1. Introduction

Mid-IR (MIR) lasers operating around 3 μm region have attracted much attention in recent years due to their wide applications in atmospheric monitoring, medical surgery, remote sensing, and scientific research [1–5]. It is well know that Ho³⁺ is a natural candidate for ∼3 μm lasers owing to the ⁵I₆→⁵I₇ transition [6, 7]. However, the ∼3 μm laser operation cannot be obtained efficiently due to (i) the lack of commercialized laser diodes (LD) corresponding to the intrinsic absorption of Ho³⁺ ions, and (ii) the population bottleneck effect that occurs with the ⁵I₆→⁵I₇ transition which is a self-terminated transition. In order to conquer these problems to turn on the probability to acquire ∼3 μm lasing from Ho³⁺, we need (i) a proper sensitizer ion with large absorption cross section for Ho³⁺ ion, and (ii) an appropriate deactivated ion with efficient depopulation of Ho³⁺:⁵I₇ for population inversion.

Fortunately, Yb³⁺ ions, which have a sufficient absorption cross section in the NIR region, are often codoped as sensitizer ions to transfer the accumulated excitation energy to the activator ions. As the energy level scheme illustrated in Fig. 1 shows, under the excitation of a common 970 nm LD pump, the Yb³⁺ ion is excited to the excited state (²F_5/2), and then transfer the excitation energy to Ho³⁺:⁵I₆. Up to now, effective energy transformation from Yb³⁺:²F_5/2 to Ho³⁺:⁵I₆ have been achieved in luminescent materials [8, 9].

 

Fig. 1 Energy level scheme of Yb³⁺, Ho³⁺ in comparison to Er³⁺. UC: up-conversion, ESA: excited state absorption, NT: nonradiative transition, ET: energy transfer.

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Figure 1 also shows the energy level scheme of Yb³⁺ and Ho³⁺ in comparison to Er³⁺. In the Er³⁺ system, the ∼3 μm laser operation on the self-terminating transition (⁴I_11/2→⁴I_13/2) is possible due to an up-conversion process from the lower laser level (⁴I_13/2) under laser diode excitation, which leads to a strong population of the excited state of erbium ion. However, up-conversion is less efficient in a single Ho³⁺ doped crystal and laser oscillation under laser diode excitation of the ⁵I₆ upper laser level is less common. Fortunately, these problems can be partly solved by Yb³⁺ codoping. After the energy transfers from Yb³⁺:²F_5/2 to Ho³⁺:⁵I₆ under a 970 nm LD excitation, an up-conversion (UC) process from ⁵I₇ multiplet to ⁵F₅ multiplet can be achieved by the energy exchange from a second excited Yb³⁺ ion. At the same time, population on the ⁵I₇ level is also excited to ⁵F₅ level by strong excited-state absorption (ESA) at the pumping of 970 nm LD. These processes not only depopulate the lower laser level (⁵I₇), but also recycle energy to the upper laser level (⁵I₆) by nonradiative transition, which makes the possibility of population inversion for Ho³⁺:⁵I₆→⁵I₇.

To date, lots of previous works have mainly paid attention to the ∼2 μm emissions owing to the ⁵I₇ → ⁵I₈ transition in Ho³⁺/Yb³⁺ co-doped crystals [10, 11]. However, to our knowledge, there are few results focusing on the ∼3 μm emissions, and limited to oxide crystals [12, 13]. It is well known that one important factor (a proper host) should be considered in achieving intense Ho³⁺:⁵I₆ → ⁵I₇ MIR emission for practical laser operation. The ideal host material is expected to possess low phonon energy, which is beneficial for suppressing multiphonon de-excitation processes. Among many alternatives, fluoride crystals are more favorable in several respects: (i) lower phonon energy suppressing nonradiative relaxation between adjacent energy levels, (ii) longer fluorescence lifetime improving energy storage, and (iii) lower refractive index limiting nonlinear effects under intense laser pump [14–16]. In our previous work [7], we have reported a new MIR laser crystal Ho³⁺:PbF₂, which has low phonon energy of 257 cm⁻¹, good 2.8 μm MIR emission performances, and low absorption coefficient in typical H₂O absorption band at 3 μm. PbF₂ crystallizes in the cubic space group (Fm3̄m) with fluorite structure, which makes it possible to grow into the form of large-size transparent single crystals [17]. Furthermore, the PbF₂ crystal has high thermal conductivity (28 W/m/K), moderate mechanical properties for handling, and is not moisture sensitive [18]. These characteristics make the PbF₂ crystal can be used as an extremely suitable host to MIR solid-state lasers.

In this Letter, we reported the efficient 2.86 μm emission in a Ho³⁺/Yb³⁺ co-doped PbF₂ crystal under a 970 nm LD pump for the first time. Yb³⁺ ion was demonstrated to be an effective sensitizer for Ho³⁺ ion in PbF₂ crystal, and to greatly facilitate the Ho³⁺:⁵I₆→⁵I₇ emission by UC and ESA from Ho³⁺:⁵I₇ to Ho³⁺:⁵F₅. Besides, the energy transfer efficiency from Yb³⁺:²F_5/2 to Ho³⁺:⁵I₆, and the spectroscopic investigation of Ho³⁺/Yb³⁺:PbF₂ crystal were also investigated to demonstrate their feasibility for MIR solid state lasers under a common 970 nm LD pump.

2. Experimental section

In the Yb³⁺, Ho³⁺ codoped system, if the concentration of Yb³⁺ is too small, the absorption coefficient at around 970 nm would be greatly reduced, resulting in a lower pumping absorption efficiency. On the contrary, if the concentration of Yb³⁺ is too large, the Yb³⁺ ions would form cluster structures involving at least Yb³⁺-Yb³⁺ ions pairs in PbF₂ crystal when the Yb³⁺ doped concentration was larger than 2 mol.%, which would result in the fluorescence quenching [19]. A middle-ground approach was taken in our experiment, the concentration ratio between Ho and Yb was chose as about 1, they were all 2 mol.%, respectively.

The Ho³⁺ single doped, Yb³⁺ single doped, and Ho³⁺/Yb³⁺ co-doped PbF₂ crystals were grown by the Bridgman method. The crystals growth process was similar to our previous work [7]. The concentration of Ho³⁺, and Yb³⁺ ions in the crystals were measured by the inductively coupled plasma-atomic emission spectrometry (ICP-AES) method. The single-doped crystals were measured to be 2.20×10²⁰ ions/cm³ of Ho³⁺, and 2.56×10²⁰ ions/cm³ of Yb³⁺, respectively. The concentrations of Ho³⁺ and Yb³⁺ in double-doped crystal were 2.29×10²⁰ ions/cm³ and 2.59×10²⁰ ions/cm³, respectively. The corresponding segregator coefficients of Ho³⁺ and Yb³⁺ were 1.15 and 1.35, respectively. The effective segregation has a close relationship with the ionic radius of doping and host ions. In PbF₂ crystal, trivalent rare earth ions usually occupy the Pb²⁺ sites, and the charge compensation is attained by the presence of interstitial fluorine ion ( ${\text{F}}_i^{-}$) [20]. The ionic radius of Yb₃⁺ (0.98 Å), and Ho³⁺ (1.02 Å) are far smaller than that of Pb²⁺ (1.29 Å), resulting in the segregator coefficients of Yb³⁺ and Ho³⁺ are large than 1, indicating that Pb²⁺ can be easily replaced by doping ions Yb³⁺, and Ho³⁺ ions and the doping concentration can be high.

The absorption spectrum of Ho³⁺/Yb³⁺:PbF₂ crystal was record with a JASCO V-570 UV/VIS spectrophotometer in the range of 300–2300 nm. The fluorescence spectrum in the wavelength of 2700–3100 nm for the Ho³⁺/Yb³⁺:PbF₂ crystal was measured with Edinburgh Instruments FLS920 under excitation of 970 nm. The fluorescence decay curves of Ho³⁺/Yb³⁺ codoped PbF₂ crystal was measured at 2860 nm under pulse excitation of 970 nm. The decay curves of the Yb³⁺:²F_5/2 energy level of Yb³⁺-doped and Yb³⁺/Ho³⁺-codoped PbF₂ crystals were measured at 1030 nm under excitation of 970 nm. All the measurements were taken at room temperature.

To reduce an artificial lifetime lengthening due to radiation trapping, (i) the thickness of crystals was very thin with a value of 0.5 mm; (ii) the excited laser beam was focused near the edge of crystal; (iii) the measurements were performed by the pin-hole method [21], the crystals were placed behind a pin-hold with a variable aperture from 0.5 mm to 1.5 mm at an angle of 45° with respect to the excited laser beam and the axis of the collection optics.

3. Experimental results and discussion

The absorption spectrum of Ho³⁺/Yb³⁺:PbF₂ crystal is shown in Fig. 2. It is obvious to see that there are many typical absorption spectrum of Ho³⁺ ion, such as the absorption bands centered at around 416, 450, 536, 643, 1150, and 1914 nm, which correspond to the transitions from Ho³⁺: ⁵I₈ to ⁵G₅, ⁵G₆+⁵F₁, ⁵S₂+⁵F₄, ⁵F₅, ⁵I₆, and ⁵I₇, respectively. These peaks are associated with the 4f¹⁰→4f¹⁰ transitions of trivalent holmium. However, there is no readily available commercial LD corresponding to these absorption bands. Nevertheless, the absorption band corresponds to the Yb³⁺ optical transition ²F_7/2→²F_5/2 centered at 970 nm with very large intensity can be obtained in Ho³⁺/Yb³⁺:PbF₂ crystal. By reason of the small energy gap between Yb³⁺:²F_5/2 level and Ho³⁺:⁵I₆ level, Yb³⁺ ion can act as a sensitizer to Ho³⁺ ion by nonradiative energy transfer, which makes this crystal propitious to be pumped by commercialized InGaAs LD, indicating that importing of Yb³⁺ ions is expected to provide an efficient excitation channel.

 

Fig. 2 Absorption spectrum of Ho³⁺/Yb³⁺:PbF₂ crystal in the range of 300–2300 nm.

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According to the Judd-Ofelt theory [22, 23], the intensity parameters Ω_2,4,6 of Ho³⁺ (shown in Table 1) was calculated from the room-temperature absorption spectrum. It can be seen that the Ω_2,4,6 of Ho³⁺ in our Ho³⁺/Yb³⁺ co-doped PbF₂ crystal are all higher than those of Ho³⁺ single doped PbF₂ crystal [7]. In particular, it is well known that Ω₂ is affected by the symmetry of rare-earth ions site. The value of Ω₂ drops with the improved symmetry [24]. The larger Ω₂ of Ho³⁺ in our Ho³⁺/Yb³⁺ co-doped PbF₂ crystal indicates that a lower symmetry surrounding Ho³⁺ ions is caused by the introduction of Yb³⁺ ions [25]. Further calculation about the fluorescence branching ratio β of ⁵I₆→⁵I₇ transition in the Ho³⁺/Yb³⁺:PbF₂ crystal is as high as 20.52%, which is comparable with the result of Ho³⁺ single doped PbF₂ crystal (20.99%), and still much higher than that of other crystals, indicating that the codoping of Yb³⁺ ions has little influence on the ∼3 μm fluorescence emission efficiency of Ho³⁺.

Table 1. Judd-Ofelt parameters Ω_2,4,6, branching ratio β, emission cross sections σ, lifetime of ⁵I₆ level for Ho³⁺ ions (τ_meas and τ_R are the measured and calculated radiative lifetime), and quantum efficiency η of different Ho³⁺ doped materials.

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To further study the effect of Yb³⁺ codoping on the ∼3 μm photoluminescence of Ho³⁺, the corresponding emission cross sections are subsequently calculated by the Fuchtbauer-Ladenburg equation [26]:

 

Fig. 3 Emission cross-section spectra of Ho³⁺ single doped and Ho³⁺/Yb³⁺ co-doped PbF₂ crystals in the wavelength of 2700–3100 nm. The inset shows the fluorescence decay curve of Ho³⁺/Yb³⁺:PbF₂ for the ⁵I₆ mainfold.

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The inset of Fig. 3 shows the fluorescence decay curves of Ho³⁺/Yb³⁺ codoped PbF₂ crystals performances monitored at 2860 nm under pulse excitation of 970 nm. The lifetime value is determined by the single exponential fitting of the decay curve, and is measured to be 5.14 ms, which is only 4.8% shorter when compared with the date for the Ho³⁺ single doped PbF₂ crystal (5.4 ms) [7], indicating that the codoping of Yb³⁺ ions has litter influence on the ⁵I₆ level of Ho³⁺. The quantum efficiency, which is evaluated by η =τ_meas/τ_R, where τ_meas and τ_R are the measured and calculated (by Judd-Ofelt theory) radiative lifetime of ⁵I₆ level for Ho³⁺ ions in Ho³⁺/Yb³⁺:PbF₂ crystal. Therefore, the value of η was calculated to be 88.8%, which is comparable to that of Ho³⁺ single doped PbF₂ crystal (88.4%) [7], confirming Yb³⁺ as an effective sensitizer.

To further understand this phenomenon, the energy transfer between Yb³⁺ and Ho³⁺ ions was studied in details. It is worth noting that the energy transfer from Yb³⁺ to Ho³⁺ ions is a phonon-assisted process because of the small energy mismatch between the ²F_5/2 level of Yb³⁺ and ⁵I₆ level of Ho³⁺ [30]. The ability of a donor (Yb³⁺) to transfer its energy to an acceptor (Ho³⁺) is an important factor to evaluate the donor (Yb³⁺) as a sensitizer. And the energy transfer efficiency η_ET from Yb³⁺ to Ho³⁺ can be described as η_ET =1−τ_Yb−Ho/τ_Yb, where τ_Yb−Ho and τ_Yb are lifetime of Yb³⁺:²F_5/2 energy level of Yb³⁺:PbF₂ crystals with and without Ho³⁺. The decay curves of the Yb³⁺:²F_5/2 energy level of Yb³⁺-doped and Yb³⁺/Ho³⁺-codoped PbF₂ crystals are shown in Fig. 4 (a) and 4(b). The inset of Fig. 4 (a) and 4(b) show the Ln of fluorescence intensity I versus time t, which can be well linear fitting, indicating that the these two decay curves of Fig. 4 (a) and 4(b) can be well fitted to single exponential functions. The measured lifetime of the Yb³⁺:²F_5/2 manifold in the Ho³⁺/Yb³⁺:PbF₂ crystal is 77 μs, which is much shorter than that of Yb³⁺:PbF₂ crystal (2.3 ms), resulting in the calculated energy transfer efficiency η_ET from Yb³⁺ to Ho³⁺ being as high as 96.7%. This confirms that Yb³⁺ ion is a suitable sensitizer in Ho³⁺/Yb³⁺:PbF₂ crystal and can efficiently transfer energy to Ho³⁺ ion, thus makes this crystal propitious to be pumped by commercialized InGaAs LD.

 

Fig. 4 (a)(b)Fluorescence decay curves of the Yb³⁺:²F_5/2 energy level of Yb³⁺ single doped and Ho³⁺/Yb³⁺ codoped PbF₂ crystals. (c)(d)Fluorescence decay curves of the ⁵I₇ multiplet of the Ho³⁺ single doped and Ho³⁺/Yb³⁺ codoped PbF₂ crystals. The inset of (a)(b)(c)(d) show the Ln of fluorescence intensity I versus time t.

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According to the energy level diagram of Ho³⁺ and Yb³⁺ ions (shown in Fig. 1), firstly ions of Yb³⁺:²F_7/2 state are excited to Yb³⁺:²F_5/2 by a 970 nm LD. Then the energy easily transfers to the Ho³⁺ ions on the ground ⁵I₈ level which will be excited to the ⁵I₆ level. One part of the Ho³⁺ ions on the ⁵I₆ level will decay radiatively to ⁵I₇ with ∼2.8 μm emission. Other ions on the ⁵I₆ level will decay radiatively to ⁵I₈ with ∼1.2 μm emission, or decay nonradiatively to the ⁵I₇ level by the multiphonon relaxation. Under the excitation of 970 nm LD, the ions on the ⁵I₇ level will undergo the UC and ESA processes to ⁵F₅ level, which depopulates the Ho³⁺:⁵I₇ level. Then, the ions on ⁵F₅ level decays mainly nonradiatively to the upper laser level ⁵I₆, makes the possibility of population inversion for Ho³⁺:⁵I₆→⁵I₇, and enhances the 2.86 μm emission. To prove this assumption, the time-resolved decays of the ⁵I₇ multiplet of the Ho³⁺ single doped and Ho³⁺/Yb³⁺ codoped PbF₂ crystals were measured, and shown in Fig. 4 (c) and 4(d). The inset of Fig. 4 (c) and 4(d) show the Ln of fluorescence intensity I versus time t, which are unable to be linear fitting, indicating that the these two decay curves of Fig. 4 (c) and 4(d) can not be fitted to single exponential functions. They can be well fitted to dual exponential decaying. The measured lifetime of the ⁵I₇ manifold in the Ho/Yb:PbF₂ crystal is 10.8 ms, which is 20.1% shorter when compared with the date for the Ho:PbF₂ crystal (13.8 ms). This shortening of the measured lifetime confirms that Yb³⁺ ions are able to depopulate the Ho³⁺:⁵I₇ for 2.86 μm emission in PbF₂ crystal, which may induce the population inversion and facilitate laser operation.

4. Conclusion

In conclusion, an efficient emission at 2.86 μm was observed in the Ho³⁺/Yb³⁺-codoped PbF₂ crystal under the excitation of a common 970 nm LD. Compared with the Ho³⁺ single doped PbF₂ crystal, the Ho³⁺/Yb³⁺ codoped PbF₂ crystal has comparable fluorescence branching ratio (20.52%), quantum efficiency (88.8%), and higher emission cross section (1.90×10⁻²⁰ cm²) corresponding to the stimulated emission of Ho³⁺:⁵I₆→⁵I₇ transition. It was demonstrated that the energy transfer efficiency from Yb³⁺:²F_5/2 to Ho³⁺:⁵I₆ is as high as 96.7%, indicates that Yb³⁺ ion can be used as an effective sensitizer for Ho³⁺ ion. Moreover, it was also shown that the introduced Yb³⁺ depopulates the Ho³⁺:⁵I₇ level, which is benefited the possible population inversion for Ho³⁺:⁵I₆→⁵I₇. The results and analyzed energy transfer indicate codoping of Yb³⁺ with Ho³⁺ in PbF₂ crystal plays an important role in 2.86 μm emission when the crystal was pumped by a conventional 970 nm LD.