Spectroscopic investigation of dysprosium doped BaF<sub>2</sub> single crystals pertaining to the 3&#x2005;&#x00B5;m mid-IR laser potential

Zackery D. Fleischman; Ei Ei Brown; Jenny Rosen; Mark Dubinskii

doi:10.1364/OME.438716

1. Introduction

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 [1], medical procedures [2], and wind lidar [3]. 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 ⁶H_13/2 → ⁶H_15/2 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 [15] and SrF₂ [16] 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 [17]. 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 (⁶H_15/2) to the ⁶H_13/2 excited manifold, fluorescence lifetime measurements of this excited state, and measurements of the fluorescence spectrum for the ⁶H_13/2 → ⁶H_15/2 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.

Fig. 1. Energy level diagram of Dy³⁺ with various near-and mid-infrared transitions noted. The 2.8 µm mid-IR transition of interest as well as the fluorescence excitation transition (898.7 nm) used in fluorescence measurements are highlighted.

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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 [18]. The maximum phonon energy has been quoted in literature to be as low as ∼320 cm⁻¹ [19], making it the lowest in the fluorite family. Rare-earth dopant ions have proven to be incorporated into the divalent Ba²⁺ lattice sites [18], 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 C_4v symmetry [18].

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 (λ_blaze: 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 (⁶H_15/2 → ⁶H_13/2) 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 ⁶H_15/2 → ⁶F_7/2 transition at 898.7 nm was used for excitation during our fluorescence spectroscopy measurements.

Fig. 2. Room temperature absorption spectrum of Dy³⁺:BaF₂.

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High resolution ground state absorption spectra into the ⁶H_13/2 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.

Fig. 3. Absorption cross section spectrum for the ⁶H_15/2 ⇒ ⁶H_13/2 transition for 2 at.% Dy³⁺:BaF₂ at 300 K (red) and 77 K (black).

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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 [20]. This reciprocity relation is written

(1)$${\sigma _{se}}(\lambda )= {\sigma _{abs}}(\lambda )\frac{{{Z_L}}}{{{Z_U}}}exp\left[ {\frac{{{E_{ZL}} - {\raise0.7ex\hbox{${hc}$} \!\mathord{\left/ {\vphantom {{hc} \lambda }} \right.}\!\lower0.7ex\hbox{$\lambda $}}}}{{{k_B}T}}} \right]$$

where σ_se(λ) and σ_abs(λ) are the respective stimulated emissions and absorption cross sections as a function of wavelength λ; Z_L and Z_U are the partition functions for the lower and upper manifold, respectively; E_ZL is the “zero line” energy between the lowest levels of the two manifolds; h is Planck’s constant; c is the speed of light in vacuum; k_B is Boltzmann’s constant; and T is the temperature. Among all these terms, the zero line energy and the partition functions are the ones that require knowledge of the exact positioning of all levels in respective upper and lower manifolds.

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 ⁶H_15/2 manifold to have 8 levels and the ⁶H_13/2 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 ⁶F_3/2 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 ⁶F_3/2 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 [18].

Fig. 4. Absorption spectra from the ground state into the a) ⁶H_13/2 and b) ⁶F_3/2 manifolds as a function of temperature for Dy³⁺:BaF₂.

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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. [21] describes a method for estimating E_ZL and the Z_L/Z_U 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 E_ZL. Measuring the low energy width of the fluorescence spectrum, from E_ZL, 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, Z_L/Z_U 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 E_ZL and Z_L/Z_U 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 Z_L/Z_U 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.

Fig. 5. Normalized absorption and fluorescence spectra for Dy³⁺:BaF₂ at a) 300 K and b) 77 K.

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Table 1. Parameters related to energy level determination in Dy³⁺:BaF₂.

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3.3 Fluorescence lifetimes

The fluorescence lifetime of Dy³⁺:BaF₂ was measured by exciting the ⁶H_11/2 manifold at 1723nm. After subsequent de-excitation, the decay transient of the ∼3 µm relevant ⁶H_13/2 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 [22].

Fig. 6. a) Fluorescence decay transient of the ⁶H_13/2 manifold of Dy³⁺:BaF₂ for room temperature and 77 K, and b) fluorescence lifetime values as a function of temperature.

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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 [23]:

(2)$${\sigma _{se}}(\lambda )= \frac{{\eta {\lambda ^5}}}{{8\pi c{n^2}{\tau _{fl}}}}\frac{{I(\lambda )}}{{\smallint I(\lambda )\lambda d\lambda }}$$

where η is the quantum efficiency of the transition, I(λ) is the fluorescence intensity at wavelength λ, n is the index of refraction of the rare earth host crystal (BaF₂), and τ_fl is the measured fluorescence lifetime. In general, there is a branching ratio term in the numerator of Eq. (2); however, for transitions between the first excited manifold and the ground manifold, the branching ratio is unity and can be omitted.

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.

Fig. 7. Stimulated emission cross section spectra for Dy³⁺:BaF₂ at room temperature and 77 K.

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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 (τ_rad):

(3)$$\frac{1}{{{\tau _{rad}}}} = 8\pi c{n^2}\smallint \frac{{{\sigma _{se}}(\lambda )}}{{{\lambda ^4}}}d\lambda $$

with all constants and variables as defined for Eq. (2). The quantum efficiency η can then be determined from the following relationship:

(4)$$\eta = \frac{{{\tau _{fl}}}}{{{\tau _{rad}}}}$$

The values for both the measured fluorescence lifetime and calculated radiative lifetime of the ⁶H_13/2 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 ⁶H_13/2 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.

Table 2. Lifetime values of the ⁶H_13/2 manifold and quantum efficiency of the ⁶H_13/2 → ⁶H_15/2 transition for room temperature and 77 K.

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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 [22].

3.6 Non-radiative decay rates

With the measured fluorescence lifetimes of the ⁶H_13/2 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 (W_nr) using the following relation:

(5)$${W_{nr}} = \frac{1}{{{\tau _{meas}}}} - \frac{1}{{{\tau _{rad}}}}$$

Values for W_nr 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, W_nr can be written as:

(6)$${W_{nr}} = {W_{MPR}} + {W_{other}}$$

where W_other contains contributions to the non-radiative rate from all other quenching processes not associated with MPR [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 [25] that can be used to calculate W_MPR from just a handful of material parameters. This model is expressed as:

(7)$${W_{MPR}} = B{e^{ - \alpha \Delta E}}{\left[ {1 - {e^{ - \left( {\frac{{\hbar {\mathrm{\omega }_{max}}}}{{{k_b}T}}} \right)}}} \right]^{ - p}}$$

where ΔE is the energy gap below the selected energy level, T is the temperature, ${\hbar {\mathrm{\omega }_{\textrm{max}}}}$ is the maximum phonon energy of the host, p is the number of phonons needed to bridge ΔE, and B and α are host-dependent fitting parameters. These parameters were determined for BaF₂ in our previous work to be 9.15×10⁸ s⁻¹ and 5.58×10⁻³ cm, respectively [17]. Using ΔE = 2950 cm⁻¹ (determined from the spectroscopic results) and the maximum phonon energy of 320 cm⁻¹ [19], W_MPR was calculated as a function of temperature and depicted in the solid curve of Fig. 8(b). With both W_nr and W_MPR known, we can use Eq. (6) to determine W_other, which is represented as the dotted line in Fig. 8(b).

Fig. 8. a) Fitting the non-radiative decay rate of the ⁶H_13/2 level, and b) comparison of MPR and other non-radiative decay rates.

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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 σ_g 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:

(8)$${\sigma _g}(\lambda )= \beta {\sigma _{se}}(\lambda )- ({1 - \beta } ){\sigma _{abs}}(\lambda )$$

where β is the population inversion parameter defined as the ratio of active ions in the excited state to the total number of active ions [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.

Fig. 9. Gain cross section spectrum at a) room temperature and b) 77 K for the 2.8 µm transition of Dy³⁺:BaF₂ calculated for a number of different population inversion ratios β.

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4. Conclusions

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.

Disclosures

The authors declare no conflict of interest.

Data availability

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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Temperature (K)	Zero Line E_ZL (cm⁻¹)	Low Energy Width (cm⁻¹)	High Energy Width (cm⁻¹)	Z_L/Z_U
300	3518	464	414	1.12
77	3518	269	265	1.01

Temperature (K)	Fluorescence Lifetime (ms)	Radiative Lifetime (ms)	Quantum Efficiency (%)
300	1.56	45.9	3.4
77	5.26	45.7	11.5

Temperature (K)	Zero Line E_ZL (cm⁻¹)	Low Energy Width (cm⁻¹)	High Energy Width (cm⁻¹)	Z_L/Z_U
300	3518	464	414	1.12
77	3518	269	265	1.01

Temperature (K)	Fluorescence Lifetime (ms)	Radiative Lifetime (ms)	Quantum Efficiency (%)
300	1.56	45.9	3.4
77	5.26	45.7	11.5

Spectroscopic investigation of dysprosium doped BaF₂ single crystals pertaining to the 3 µm mid-IR laser potential

Abstract

1. Introduction

2. Experimental details

3. Results and discussion

3.1 Absorption measurements

3.2 Energy level analysis

3.3 Fluorescence lifetimes

3.4 Stimulated emission cross sections

3.5 Radiative lifetime and quantum efficiency

3.6 Non-radiative decay rates

3.7 Gain cross sections

4. Conclusions

Disclosures

Data availability

References

Data availability

Cited By

Figures (9)

Tables (2)

Equations (8)

Optical Materials Express