Metalle,” Z. Phys. Chem. 92U(1), 219–221 (1918).
[Crossref]

Aggarwal, R. L.

T. Y. Fan, D. J. Ripin, R. L. Aggarwal, J. R. Ochoa, B. Chann, M. Tilleman, and J. Spitzberg, “Cryogenic Yb3+-doped solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 448–459 (2007).
[Crossref]

R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAlO3, LiYF4, LiLuF4, BaY2F8, KGd(WO4)2, and KY(WO4)2 laser crystals in the 80–300 K temperature range,” J. Appl. Phys. 98(10), 103514 (2005).
[Crossref]

Albrecht, A. R.

A. Volpi, J. Meng, A. Gragossian, A. R. Albrecht, S. Rostami, A. Di Lieto, R. I. Epstein, M. Tonelli, M. P. Hehlen, and M. Sheik-Bahae, “Optical refrigeration: The role of parasitic absorption at cryogenic temperatures,” Opt. Express 27(21), 29710–29718 (2019).
[Crossref]

S. Rostami, A. R. Albrecht, A. Volpi, M. P. Hehlen, M. Tonelli, and M. Sheik-Bahae, “Tm-doped crystals for mid-IR optical cryocoolers and radiation balanced lasers,” Opt. Lett. 44(6), 1419–1422 (2019).
[Crossref]

S. Rostami, A. R. Albrecht, A. Volpi, and M. Sheik-Bahae, “Observation of optical refrigeration in a holmium-doped crystal,” Photonics Res. 7(4), 445–451 (2019).
[Crossref]

Z. Yang, J. Meng, A. R. Albrecht, and M. Sheik-Bahae, “Radiation-balanced Yb:YAG disk laser,” Opt. Express 27(2), 1392–1400 (2019).
[Crossref]

M. P. Hehlen, J. Meng, A. R. Albrecht, E. R. Lee, A. Gragossian, S. P. Love, C. E. Hamilton, R. I. Epstein, and M. Sheik-Bahae, “First demonstration of an all-solid-state optical cryocooler,” Light: Sci. Appl. 7(1), 15 (2018).
[Crossref]

S. D. Melgaard, A. R. Albrecht, M. P. Hehlen, and M. Sheik-Bahae, “Solid-state optical refrigeration to sub-100 Kelvin regime,” Sci. Rep. 6(1), 20380 (2016).
[Crossref]

Anzai, Y.

A. Sugiyama, M. Katsurayama, Y. Anzai, and T. Tsuboi, “Spectroscopic properties of Yb doped YLF grown by a vertical Bridgman method,” J. Alloys Compd. 408-412, 780–783 (2006).
[Crossref]

Asmerom, Y.

Aubert, N.

Q. Mermillod, J. Cazals, A. Glière, M. Dupoy, S. Chabardès, and N. Aubert, “Laser cooling of solids: towards biomedical applications,” in Photonic Heat Engines: Science and Applications, R. I. Epstein, D. V. Seletskiy, and M. Sheik-Bahae, eds. (SPIE, 2019), p. 21.

Aull, B.

B. Aull and H. Jenssen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. 18(5), 925–930 (1982).
[Crossref]

Bass, M.

Bensalah, A.

A. Bensalah, Y. Guyot, M. Ito, A. Brenier, H. Sato, T. Fukuda, and G. Boulon, “Growth of Yb3+-doped YLiF4 laser crystal by the Czochralski method. Attempt of Yb3+ energy level assignment and estimation of the laser potentiality,” Opt. Mater. (Amsterdam, Neth.) 26(4), 375–383 (2004).
[Crossref]

Birks, J. B.

J. B. Birks, “Energy Transfer in Organic Phosphors,” Phys. Rev. 94(6), 1567–1573 (1954).
[Crossref]

Bludau, W.

G. Huber, W. W. Krühler, W. Bludau, and H. G. Danielmeyer, “Anisotropy in the laser performance of NdP5O14,” J. Appl. Phys. 46(8), 3580–3584 (1975).
[Crossref]

Bonelli, L.

Boulon, G.

A. Bensalah, Y. Guyot, M. Ito, A. Brenier, H. Sato, T. Fukuda, and G. Boulon, “Growth of Yb3+-doped YLiF4 laser crystal by the Czochralski method. Attempt of Yb3+ energy level assignment and estimation of the laser potentiality,” Opt. Mater. (Amsterdam, Neth.) 26(4), 375–383 (2004).
[Crossref]

Bowman, S. R.

S. R. Bowman, “Lasers without internal heat generation,” IEEE J. Quantum Electron. 35(1), 115–122 (1999).
[Crossref]

Brenier, A.

A. Bensalah, Y. Guyot, M. Ito, A. Brenier, H. Sato, T. Fukuda, and G. Boulon, “Growth of Yb3+-doped YLiF4 laser crystal by the Czochralski method. Attempt of Yb3+ energy level assignment and estimation of the laser potentiality,” Opt. Mater. (Amsterdam, Neth.) 26(4), 375–383 (2004).
[Crossref]

Brown, E. A.

E. A. Brown, Harry Diamond Laboratories Reports TR-1932 (1980).

Buchwald, M. I.

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnellt, and C. E. Mungant, “Fluorescent Cooling of a Solid,” Nature 377(6549), 500–503 (1995).
[Crossref]

Caird, J. A.

Cankaya, H.

Cazals, J.

Q. Mermillod, J. Cazals, A. Glière, M. Dupoy, S. Chabardès, and N. Aubert, “Laser cooling of solids: towards biomedical applications,” in Photonic Heat Engines: Science and Applications, R. I. Epstein, D. V. Seletskiy, and M. Sheik-Bahae, eds. (SPIE, 2019), p. 21.

Chabardès, S.

Q. Mermillod, J. Cazals, A. Glière, M. Dupoy, S. Chabardès, and N. Aubert, “Laser cooling of solids: towards biomedical applications,” in Photonic Heat Engines: Science and Applications, R. I. Epstein, D. V. Seletskiy, and M. Sheik-Bahae, eds. (SPIE, 2019), p. 21.

Chann, B.

T. Y. Fan, D. J. Ripin, R. L. Aggarwal, J. R. Ochoa, B. Chann, M. Tilleman, and J. Spitzberg, “Cryogenic Yb3+-doped solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 448–459 (2007).
[Crossref]

Chase, L. L.

L. D. DeLoach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Evaluation of Absorption and Emission Properties of Yb3+ Doped Crystals for Laser Applications,” IEEE J. Quantum Electron. 29(4), 1179–1191 (1993).
[Crossref]

Coluccelli, N.

Czochralski, J.

J. Czochralski, “Ein neues Verfahren zur Messung der Kristallisationsgeschwindigkeit der Metalle,” Z. Phys. Chem. 92U(1), 219–221 (1918).
[Crossref]

Dai, S.

S. Dai, A. Sugiyama, L. Hu, Z. Liu, G. Huang, and Z. Jiang, “The spectrum and laser properties of ytterbium doped phosphate glass at low temperature,” J. Non-Cryst. Solids 311(2), 138–144 (2002).
[Crossref]

Danielmeyer, H. G.

G. Huber, W. W. Krühler, W. Bludau, and H. G. Danielmeyer, “Anisotropy in the laser performance of NdP5O14,” J. Appl. Phys. 46(8), 3580–3584 (1975).
[Crossref]

Davis, E. J.

A. Pant, X. Xia, E. J. Davis, and P. J. Pauzauskie, “Solid-state laser refrigeration of a composite semiconductor Yb:YLiF4 optomechanical resonator,” Nat. Commun. 11(1), 3235 (2020).
[Crossref]

DeLoach, L. D.

L. D. DeLoach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Evaluation of Absorption and Emission Properties of Yb3+ Doped Crystals for Laser Applications,” IEEE J. Quantum Electron. 29(4), 1179–1191 (1993).
[Crossref]

Demirbas, U.

U. Demirbas, J. Thesinga, M. Kellert, F. X. Kärtner, and M. Pergament, “Detailed investigation of absorption, emission and gain in Yb:YLF in the 78–300 K range,” Opt. Mater. Express 11(2), 250–272 (2021).
[Crossref]

U. Demirbas, J. Thesinga, M. Kellert, M. Pergament, and F. X. Kärtner, “Temperature and doping dependence of fluorescence lifetime in Yb:YLF (role of impurities),” Opt. Mater. (Amsterdam, Neth.) 112, 110792 (2021).
[Crossref]

Y. Liu, U. Demirbas, M. Kellert, J. Thesinga, H. Cankaya, Y. Hua, L. E. Zapata, M. Pergament, and F. X. Kärtner, “Eight-pass Yb:YLF cryogenic amplifier generating 305-mJ pulses,” OSA Continuum 3(10), 2722–2729 (2020).
[Crossref]

U. Demirbas, H. Cankaya, M. Pergament, and F. X. Kärtner, “Power and energy scaling of rod-type cryogenic Yb:YLF regenerative amplifiers,” J. Opt. Soc. Am. B 37(6), 1865–1877 (2020).
[Crossref]

U. Demirbas, J. Thesinga, H. Cankaya, M. Kellert, F. X. Kärtner, and M. Pergament, “High-power passively mode-locked cryogenic Yb:YLF laser,” Opt. Lett. 45(7), 2050–2053 (2020).
[Crossref]

U. Demirbas, H. Cankaya, Y. Hua, J. Thesinga, M. Pergament, and F. X. Kärtner, “20-mJ, sub-ps pulses at up to 70 W average power from a cryogenic Yb:YLF regenerative amplifier,” Opt. Express 28(2), 2466–2479 (2020).
[Crossref]

H. Cankaya, U. Demirbas, Y. Hua, M. Hemmer, L. E. Zapata, M. Pergament, and F. X. Kaertner, “190-mJ cryogenically-cooled Yb:YLF amplifier system at 1019.7 nm,” OSA Continuum 2(12), 3547–3553 (2019).
[Crossref]

Demirkhanyan, G. G.

G. G. Demirkhanyan, “Intensities of inter-Stark transitions in YAG-Yb3+ crystals,” Laser Phys. 16(7), 1054–1057 (2006).
[Crossref]

Deng, P.

Di Lieto, A.

Distel, J.

Dong, J.

Dubinskii, M.

Dupoy, M.

Q. Mermillod, J. Cazals, A. Glière, M. Dupoy, S. Chabardès, and N. Aubert, “Laser cooling of solids: towards biomedical applications,” in Photonic Heat Engines: Science and Applications, R. I. Epstein, D. V. Seletskiy, and M. Sheik-Bahae, eds. (SPIE, 2019), p. 21.

Edwards, B. C.

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnellt, and C. E. Mungant, “Fluorescent Cooling of a Solid,” Nature 377(6549), 500–503 (1995).
[Crossref]

Epstein, R.

D. V. Seletskiy, R. Epstein, and M. Sheik-Bahae, “Laser cooling in solids: Advances and prospects,” Rep. Prog. Phys. 79(9), 096401 (2016).
[Crossref]

Epstein, R. I.

A. Volpi, J. Meng, A. Gragossian, A. R. Albrecht, S. Rostami, A. Di Lieto, R. I. Epstein, M. Tonelli, M. P. Hehlen, and M. Sheik-Bahae, “Optical refrigeration: The role of parasitic absorption at cryogenic temperatures,” Opt. Express 27(21), 29710–29718 (2019).
[Crossref]

M. P. Hehlen, J. Meng, A. R. Albrecht, E. R. Lee, A. Gragossian, S. P. Love, C. E. Hamilton, R. I. Epstein, and M. Sheik-Bahae, “First demonstration of an all-solid-state optical cryocooler,” Light: Sci. Appl. 7(1), 15 (2018).
[Crossref]

D. V. Seletskiy, M. P. Hehlen, R. I. Epstein, and M. Sheik-Bahae, “Cryogenic optical refrigeration,” Adv. Opt. Photonics 4(1), 78–107 (2012).
[Crossref]

M. Sheik-Bahae and R. I. Epstein, “Laser Cooling of Solids,” Laser Photonics Rev. 3, 67–84 (2009).
[Crossref]

C. W. Hoyt, M. P. Hasselbeck, M. Sheik-Bahae, R. I. Epstein, S. Greenfield, J. Thiede, J. Distel, and J. Valencia, “Advances in laser cooling of thulium-doped glass,” J. Opt. Soc. Am. B 20(5), 1066–1073 (2003).
[Crossref]

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnellt, and C. E. Mungant, “Fluorescent Cooling of a Solid,” Nature 377(6549), 500–503 (1995).
[Crossref]

Fan, T. Y.

L. E. Zapata, D. J. Ripin, and T. Y. Fan, “Power scaling of cryogenic Yb:LiYF4 lasers,” Opt. Lett. 35(11), 1854–1856 (2010).
[Crossref]

T. Y. Fan, D. J. Ripin, R. L. Aggarwal, J. R. Ochoa, B. Chann, M. Tilleman, and J. Spitzberg, “Cryogenic Yb3+-doped solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 448–459 (2007).
[Crossref]

R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAlO3, LiYF4, LiLuF4, BaY2F8, KGd(WO4)2, and KY(WO4)2 laser crystals in the 80–300 K temperature range,” J. Appl. Phys. 98(10), 103514 (2005).
[Crossref]

D. S. Sumida and T. Y. Fan, “Emission Spectra and Fluorescence Lifetime Measurements of Yb:YAG as a Function of Temperature,” in Advanced Solid State Lasers (OSA, 2004), p. YL4.

Fredrich-Thornton, S. T.

Fromzel, V.

Fukuda, T.

A. Bensalah, Y. Guyot, M. Ito, A. Brenier, H. Sato, T. Fukuda, and G. Boulon, “Growth of Yb3+-doped YLiF4 laser crystal by the Czochralski method. Attempt of Yb3+ energy level assignment and estimation of the laser potentiality,” Opt. Mater. (Amsterdam, Neth.) 26(4), 375–383 (2004).
[Crossref]

Galzerano, G.

Gan, F.

Gaumé, R.

Glière, A.

Q. Mermillod, J. Cazals, A. Glière, M. Dupoy, S. Chabardès, and N. Aubert, “Laser cooling of solids: towards biomedical applications,” in Photonic Heat Engines: Science and Applications, R. I. Epstein, D. V. Seletskiy, and M. Sheik-Bahae, eds. (SPIE, 2019), p. 21.

Gosnellt, T. R.

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnellt, and C. E. Mungant, “Fluorescent Cooling of a Solid,” Nature 377(6549), 500–503 (1995).
[Crossref]

Gragossian, A.

A. Volpi, J. Meng, A. Gragossian, A. R. Albrecht, S. Rostami, A. Di Lieto, R. I. Epstein, M. Tonelli, M. P. Hehlen, and M. Sheik-Bahae, “Optical refrigeration: The role of parasitic absorption at cryogenic temperatures,” Opt. Express 27(21), 29710–29718 (2019).
[Crossref]

M. P. Hehlen, J. Meng, A. R. Albrecht, E. R. Lee, A. Gragossian, S. P. Love, C. E. Hamilton, R. I. Epstein, and M. Sheik-Bahae, “First demonstration of an all-solid-state optical cryocooler,” Light: Sci. Appl. 7(1), 15 (2018).
[Crossref]

Greenfield, S.

Guyot, Y.

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A. Bensalah, Y. Guyot, M. Ito, A. Brenier, H. Sato, T. Fukuda, and G. Boulon, “Growth of Yb3+-doped YLiF4 laser crystal by the Czochralski method. Attempt of Yb3+ energy level assignment and estimation of the laser potentiality,” Opt. Mater. (Amsterdam, Neth.) 26(4), 375–383 (2004).
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N. Uehara, K. Ueda, and Y. Kubota, “Spectroscopic Measurements of a High-Concentration Yb3+:LiYF4 Crystal,” Jpn. J. Appl. Phys. 35(Part 2, No. 4B), L499–L501 (1996).
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A. Pant, X. Xia, E. J. Davis, and P. J. Pauzauskie, “Solid-state laser refrigeration of a composite semiconductor Yb:YLiF4 optomechanical resonator,” Nat. Commun. 11(1), 3235 (2020).
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Adv. Opt. Photonics (1)

D. V. Seletskiy, M. P. Hehlen, R. I. Epstein, and M. Sheik-Bahae, “Cryogenic optical refrigeration,” Adv. Opt. Photonics 4(1), 78–107 (2012).
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L. D. DeLoach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Evaluation of Absorption and Emission Properties of Yb3+ Doped Crystals for Laser Applications,” IEEE J. Quantum Electron. 29(4), 1179–1191 (1993).
[Crossref]

B. Aull and H. Jenssen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. 18(5), 925–930 (1982).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

W. F. Krupke, “Ytterbium solid-state lasers - the first decade,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1287–1296 (2000).
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T. Y. Fan, D. J. Ripin, R. L. Aggarwal, J. R. Ochoa, B. Chann, M. Tilleman, and J. Spitzberg, “Cryogenic Yb3+-doped solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 448–459 (2007).
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J. Alloys Compd. (1)

A. Sugiyama, M. Katsurayama, Y. Anzai, and T. Tsuboi, “Spectroscopic properties of Yb doped YLF grown by a vertical Bridgman method,” J. Alloys Compd. 408-412, 780–783 (2006).
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J. Appl. Phys. (3)

R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAlO3, LiYF4, LiLuF4, BaY2F8, KGd(WO4)2, and KY(WO4)2 laser crystals in the 80–300 K temperature range,” J. Appl. Phys. 98(10), 103514 (2005).
[Crossref]

J. E. Miller and E. J. Sharp, “Optical Properties and Energy Transfer in LiYF4:Nd 3+, Yb3+,” J. Appl. Phys. 41(11), 4718–4722 (1970).
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G. Huber, W. W. Krühler, W. Bludau, and H. G. Danielmeyer, “Anisotropy in the laser performance of NdP5O14,” J. Appl. Phys. 46(8), 3580–3584 (1975).
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J. Non-Cryst. Solids (1)

S. Dai, A. Sugiyama, L. Hu, Z. Liu, G. Huang, and Z. Jiang, “The spectrum and laser properties of ytterbium doped phosphate glass at low temperature,” J. Non-Cryst. Solids 311(2), 138–144 (2002).
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J. Opt. Soc. Am. B (5)

Jpn. J. Appl. Phys. (1)

N. Uehara, K. Ueda, and Y. Kubota, “Spectroscopic Measurements of a High-Concentration Yb3+:LiYF4 Crystal,” Jpn. J. Appl. Phys. 35(Part 2, No. 4B), L499–L501 (1996).
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Laser Photonics Rev. (1)

M. Sheik-Bahae and R. I. Epstein, “Laser Cooling of Solids,” Laser Photonics Rev. 3, 67–84 (2009).
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Laser Phys. (1)

G. G. Demirkhanyan, “Intensities of inter-Stark transitions in YAG-Yb3+ crystals,” Laser Phys. 16(7), 1054–1057 (2006).
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Light: Sci. Appl. (1)

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[Crossref]

Nat. Commun. (1)

A. Pant, X. Xia, E. J. Davis, and P. J. Pauzauskie, “Solid-state laser refrigeration of a composite semiconductor Yb:YLiF4 optomechanical resonator,” Nat. Commun. 11(1), 3235 (2020).
[Crossref]

Nature (1)

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnellt, and C. E. Mungant, “Fluorescent Cooling of a Solid,” Nature 377(6549), 500–503 (1995).
[Crossref]

Opt. Express (7)

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Figures (11)

Fig. 1.
Fig. 1. Polarization-resolved (a) absorption coefficient and (b) fluorescence intensity spectra of the Yb(5 at.%):YLF samples recorded at 17 K. The absorption spectra left of the dashed line at 955 nm in (a) were taken with a sample of 4.5 mm thickness and are enhanced by a factor of 10 for clarity. The region above 955 nm was recorded with a 180 µm thick sample. In both figures the peaks assigned as the resonant transitions between the Stark levels are marked with black dots.
Fig. 2.
Fig. 2. (a) Energy diagram of Yb3+ in the host material YLF with corresponding absorption and emission lines. (b) Fractional occupancy of the Stark levels in the 2F5/2 multiplet based on the Boltzmann distribution as a function of temperature calculated by Eq. (6).
Fig. 3.
Fig. 3. (a) Fluorescence lifetime measured with pinholes of different diameter. The intrinsic fluorescence lifetime is extrapolated to be 2.20 ± 0.03 ms. (b) Time-dependent fluorescence signal at 17 K and 440 K from a Yb(5 at.%):YLF sample of a 180 µm thickness suppressing radiation trapping. (c) Fluorescence lifetime versus temperature measured with a Yb(5 at.%):YLF sample of a 180 µm. Circular symbols represent the measured lifetime. Diamond symbols correspond to the fluorescence lifetime corrected for remaining radiation trapping by Eq. (5). Star symbol indicates the lifetime at room temperature determined by the pinhole method used as τ0 in Eq. (5). Dashed line is the result of fitting with Eq. (7) with the radiative lifetimes of each individual Stark level τi denoted in the figure.
Fig. 4.
Fig. 4. Reabsorption factor with respect to temperature calculated by Eq. (4) using the fluorescence spectra and using the absorption spectra.
Fig. 5.
Fig. 5. Polarization-resolved absorption and emission cross sections of Yb:YLF at 300 K. The emission cross sections drawn with solid lines are calculated by the Füchtbauer-Ladenburg (F-L) equation (Eq. (3)) using the radiative lifetime of 2.2 ms determined by the pinhole method. The emission cross sections shown with dashed lines are obtained using the reciprocity relation (Eq. (2)) from the absorption cross sections.
Fig. 6.
Fig. 6. Emission cross sections of Yb:YLF at selected temperatures between 17 K and 440 K. The cross section values were calculated from the fluorescence spectra by the Füchtbauer-Ladenburg equation using the temperature-dependent radiative lifetime model shown as dashed line in Fig. 3(c). The observed resonant transition peaks are labeled.
Fig. 7.
Fig. 7. (a) Absorption cross section values at 960.2 nm and (b), (c) emission cross section values at 995.1, and 1019.7 nm for π-polarization with respect to temperature. Each data set is fitted by a sigmoidal Boltzmann function. The best fit parameters are shown in the respective figures. Dashed lines in (b) and (c) are the proposed fit equations in [31].
Fig. 8.
Fig. 8. Mean fluorescence wavelength λf from 17 to 440 K calculated from fluorescence spectra recorded with Yb:YLF samples of 180 µm and 4.5 mm thickness. A fitting with a sigmoidal Boltzmann function is applied to the values for the 180 µm sample above 50 K. The equation and the best fit parameters are also shown in the figure. Realignment and corresponding change of the reabsorption conditions with different temperature controllers above and below room temperature explains the minor discontinuity for the 4.5 mm sample. The dashed line is the linear fit equation presented in [7].
Fig. 9.
Fig. 9. Temperature-dependent absorption cross sections of Yb:YLF calculated from the emission cross sections by the reciprocity relation (Eq. (2)). The temperature interval between each line is 20 K.
Fig. 10.
Fig. 10. Optimum pump wavelengths λopt (top) and maximum cooling efficiencies (bottom) for (a) 5 at.%, (b) 10 at.%, and (c) 20 at.% Yb:YLF for π-polarization calculated for different background absorption coefficients. The external quantum efficiency was assumed to be 99.5% for all cases. Due to the lack of data for longer wavelengths, the optimum pump wavelength was restricted to a maximum value of 1070 nm. This underestimates the maximum cooling efficiency for the data points with λopt = 1070 nm.
Fig. 11.
Fig. 11. Global minimum achievable temperature (MATg) of 1 at.%, 2.5 at.%, 5 at.%, 10 at.%, and 20 at.% Yb:YLF for an external quantum efficiency ηext of (a) 98.5%, (b) 99.0%, and (c) 99.5% with respect to background absorption coefficient αb. The excitation is at 1020 nm for π-polarization to achieve the MATg for all cases.

Equations (9)

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f reabs ( T ) = [ σ em , π ( λ , T ) σ abs , π ( λ , T ) + 2 σ em , σ ( λ , T ) σ abs , σ ( λ , T ) ] d λ [ σ em , π 2 ( λ , T ) + 2 σ em , σ 2 ( λ , T ) ] d λ .
σ em , ζ ( λ , T ) = σ abs , ζ ( λ , T ) Z l Z u exp ( h c / λ E ZPL k B T ) , where  Z k = i g i exp ( E i k B T ) .
σ em , ζ ( λ , T ) = λ 5 8 π c n ζ ( λ ) τ rad I ζ ( λ , T ) 1 3 [ λ I π ( λ , T ) + 2 λ I σ ( λ , T ) ] d λ ,
f reabs ( T ) = Z u ( T ) Z l ( T ) exp ( E ZPL k B T ) λ 10 [ I π 2 ( λ , T ) + 2 I σ 2 ( λ , T ) ] exp ( h c / λ k B T ) d λ λ 10 [ I π 2 ( λ , T ) + 2 I σ 2 ( λ , T ) ] d λ .
τ meas ( T ) = τ 0 ( T ) 1 β f reabs ( T ) .
f i ( T ) = exp ( E i E ZPL k B T ) k = 5 7 exp ( E k E ZPL k B T ) ,
τ rad ( T ) = [ i = 5 7 f i ( T ) τ i ] 1 ,
η c ( λ , T ) = η ext [ 1 + α b α r ( λ , T ) ] 1 λ λ f ( T ) 1 ,
λ f ( T ) = λ [ I f , π ( λ , T ) + 2 I f , σ ( λ , T ) ] d λ [ I f , π ( λ , T ) + 2 I f , σ ( λ , T ) ] d λ ,

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