We present the results of a comprehensive spectroscopic investigation pertaining to laser potential evaluation of the 3-micron Dy3+ mid-IR transition in the low-maximum phonon energy host barium fluoride (BaF2). This investigation involved absorption, fluorescence, and decay time measurements, recorded for a range of temperatures. Laser-relevant parameters such as absorption and stimulated-emission cross sections, quantum-efficiencies, and radiative lifetimes were determined for room temperature (300 K) and liquid nitrogen temperature. The peak stimulated emission cross section was found to be 0.45×10−20 cm2 at room temperature and 1.58×10−20 cm2 at 77 K. The gain cross sections, predictive of laser potential, were also derived. Finally, an examination of the nature of the non-radiative decay rates as a function of temperature was performed, showing the degree to which multi-phonon relaxation and other non-radiative pathways affect the overall fluorescence behavior.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Laser development in the mid-infrared spectral region (2–5 µm) has been of particular interest recently due to a wide range of potential applications. In particular, lasers operating between 2.5 and 3 µm can take advantage of the strong absorption by water and OH-radicals in that region to be instrumental in such applications as remote atmospheric sensing , medical procedures , and wind lidar . A significant amount of the ongoing mid-infrared laser research is focused on rare-earth (RE) doped materials, because RE active ions can provide a number of favorable energy transitions in the desired wavelength range [4–6]. Among the various RE ions, erbium (Er3+) and holmium (Ho3+) have been studied extensively for their transitions in the 2.5 to 3 µm spectral region [7,8]. However, in recent years dysprosium (Dy3+) has received increased interest for its 6H13/2 → 6H15/2 transition which produces emission around 3 µm [9,10].
Complications in the development of mid-infrared lasers arise because the relatively small energy gaps needed to generate mid-infrared photons are especially susceptible to non-radiative decay mechanisms such as multi-phonon relaxation (MPR). To achieve higher emission efficiencies, the RE dopants must be hosted by materials with low maximum phonon energies to mitigate these MPR processes [11,12]. Fluorites (CaF2, SrF2, and BaF2) have emerged as interesting host crystals due to their low maximum phonon energies, high thermal conductivities, and ability to incorporate RE dopants [9,13,14]. Dy3+ has been studied in CaF2  and SrF2  but its spectroscopic properties are largely unexplored in BaF2.
Recently, we presented a detailed spectroscopic study of the mid-IR fluorescence from Er3+-doped BaF2 crystals . In this work, we present a spectroscopic investigation pertinent to ∼2.8 µm mid-infrared laser potential of Dy3+:BaF2. The Dy3+ ion offers a number of possible transitions in the near- and mid-infrared, as shown by the energy level diagram in Fig. 1. For spectroscopic characterization of the ∼2.8 µm mid-infrared transition of Dy3+:BaF2, only the two lowest manifolds of the dysprosium ion are relevant. The present study involves absorption measurements from the ground state (6H15/2) to the 6H13/2 excited manifold, fluorescence lifetime measurements of this excited state, and measurements of the fluorescence spectrum for the 6H13/2 → 6H15/2 transition. These basic measurements, performed over a wide range of temperatures, provide information on the quantum efficiency, the stimulated-emission cross section, and the gain cross-section for the 2.8 µm transition.
2. Experimental details
BaF2 is a cubic crystal with a space group symmetry of Fm3 m and a density of 4.89 g/cm3. Its transmission window extends from 0.2 to 14 µm due to its wide bandgap of ∼11 eV . The maximum phonon energy has been quoted in literature to be as low as ∼320 cm−1 , making it the lowest in the fluorite family. Rare-earth dopant ions have proven to be incorporated into the divalent Ba2+ lattice sites , requiring a charge compensation if multi-site activation is undesirable. It was reported that, for rare-earth doped into fluorites the charge is compensated by an interstitial fluorine ion at the nearest neighbor position of C4v symmetry .
The Dy3+ doped BaF2 single crystals studied in this work were grown by Bridgman technique with RE concentration of nominally 1 at.% corresponding to 1.67×1020 ions/cm3. The as-grown boule was diced and polished prior to spectroscopic characterization.
Room temperature absorption spectra were recorded using a Cary 6000i UV-Vis-NIR spectrophotometer for the region from 600–1700nm and a Nicolet 6700 Fourier-transform infrared spectrometer for wavelengths greater than 1700 nm. Both the Cary and the Nicolet achieved maximum resolutions of 0.1 nm. All mid-IR fluorescence spectra were excited at 898.7 nm by a continuous-wave Spectra-Physics Tsunami Ti:Sapphire laser. Mid-infrared fluorescence spectra were collected using a Horiba Fluorolog-3 system with an iHR-320 monochromator (λblaze: 2 µm, 300 grooves/mm) and the emission signal was recorded by an Infrared Associates liquid-nitrogen-cooled InSb detector in conjunction with a Stanford Research Systems SR830 dual-phase lock-in amplifier. The mid-infrared fluorescence resolution of this system was 0.2 nm. Fluorescence decay measurements were excited at 1723nm using the output of a pulsed (10 ns pulses, 10 Hz) PrimoScan ULD Optical Parametric Oscillator (OPO) pumped with a Spectra Physics Nd: YAG laser. The decay signal was recorded with a home-made LabView program using National Instruments data acquisition system. For temperature dependent emission studies down to 10 K, the sample was mounted on the cold finger of a two-stage closed-cycle CTI Cryodyne helium refrigerator.
3. Results and discussion
3.1 Absorption measurements
Initial absorption measurements of the 1 at.% Dy3+:BaF2 sample were conducted at room temperature across the spectral range from 600 nm to 3300 nm. These results, shown in Fig. 2, provide important information on the absorption band of interest for in-band pumping (6H15/2 → 6H13/2) as well as a number of other absorption lines in the near-infrared which could be used for excitation purposes. Of particular interest are the absorption peaks in the 800–1000 nm region because those could be pumped by the most powerful and efficient commercial diode pump modules. In fact, the absorption line associated with the 6H15/2 → 6F7/2 transition at 898.7 nm was used for excitation during our fluorescence spectroscopy measurements.
High resolution ground state absorption spectra into the 6H13/2 manifold were measured at several temperatures in the range of 10–300 K for the Dy3+:BaF2 sample. Absorption cross sections were calculated from the 300 K (room temperature) and 77 K (cryogenic temperature) absorption data using Beer’s law and the rare earth dopant concentration of 1.67×1020 ions/cm3. Figure 3 shows that the highest absorption peak (∼2842 nm) grows by a factor of 4 when cooling the sample from room temperature to 77 K, with peak cross section values of 0.4×10−20 cm2 and 1.6×10−20 cm2, respectively.
3.2 Energy level analysis
Detailed information on the energy levels relevant to the ∼2.8 µm transition is imperative for determining the stimulated emission cross section using the McCumber method which exploits the reciprocal nature of the absorption and stimulated emission transitions . This reciprocity relation is written
Taking into account that the static BaF2 crystal field experienced by the dysprosium ion should split its manifolds into 2J+1 Stark levels, and also factoring in the Kramers degeneracy rule, we should expect the 6H15/2 manifold to have 8 levels and the 6H13/2 manifolds to have 7 levels. In order to determine these energy levels, we typically record numerous absorption and emission spectra and observe how the spectral peaks change as a function of temperature. At the lowest sample temperatures, the spectrum should be dominated by transitions originating from the lowest energy level of the initial manifold. As the sample temperature is increased, transitions from thermally excited levels (i.e. “hot lines”) of the initial manifold grow in intensity.
Figure 4(a) shows absorption spectra from the ground state into the first excited state of Dy3+ for a number of sample temperatures down to 15 K. While the spectral lines do get significantly narrower at the lower temperatures, they are still much too wide to allow for non-arbitrary energy level assignments. Additionally, even at the lowest temperature, there are many more than the expected 7 spectral peaks that present themselves as coming from the lowest level of the ground manifold. In order to look at a simpler manifold, a similar series of measurements was performed for absorption into the 6F3/2 level at ∼750 nm, where there should only be 2 dominant peaks at the lowest temperature. The results, shown in Fig. 4(b), display 8 distinct peaks all presenting the opposite behavior from what would be expected for “hot lines”, namely an increasing relative intensity with increasing temperature. While the 6F3/2 absorption results also proved too difficult to allow for energy level assignments, they do imply that there may be multiple Dy3+ incorporation sites in our material. Such a conclusion is not unwarranted considering that no charge-compensating co-dopant was used during the crystal growth. Because there is a charge mismatch between the rare earth dopant and its substitutional counterpart Ba2+, this should lead to all kinds of distortions of the crystal lattice, due to the variety of ways in which non-local charge compensation can happen .
Since analysis of the low temperature absorption spectra proved fruitless in the determination of the Dy3+ energy levels, an alternative approach was necessary. The work of Zhang et al.  describes a method for estimating EZL and the ZL/ZU ratio that does not require knowledge of the discrete level energies. Instead, all that is needed is a comparison between absorption and fluorescence spectra. In practice, these two spectra are separately normalized and then plotted on the same graph as a function of energy. According to the reciprocity principle, the cross point of the spectra should be the zero line EZL. Measuring the low energy width of the fluorescence spectrum, from EZL, gives information about the energy spacing of the lower manifold, while similarly measuring the high energy width of the absorption spectrum gives information about the energy spacing of the upper manifold. Assuming the levels of each manifold are equally spaced, ZL/ZU can be estimated to be the ratio of the low energy width to the high energy width. Because the baselines between the two spectra can be ambiguous, the energy widths are determined for the point where the spectral intensity drops below 5% of the peak intensity.
The plots in Fig. 5(a) and 5(b) depict the normalized Dy3+:BaF2 absorption and fluorescence spectra used to determine EZL and ZL/ZU for room temperature (300 K) and cryogenic temperature (77 K), respectively. These parameters for both temperatures are presented in Table 1. It is interesting to note that ZL/ZU for the 300 K data is very close in value to the ratio 8/7 ≈ 1.14 which we would get from simply dividing the number of upper manifold Stark levels by the number of lower manifold Stark levels. The overall smaller energy widths observed in the 77 K results are attributed to less thermal population of higher-lying levels in the upper and lower manifolds.
3.3 Fluorescence lifetimes
The fluorescence lifetime of Dy3+:BaF2 was measured by exciting the 6H11/2 manifold at 1723nm. After subsequent de-excitation, the decay transient of the ∼3 µm relevant 6H13/2 manifold of Dy3+ was measured for a number of temperatures between 77 K and room temperature. For all temperatures, the decay waveforms exhibited nearly single exponential behavior, as shown in Fig. 6(a), with less than 5% of the overall signal representing a faster decay component. This fast component could be indicative of several processes including energy transfer between rare earth sites or to other impurities. The lifetime trend as a function of temperature is shown in Fig. 6(b), exhibiting an increase from 1.5 ms at room temperature to 5.3 ms at 77 K. Additionally, while at high temperatures the lifetime increases linearly with temperature, there is an apparent leveling off as the sample drops below 125 K. This behavior implies that non-radiative phonon decay is competing with the fluorescence at high temperatures, but this process decreases as phonons are frozen out at the lowest temperatures. These results compare very well with those seen for Dy3+ doped BaY2F8 which has a reported maximum phonon energy of 350 cm−1 .
3.4 Stimulated emission cross sections
Stimulated emission cross sections were obtained using a combination of the McCumber and Fuchtbauer-Ladenburg (F-L) methods. The McCumber method uses the reciprocity relation shown in Eq. (1) to calculate the stimulated emission cross section from the absorption cross section and the energy level related parameters given in Table 1. The stimulated emission cross section can also be calculated from the fluorescence and lifetime data using the F-L equation :
By themselves, the reciprocity equation and the F-L equation are often inadequate to obtain a complete and accurate stimulated emission cross section. The reciprocity solution, while accurate at shorter wavelengths, tends to blow up at wavelengths longer than the zero line due to the exponential factor in Eq. (1). And the F-L equation easily provides the correct spectral shape of the cross section but hard-to-measure quantities like the quantum efficiency make determining the correct scale difficult. For these reasons, the stimulated emission cross sections in this work were obtained by scaling the F-L data to match the reciprocity results in the short wavelength region, and then stitching together the data sets at a convenient crossover point.
The stimulated emission cross sections of Dy3+:BaF2 for room temperature and 77 K are shown in Fig. 7. At room temperature, the highest intensity peak occurs at 2847 nm with a value of 0.45×10−20 cm2. Cooling to liquid nitrogen temperature shows a nearly four-fold increase in the peak cross section, with a value of 1.58×10−20 cm2, as well as a seven-fold reduction of the spectral linewidth.
3.5 Radiative lifetime and quantum efficiency
Once an accurate stimulated emission cross section is obtained, the F-L equation can be rearranged to calculate for the radiative lifetime (τrad):
The values for both the measured fluorescence lifetime and calculated radiative lifetime of the 6H13/2 manifold, as well as the quantum efficiency of the transition to the ground state, are presented in Table 2 for room temperature and 77 K. Immediately apparent is the large difference between fluorescence and radiative lifetimes for both temperatures which leads to low quantum efficiency values. This difference implies an efficient non-radiative process is depopulating the 6H13/2 manifold. A likely candidate would be multi-phonon relaxation (MPR); however, the temperature dependent lifetime behavior presented in Fig. 6, showing a leveling off at low temperatures, implies that this process should be decreasing in magnitude as the phonons are frozen out. Since even at low temperatures, there is quite a difference between measured and radiative lifetimes, it is likely that other non-radiative processes are affecting this transition behavior. Attempts to quantify the extent of these other non-radiative processes, with respect to those involving MPR will be presented in the next section.
It should be pointed out that the radiative lifetime should inherently be independent of temperature; and the fact that these values, as determined independently from the room temperature and 77 K data, are so similar is encouraging. Additionally, the radiative lifetime values calculated for Dy3+ doped BaF2 are comparable to those published for BaY2F8, another low maximum phonon energy fluoride .
3.6 Non-radiative decay rates
With the measured fluorescence lifetimes of the 6H13/2 level shown in Fig. 6 and the calculated radiative lifetimes listed in Table 2, it is possible to determine the overall non-radiative decay rate (Wnr) using the following relation:
Values for Wnr obtained in this way, as a function of temperature, are presented as square markers in Fig. 8 along with a best fit line. In the previous section, it was surmised that multiple non-radiative processes were at play in this material, with at least one of them being multi-phonon relaxation (MPR). Therefore, Wnr can be written as:24]. It is advantageous to separate out the MPR contribution in this way because there exists a simplified decay rate equation known as the Reisfeld model  that can be used to calculate WMPR from just a handful of material parameters. This model is expressed as:
From Fig. 8(b), it can be seen that the decay rate due to quenching processes not associated with MPR is fairly constant with temperature, exhibiting a value of ∼100 s−1. The multi-phonon decay mechanism is the dominant non-radiative channel at temperatures greater than 150 K but falls below the other processes at lower temperatures. While the quenching processes not associated with MPR are largely unidentified, their nearly constant behavior points toward mechanisms not affected by the temperature of the crystal.
3.7 Gain cross sections
Gain cross section σg is a useful parameter for predicting potential operation wavelengths of a laser. The gain cross section is calculated from the absorption and stimulated emission cross sections using the following relationship:26]. In general, lasing can occur when the gain cross section achieves a positive value. The calculated gain cross section spectra for a number of values of β are presented in Fig. 9 for room temperature and 77 K. From Fig. 9(a), it can be seen that a population inversion between 20% and 40% is needed to achieve positive gain for a broad wavelength region between 2900 nm and 3200 nm. Positive gain at the peak wavelength of 2847 nm requires an inversion of about 50%. A positive gain cross section is easier to achieve at 77 K, as can be seen in Fig. 9(b). For this temperature, positive gain is achieved by 20% inversion with a clearly defined peak at 2925 nm.
In summary, comprehensive spectroscopic characterization of the Dy3+ ion doped into the low maximum phonon crystal host BaF2 was performed with an emphasis on the ∼2.8 µm emission. Laser relevant parameters including absorption and stimulated emission cross section, radiative lifetime, quantum efficiency, and gain cross section were determined for both room temperature and cryogenic temperature (77 K). Room temperature laser operation of this transition would suffer from low quantum efficiency and would require a high population inversion of ∼40%. The parameters at 77 K show major improvements including multiple times higher cross section intensities, nearly four-fold higher quantum efficiency, and a positive gain cross section requiring less than 20% population inversion.
Efforts to determine the discrete Stark splittings of various Dy3+ manifolds in this host material were hampered by apparent multi-site behavior of the rare earth dopant. The multiple sites could play a major role in the quenching processes not associated with MPR prevalent in this transition.
The authors declare no conflict of interest.
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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