1. Introduction

Calcium fluoride (CaF₂, also known as fluorite in the mineral form) is a well-known laser host material for doping with trivalent rare-earth ions (RE³⁺) [1–3]. Undoped CaF₂ features good thermal properties (high thermal conductivity and isotropic thermal expansion), low phonon energy, low refractive index and broadband transparency. It also exhibits a unique tendency for strong RE³⁺ ion clustering even at moderate doping concentrations (>0.1 at.%), leading to inhomogeneously broadened spectral bands [4–6]. As a result, the absorption and emission spectra of RE³⁺ ions in CaF₂ greatly resemble those in fluoride glasses being almost structureless and very broad. Such a “glassy-like” spectroscopic behavior is very appealing for broadband wavelength tuning [7,8] and generation of ultrashort pulses in mode-locked lasers [9,10]. The energy-transfer processes among the neighboring RE³⁺ ions (nonradiative energy-transfer, cross-relaxation, and energy-transfer upconversion) are greatly promoted in clusters [11]. This can be used for boosting the efficiency of certain laser transitions of RE³⁺ ions. CaF₂ is a low-melting-point compound. Its growth is well-developed, e.g., by the Czochralski or Bridgman-Stockbarger methods.

CaF₂ belongs to the family of divalent metal fluorides, MF₂ (where M = Ca, Sr, Ba, Cd, or Pb) [12–15]. These materials all belong to the cubic class (sp. gr. Fm3⁻m, fluorite-type structure). The M²⁺ and F⁻ are located at face-centered cubic lattice points and tetrahedral voids, respectively. Compared to CaF₂, other MF₂ crystals are less studied for RE³⁺ doping but they are also attractive as laser host media as they benefit from either a lower melting point, or better thermal properties, or lower phonon energies. Fluorite-type crystals can also form substitutional solid-solutions (M1_1-xM2_x)F₂ for the entire range of 0 < x < 1 [16–18]. For such “mixed” compositions, the melting point is expected to decrease further as compared to the parent compounds [19,20]. An additional spectral broadening is also expected due to the compositional disorder. The growth and laser operation of some RE³⁺-doped “mixed” fluorite-type crystals were reported mainly focusing on (Ca,Sr)F₂ [21–23].

Erbium ions (Er³⁺) are of interest for generation of mid-infrared radiation at ∼2.8 µm [24,25] according to the ⁴I_11/2 → ⁴I_13/2 transition, Fig. 1. The low-phonon-energy behavior of MF₂ crystals and the tendency for strong ion clustering promoting the energy-transfer upconversion stimulate the interest in the development of mid-infrared Er³⁺:MF₂ lasers. Labbe et al. first reported on a mid-infrared 5 at.% Er³⁺:CaF₂ laser delivering 80 mW at 2.80 µm with a slope efficiency of 30% and a small laser threshold of 23 mW [1]. Basyrova et al. demonstrated power scaling of a similar laser generating 0.83 W at 2.80 µm with a slightly higher slope efficiency of 31.6% [26]. In these studies, high-brightness laser pumping was implemented. Further power scaling was achieved using commercial InGaAs diode lasers as pump sources. Zong et al. developed a diode-pumped 1.7 at.% Er³⁺:CaF₂ laser generating 2.32 W at 2.76 µm at the expense of a lower slope efficiency of 21.2% [27]. So far, Er³⁺:CaF₂ [26,27], Er³⁺:SrF₂ [28] and Er³⁺:(Ca,Sr)F₂ [23] crystals have been studied for mid-infrared lasers. Note that Er³⁺:CaF₂ can also be obtained in the form of transparent ceramics. Šulc et al. reported on a pulsed diode-pumped 5 at.% Er³⁺:CaF₂ ceramic laser with a broad tuning range of 2687–2805 nm (118 nm) [29].

Despite the existence of multiple studies for several Er³⁺:MF₂ crystal compositions, their spectroscopic and mid-infrared laser properties have not been directly compared so far. In the present work, we report on a comparative study of mid-infrared emission properties of five fluorite-type Er³⁺-doped MF₂ crystals, including parent and solid-solution compounds.

 

Fig. 1. Energy level scheme of Er³⁺ ions showing all the manifolds assigned in the absorption spectra of Er³⁺:MF₂ crystals, pump and laser transitions, ETU – energy-transfer upconversion.

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2. Crystal growth

The MF₂ crystals (M = Ca, Sr, Ba) melt congruently at relatively low temperatures and they can be grown by the Bridgman-Stockbarger or Czochralski methods. The Er³⁺:MF₂ crystals were grown by the Bridgman method using graphite crucibles (Ф7-8 mm, height: 40 mm). The MF₂ (M = Ca, Sr, Ba) powders (purity: 4N, Sigma-Aldrich) and ErF₃ powder obtained by fluorination of the Er₂O₃ precursor (4N, Alfa Aesar). Five compositions were tested: M = Ca, Sr, Ba, Ca_0.5Sr_0.5 and Sr_0.5Ba_0.5. The doping level was 5 at.% Er³⁺ (with respect to M²⁺ cations). The optical quality and spectroscopic properties of RE³⁺-doped MF₂ crystals are sensitive to even small pollution of oxygen / water in the growth chamber as they can lead to the presence of oxygen-assisted sites for the dopant ions or even formation of a translucent oxyfluoride phase. To avoid that, the growth chamber was sealed to vacuum (<10⁻⁵ mbar) and refilled with a mixture of Ar + CF₄ gases. The starting reagents were well mixed and placed into the crucible which was then heated slightly above (∼30-50 °C) the melting point and the solution was homogenized for 3-4 hours (h). The growth was ensured by a vertical translation of the crucible in a vertical temperature gradient of 30-40 °C/cm. After the growth was completed, the crystals were cooled down to room temperature (20 °C) within 48 h.

For the “mixed” crystals, the melting point is reduced as compared to those of the parent compounds. E.g., for Er³⁺:(Ca,Sr)F₂ and Er³⁺:(Sr,Ba)F₂, it is T_f = 1373 °C and 1315 °C, respectively (compare with 1477 °C, 1418 °C and 1386 °C for SrF₂, CaF₂ and BaF₂, respectively).

The as-grown Er³⁺:MF₂ crystals with a cylindrical shape (Ф7-8 mm, length: 35 - 40 mm) were transparent and rose-colored due to the Er³⁺ doping, Fig. 2(a). Samples for spectroscopic and laser studies were cut from the central part of the cylindrical barrels with a thickness of 6-7 mm and then polished to laser-grade quality, Fig. 2(b).

 

Fig. 2. Photographs of Er³⁺:MF₂ crystals: (a) an as-grown Er³⁺:CaF₂ crystal boule; (b) cut and polished Er³⁺:MF₂ samples.

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3. Raman spectra

The Raman spectra of Er³⁺:MF₂ crystals, Fig. 3(a), were measured using a confocal microscope (InVia, Renishaw) equipped with a × 50 Leica objective and an Ar⁺ ion laser (457 nm). Fluorite-type crystals have O_h symmetry and a triatomic unit cell thus exhibiting only one Raman-active mode at the center of the Brillouin zone having a T_2g symmetry [30]. Indeed, the Raman spectra of all the studied Er³⁺:MF₂ crystals contain a single intense peak assigned to this vibration. Frequently, MF₂ crystals may exhibit additional broad Raman bands in the spectral range of 100–600 cm^-1 owing to structure defects (interstitial / vacant anion sites) [30, 31]. Such a behavior is not observed in our crystals.

 

Fig. 3. Raman spectroscopy of Er³⁺:MF₂ crystals: (a) Raman spectra, λ_exc = 457 cm^-1, numbers – peak frequencies; (b) phonon energy vs. the square root of the average cationic mass.

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For Er³⁺:CaF₂, Er³⁺:SrF₂ and Er³⁺:BaF₂ crystals, the peak frequency of the Raman mode and its linewidth (FWHM) are 321 / 11.0 cm^-1, 285 / 10.2 cm^-1 and 242 / 12.0 cm^-1, respectively. Thus, the latter compound is the most favorable one in terms of low-phonon-energy behavior. For the “mixed” compositions, the Raman peak broadens and is reduced in intensity and the peak position takes an intermediate place between those for the corresponding parent compounds, indicating an even distribution of the host-forming cations throughout the structure (a formation of a substitutional solid-solution) [32]. E.g., for Er³⁺:(Ca,Sr)F₂, the peak Raman frequency is 304 cm^-1 and the peak linewidth is 25.9 cm^-1.

The phonon energy of Er³⁺:MF₂ decreased monotonically with increasing the cationic mass in agreement with the classical approach, ν = (1/2π)(k/µ)^1/2, where k is the force constant and µ is the reduced mass of the M – F system [33].

4. Optical spectroscopy

4.1 Optical absorption

The absorption spectra of Er³⁺ ions were measured using a spectrophotometer (Lambda 1050, Perkin Elmer). They are shown in Fig. 4. Here, the assignment of Er³⁺ transitions is according to Carnall et al. [34]. The absorption spectra for both parent and “mixed” Er³⁺:MF₂ crystals are smooth and broad owing to inhomogeneous spectral broadening caused by a strong ion clustering. In the series M = Ca → Sr → Ba, the complexity and diversity of RE³⁺ ion clusters in MF₂ crystals decrease leading to more intense and structured absorption bands which also exhibit a slight blue-shift [12]. Indeed, for the ⁴I_15/2 → ⁴I_11/2 transition, which is used for pumping mid-infrared erbium lasers, the peak absorption cross-section, σ_abs, varies from 2.77 × 10⁻²¹ cm² at 972.3 nm (Er³⁺:BaF₂) to 2.59 × 10⁻²¹ cm² at 969.5 nm (Er³⁺:SrF₂), and further to 2.22 × 10⁻²¹ cm² at 967.6 nm (Er³⁺:CaF₂), while the corresponding absorption bandwidth is 12.9 nm (Er³⁺:BaF₂), 16.9 nm (Er³⁺:SrF₂), and 22.2 nm (Er³⁺:CaF₂).

 

Fig. 4. (a-h) Absorption spectra of Er³⁺ ions in MF₂ crystals.

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A close look at the absorption spectra of “mixed” crystals indicate that there is a great similarity between those of (Er³⁺:(Ca,Sr)F₂ and Er³⁺:SrF₂) and (Er³⁺:(Sr,Ba)F₂ and Er³⁺:BaF₂) ones, suggesting that the dopant ions in such solid-solution compounds tend to reside in clusters with a local surrounding predominantly composed of one of the two host-forming cations (namely, the heavier / larger one – Sr²⁺ or Ba²⁺, respectively). This suggests that Er³⁺ clusters have a tendency to sit in the heavier-cation environment within the solid-solution (M1_1-xM2_x)F₂ crystals. A similar behavior was observed previously for clusters of Nd³⁺/Lu³⁺ ions in “mixed” (Sr,Ba)F₂ crystals [35].

4.2 Judd-Ofelt analysis

The measured absorption spectra of Er³⁺ ions in the five studied MF₂ crystals were used to calculate the transition probabilities by means of the standard Judd-Ofelt (J-O) theory [36,37]. The reduced squared matrix elements U^(k) (k = 2, 4, 6) were calculated using the free-ion parameters from [38]. The magnetic dipole (MD) contributions to transition intensities (for ΔJ = J – J’ = 0, ± 1) were calculated within the Russell–Saunders approximation using Er³⁺ wave functions under the free-ion assumption.

Table 1 summarizes the experimental and calculated absorption oscillator strengths (f_exp and f_calc, respectively) for the three parent compounds, Er³⁺:CaF₂, Er³⁺:SrF₂ and Er³⁺:BaF₂. There exists a direct relation between the absorption oscillator strength / integrated absorption cross-section and the radiative lifetime of the excited-state (the principle of reciprocity, referring to Einstein coefficients). For Er³⁺ transitions from the ground-state (⁴I_15/2) to the two lower-lying excited-states (⁴I_13/2 and ⁴I_11/2), the f_calc value decreases in the M = Ca → Sr → Ba series, so that an opposite tendency is expected for the radiative lifetimes of these two states. The root mean square (r.m.s.) deviation between the f_exp and f_calc values is relatively low for all the tested Er³⁺:MF₂ crystals, lying in the range of 0.137–0.257.

Table 1. Absorption Oscillator Strengths^a for Er³⁺ Ions in Parent MF₂ (M = Ca, Sr, Ba) Crystals

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The J-O (intensity) parameters Ω₂, Ω₄, Ω₆ for Er³⁺ ions in MF₂ crystals are listed in Table 2.

Table 2. Judd-Ofelt Parameters of Er³⁺ Ions in MF₂ Crystals

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The determined J-O parameters were used to calculate the probabilities of spontaneous radiative transitions of Er³⁺ ions. In Table 3, we list the parameters relevant for mid-infrared laser operation, i.e., the radiative lifetimes τ_rad of the ⁴I_13/2 and ⁴I_11/2 states and the luminescence branching ratio β_JJ’ for the ⁴I_11/2 → ⁴I_13/2 transition. As expected, in the M = Ca → Sr → Ba series, the τ_rad values for the considered excited-states tend to increase from 7.09 / 6.53 ms (Er³⁺:CaF₂) to 7.57 / 6.99 ms (Er³⁺:SrF₂) and further to 7.52 / 7.11 ms (Er³⁺:BaF₂). The considered β_JJ’ value is also higher for Sr²⁺ and Ba²⁺-containing crystals.

Table 3. Selected Probabilities^a of Spontaneous Radiative Transitions of Er³⁺ in MF₂ crystals

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4.3 Emission spectra and luminescence lifetimes

The luminescence spectra of Er³⁺ ions in the mid-infrared (the ⁴I_11/2 → ⁴I_13/2 transition) were measured using an optical spectrum analyzer (OSA, Yokogawa AQ6376) and a ZrF₄ fiber. The excitation source was a Ti:Sapphire laser tuned to ∼970 nm. The OSA was purged with N₂ gas. To remove the effect of the residual water vapor absorption in air, the set-up was calibrated using a 20 W quartz iodine lamp.

The stimulated-emission (SE) cross-sections, σ_SE, were calculated using the Füchtbauer-Ladenburg equation [39]:

The SE cross-section spectra for Er³⁺ ions in MF₂ crystals are shown in Fig. 5. Similarly to the absorption spectra, a profound inhomogeneous broadening is observed for both the parent and “mixed” Er³⁺:MF₂ crystals owing to the rare earth ion clustering. For all the studied crystals, the emission spectra are very broad extending from 2.55 to 3.05 µm and the main emission peak appears around 2.72 µm. Such a behavior is beneficial for broadly tunable and potentially mode-locked lasers. The spectra become more structured in the M = Ca → Sr → Ba series. Also for the solid-solution compounds, a great similarity between the emission spectra of (Er³⁺:(Ca,Sr)F₂ and Er³⁺:SrF₂) and (Er³⁺:(Sr,Ba)F₂ and Er³⁺:BaF₂) crystals is observed.

 

Fig. 5. Stimulated-emission (SE) cross-sections, σ_SE, for the ⁴I_11/2 → ⁴I_13/2 Er³⁺ transition in MF₂ crystals, corrected for the structured water vapor absorption in air (in grey, arb. units, according to the HITRAN database).

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The highest SE cross-section is observed for Er³⁺:SrF₂, σ_SE = 7.19 × 10⁻²¹ cm² at 2729 nm and at longer wavelengths, two other intense and broad peaks appear (σ_SE = 6.38 × 10⁻²¹ cm² at 2745 nm and 4.69 × 10⁻²¹ cm² at 2794 nm).

Luminescence decays were studied under resonant excitation using a ns optical parametric oscillator (Horizon, Continuum), a 1/4 m monochromator (Oriel 77200), an InGaAs detector and an 8 GHz oscilloscope (DSA70804B, Tektronix). To reduce the reabsorption (radiation trapping) effect on the measured kinetics, the samples were finely ground into powders. The measured luminescence decay curves from the ⁴I_13/2 and ⁴I_11/2 Er³⁺ states in the three parent crystals, CaF₂, SrF₂ and BaF₂, are shown in Fig. 6(a). They deviate from the single-exponential law (especially for ⁴I_13/2) owing to the strong ETU from these long-living states. Thus, the mean luminescence lifetimes <τ_lum> = ∫t·I(t)dt/∫I(t)dt were determined.

 

Fig. 6. Luminescence dynamics from the ⁴I_13/2 and ⁴I_11/2 Er³⁺ manifolds in MF₂ crystals: (a) luminescence decay curves under resonant excitation of Er³⁺ ions in CaF₂, SrF₂, and BaF₂, λ_exc = 1.48 µm, λ_lum = 1.57 µm (the ⁴I_13/2 state), λ_exc = 0.97 µm, λ_lum = 1.01 µm (the ⁴I_11/2 state); (b) mean luminescence lifetimes <τ_lum> as a function of the host composition.

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The summary of the <τ_lum> values for the five studied Er³⁺:MF₂ crystals is given in Fig. 6(b). With increasing the average radius / atomic mass of the M²⁺ host-forming cations (in the M = Ca → Sr → Ba series), and, accordingly, decreasing the phonon energy of the host matrix, both the ⁴I_13/2 and ⁴I_11/2 luminescence lifetimes tend to increase, from 8.06 / 8.85 ms (Er³⁺:CaF₂) to 8.54 / 9.55 ms (Er³⁺:SrF₂) and further to 9.17 / 10.36 ms (Er³⁺:BaF₂). This behavior agrees with that for the calculated radiative lifetimes of these manifolds. The ratio of the upper-to-lower laser level lifetimes is favorable for all the studied crystals being weakly dependent on the host matrix composition. The long luminescence lifetime of the upper laser level for the mid-infrared transition (⁴I_11/2) is a prerequisite for a low-threshold behavior.

Note that the measured luminescence lifetimes are slightly exceeding the radiative ones calculated using the J-O theory (cf. Table 3). One possible reason for that is the residual reabsorption effect within the Er³⁺ ion clusters. Table 4 summarizes the key spectroscopic properties of Erbium ions in fluorite-type crystals being relevant for mid-infrared laser operation.

4.4 Low-temperature spectroscopy

For low-temperature (LT, 12 K) absorption and luminescence studies, we have used an APD DE-202 closed-cycle cryo-cooler equipped with an APD HC 2 Helium vacuum cryo-compressor and a Laceshore 330 temperature controller. For absorption measurements, a 20 W quartz lamp with a calibrated spectral output was used. The spectra were measured using optical spectrum analyzers (Ando AQ6315A and Yokogawa AQ6375E). The luminescence was excited by a Ti:Sapphire laser tuned to ∼800 nm.

The LT absorption and emission spectra are shown in Fig. 7 and Fig. 8, respectively. In each graph, we compare the spectrum of a “mixed” compound with those of both parent crystals. The LT absorption spectra were lotted versus the photon energy giving access to the splitting of the ⁴I_13/2 and ⁴I_11/2 excited-states, while the LT emission spectra were plotted versus (E_ZPL – photon energy), where E_ZPL is the zero-phonon line (ZPL) energy giving access to the splitting of the ground-state ⁴I_15/2.

 

Fig. 7. (a-d) LT (12 K) absorption spectra of Er³⁺ ions in fluorite-type crystals: (a,b) the ⁴I_15/2 → ⁴I_13/2 transition; (c,d) ⁴I_15/2 → ⁴I_11/2 transition. α_abs – absorption coefficient.

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Fig. 8. (a-d) LT (12 K) luminescence spectra of Er³⁺ ions in fluorite-type crystals: (a,b) the ⁴I_13/2 → ⁴I_15/2 transition; (c,d) ⁴I_11/2 → ⁴I_15/2 transition. E_ZPL – zero-phonon-line energy.

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By analyzing the spectra, several conclusions can be derived:

Based on the LT absorption and emission spectra, the crystal-field splitting of the ⁴I_15/2, ⁴I_13/2 and ⁴I_11/2 multiplets of Er³⁺ ions forming clusters in the three parent MF₂ crystals (M = Ca, Sr, Ba), was determined, Table 5. The experimental Stark splitting of the ⁴I_11/2 and ⁴I_13/2 multiplets relevant for the 2.8 µm laser operation is also compared in Fig. 9. In the previous studies on site-selective spectroscopy of Er³⁺ ions in CaF₂ crystals grown under oxygen-free atmosphere, multiple possible sites were identified [40–42]. At very low doping levels (<0.05 at.%), the Er³⁺ ions are mostly isolated and are distributed over tetragonal (A, C_4v), trigonal (B, C_3v) and cubic (O_h) sites, depending on the relative position of the charge-compensating interstitial fluorine anion (F_i^-), namely at the (1,0,0) positions, at the (1,1,1) positions or sufficiently far from the dopant ion to exert negligible perturbation, respectively [40]. For higher doping levels of >0.1 at.%, the dopant ions form clusters of several types (assigned as C-sites, being close to dimers with a distorted C_3v symmetry, and D(1) and D(2) sites corresponding to larger agglomerates of Er³⁺ - F_i^- pairs).

 

Fig. 9. Experimental Stark splitting of the ⁴I_11/2 and ⁴I_13/2 multiplets of Er³⁺ ions forming clusters in heavily doped Er³⁺:MF₂ crystals.

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Table 4. Spectroscopic Characteristics^a of Er³⁺:MF₂ Crystals

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Table 5. Crystal-Field Splitting of Selected Er³⁺ Multiplets in CaF₂, SrF₂, and BaF₂

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For the studied heavily doped Er³⁺:MF₂ crystals, we were not able to confirm the existence of two significantly different groups of ion clusters (D(1) and D(2)), as the LT emission spectra were almost independent on the excitation wavelength. Moreover, the bands in the LT spectra of ∼5 at.% Er³⁺-doped crystals (assigned to a single type of cluster D sites) experience an additional broadening and spectral shifts as compared to those in 0.1 at.% Er³⁺-doped crystals (assigned to D(1) and D(2) sites). Thus, we assumed that almost all the Er³⁺ ions form large-scale agglomerates (D) with relatively close spectroscopic properties. Previously, it was suggested that for all the heavily doped MF₂ crystals (M = Ca, Sr, Ba) and their solid-solutions, such agglomerates most likely correspond to hexameric Y₆F₃₇ superstructure units, which are nearly identical in volume and shape to the Ca₂F₃₂ building blocks of the fluorite lattice and, consequently, they can be easily incorporated into this lattice while accommodating the excess F_i^- anions [5,43]. The local crystal-field symmetry for the dopant ions in Y₆F₃₇ clusters is tetragonal (C_4v) [5].

The analysis of Table 2 confirms a decreased total Stark splitting of the multiplets and a red-shift of the zero-phonon line for Er³⁺ ions in the M = Ca → Sr → Ba series.

5. Laser operation

5.1 Laser setup

The scheme of the laser set-up is shown in Fig. 10. Cylindrical samples with a thickness of 6.53-6.99 mm and a diameter of ∼7 mm were cut from the central parts of the as-grown Er³⁺:MF₂ crystal boules. They were polished to laser-grade quality with good parallelism (<5’) from both sides and left uncoated. The laser elements were mounted on a passively cooled Cu-holder using a silver paint for better heat removal. A hemispherical cavity was implemented. It was formed by a flat pump mirror (PM) coated for high transmission (HT, T = 85.7%) at 0.97 µm and high reflection (HR) at 2.6–3.0 µm, and a set of concave (radius of curvature: RoC = -100 mm) output couplers (OC) having a transmission T_OC in the range of 0.33% - 4% at 2.7–2.9 µm. The crystal was placed near the PM at a small distance (<1 mm). The geometrical cavity length was ∼99 mm. The pump source was a CW Ti:Sapphire laser delivering up to 3.2 W at 0.97 µm (addressing the ⁴I_15/2 → ⁴I_11/2 Er³⁺ absorption peak) with a diffraction-limited beam quality (M² ≈ 1). The pump radiation was focused into the laser crystal through the PM using an antireflection-coated achromatic lens (focal length: f = 75 mm) resulting in a pump spot size of 2w_P = 66 ± 5 µm. The pumping was in single pass. The residual (non-absorbed) pump after the OC was filtered out using a long-pass filter (Spectrogon, LP1400). The laser spectra were measured using a ZrF₄ fiber (Thorlabs) and a spectrum analyzer (Bristol, 771 series). The laser mode profile in the far-field was captured using a camera (Pyrocam IIIHR, Ophir-Spiricon).

 

Fig. 10. Schematic of the laser setup: L – aspherical focusing lens; PM – flat pump mirror; OC – curved output coupler.

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5.2 Laser performance

CW mid-infrared laser operation was obtained with all five studied Er³⁺:MF₂ crystals. The best laser performance was achieved with the Er³⁺:CaF₂ crystal: an output power of 702 mW was extracted at 2800 nm with a slope efficiency η of 37.9% (vs. the absorbed pump power) when using the output coupler with T_OC = 4%, Fig. 11(a). With increasing output coupling from 0.33% to 4%, the laser threshold gradually increased from 16 mW to 60 mW. For Er³⁺:CaF₂, the measured pump absorption reached 81.9%. The optical-to-optical efficiency (vs. the pump power incident on the crystal) η_opt was 31.0%. The output dependences were linear within the studied range of pump powers. Further power scaling was limited by the available pump. The achieved laser slope efficiency is slightly higher than the Stokes limit, η_St,L = λ_P/λ_L = 34.6%, indicating the role of the ETU process ⁴I_13/2 + ⁴I_13/2 → ⁴I_9/2 + ⁴I_15/2, cf. Figure 1, refilling the upper laser level and depopulating the intermediate ⁴I_13/2 state.

 

Fig. 11. Mid-infrared Er³⁺:MF₂ lasers: (a,b) Er³⁺:CaF₂ laser: (a) input-output dependences, η – slope efficiency, inset – far-field mode profile, P_abs ∼1.5 W, T_OC = 1.7%; (b) typical laser spectra; (c,d) a comparison of (c) power transfer characteristics and (d) laser spectra for five Er³⁺:MF₂ crystals, T_OC = 1.7%.

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The typical emission spectra of the Er³⁺:CaF₂ laser are shown in Fig. 11(b), measured well above the laser threshold. For small output coupling (<1%), laser emission at 2810 and 2814 nm was observed and for higher T_OC, the laser operated at 2800 nm. These wavelengths correspond to the long-wave emission peak of Er³⁺ ions in CaF₂ and match the transparency ranges between the structured water vapor absorption lines (cf. Figure 5). Note that due to strong resonant excited-state absorption from the terminal laser level with a non-negligible population, ⁴I_13/2 → ⁴I_11/2, causing reabsorption of the laser photons, the ⁴I_11/2 → ⁴I_13/2 Er³⁺ laser transition represents a quasi-three-level laser scheme with reabsorption, which explains the blue-shift of the laser spectra with increasing the output coupling.

The Er³⁺:CaF₂ laser operated on the fundamental transverse mode, as confirmed by the measured M² < 1.1, and the beam profile in the far-field was nearly circular, see the inset in Fig. 11(a).

The output performance and laser spectra of five Er³⁺:MF₂ crystals are directly compared in Fig. 11(c,d) using the same output coupling (T_OC = 1.7%). The slope efficiency gradually decreased in the sequence Er³⁺:CaF₂ → Er³⁺:SrF₂ and Sr-containing crystals → Er³⁺:BaF₂, while the laser threshold was in the range of 17–28 mW for all the crystals, being only slightly higher for Ba-containing ones. The laser emission occurred at 2792–2800 nm, except of Er³⁺:SrF₂ for which the laser operated at shorter wavelengths, 2730 and 2747 nm. The output characteristics of mid-infrared Er³⁺:MF₂ lasers are summarized in Table 6. More details about the 2.8 µm laser performance of Ba-containing crystals can be found in [44].

Table 6. Output Characteristics^a of Mid-Infrared Er³⁺:MF₂ Lasers (T_OC = 1.7%)

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6. Conclusions

Fluorite-type Er³⁺:MF₂ parent and solid-solution crystals feature low-phonon-energy behavior, very broad absorption and mid-infrared emission spectral bands, owing to the profound Er³⁺ ion clustering and long ⁴I_11/2 and ⁴I_13/2 luminescence lifetimes. As for the “mixed” compounds, their advantage is the lower melting points with respect to the corresponding parents. Considering the high thermal conductivity of these materials, the Er³⁺:MF₂ crystals are very promising for the development of power-scalable and broadly tunable low-threshold mid-infrared lasers emitting at ∼2.8 µm. Based on a detailed comparative spectroscopic study of five 5 at.% Er³⁺:MF₂ fluorite-type crystals, including the parent compounds CaF₂, SrF₂, BaF₂, and “mixed” ones, (Ca,Sr)F₂ and (Sr,Ba)F₂, the following conclusions are derived:

In the present work, we employed high-brightness pumping to reveal the potential of Er³⁺:MF₂ crystals for efficient lasing at ∼2.8 µm. Further power scaling is envisioned by using powerful InGaAs laser diodes as pump sources which is feasible owing to the good thermal properties of these compounds. Further improvement of the slope efficiency, especially for Sr and Ba-containing crystals should involve an optimization of the Er³⁺ doping level for boosting the ETU efficiency. One hypothesis here is that a reduction in the cluster complexity may lead to weaker energy-transfer processes. Another idea is the Er³⁺,Pr³⁺ codoping for quenching the metastable Er³⁺ lower-laser level (⁴I_13/2).