Growth and spectroscopic properties of Er:Lu₂O₃ crystal grown by floating zone method

Rare earth doped luminescent materials have been widely applied in many fields such as integrated optical systems, high-definition displays, solid-state laser emitters and bioanalyzers due to their excellent luminescent properties, and have broad application prospects [1]. Er doped laser materials have attracted increasing interests due to their various important applications in the visible and mid-infrared (at 1.5 μm and 2.8 μm) wavelength regions. Laser operations of Er³⁺ at 2.8 μm corresponding to ⁴I_11/2 → ⁴I_13/2 transitions attract much more attentions because it can be used for far-infrared optical parametric oscillators (OPO) applied in scientific research, atmospheric pollution monitoring and directional infrared countermeasure [2]. In addition, laser at 2.8 μm can be used for medical treatments because of the strong water absorption in this region. The absorption efficiency of water molecule on Er³⁺ based 2.8 μm laser is 200 times than that of Ho³⁺ based 2.1 μm laser, 10 000 times than that of Nd³⁺ based 1.06 μm laser. Er³⁺ based 2.8 μm laser could cut and remove soft tissue and bones accurately, and it is known as the 'Gold Laser' of stomatology [3–5]. However, the lifetime of the upper level ⁴I_11/2 is considerably shorter than that of the lower level ⁴I_13/2. The laser transition will be prevented by the accumulation of population in the ⁴I_13/2 level, and this is known as the 'self-terminating' effect [6]. The unfavorable fluorescence lifetime ratio of the two laser levels impedes the improvement of Er³⁺ based 2.8 μm lasers. Typically, there are two major solutions: Er³⁺ heavily doping or co-doping deactivating ions Pr³⁺ [7]. Both solutions could reduce the fluorescence lifetime gap between the ⁴I_11/2 and ⁴I_13/2 level, thus makes stable continuous-wave 2.8 μm laser possible and could further improves the spectroscopic properties and laser performance.

The cubic sesquioxide crystal Lu₂O₃ has attracted widely attention as the host for laser crystals, it owns better abilities of low phonon energy (618 cm⁻¹), high thermal conductivity (12.8 W·m⁻¹·K⁻¹) and robust thermal stability compared to the most common host material YAG (Y₃Al₅O₁₂) [8, 9]. However, the growth of Lu₂O₃ single crystal is particularly difficult because of the high melting point (∼2450 °C) [9]. Few high-quality Lu₂O₃ crystals have been obtained. For Er³⁺ based oxide crystals, such as GYSGG [10], GSGG [11], GGG [7], YSGG [12], YAG [12], SrLaGa₃O₇ [13], BaLaGa₃O₇ [14], CaLaGa₃O₇ [15] and SrGdGa₃O₇ [16] etc, the doping concentrations of Er³⁺ are higher Lu₂O₃ crystal and fluoride crystals such as CaF₂ [17] and SrF₂ [17]. The laser performance of Er:Lu₂O₃ have been reported with cw output power of 1.4 W and slope efficiency of 36% at 2.85 μm [18]. However, high doping concentration decreases the thermal conductivity of crystal and extremely shorten lifetime of the upper level. Moreover, Lu₂O₃ crystal also has higher thermal conductivity than CaF₂ crystal and SrF₂ crystal in low doping concentration [19, 20]. So far, there are few studies of optical characteristics of Er:Lu₂O₃ crystals have been investigated.

In this work, we report on the growth and spectroscopic properties of Er³⁺ doped Lu₂O₃ laser crystal. 1.5.at% Er:Lu₂O₃ single crystal with high optical quality was grown by Floating zone (Fz) method. The crystalline quality of the as-grown Er:Lu₂O₃ crystal was investigated by x-ray diffraction (XRD). The radiative lifetimes of the relevant excited states of Er³⁺ were calculated by the Judd–Ofelt (J–O) theory. A detailed spectroscopic properties of the 1.5 at% Er:Lu₂O₃ crystal was performed. Absorption and luminescence spectra were presented and emission cross-sections were calculated for the 1.5 μm and 2.8 μm laser transitions. In addition, we compare the optical characteristics of Er doped Lu₂O₃ crystals with other materials in 2.8 μm.

2.1. Crystal growth

The Er doped Lu₂O₃ crystal was designed according to the formula (Er_xLu_1−x)₂O₃ (x = 0.015). The raw materials were Lu₂O₃ (99.99%) and Er₂O₃ (99.99%) powders. The oxides were weighed accurately and mixed in a beaker and then shaped into two rods. After pressed at 220 MPa for 3 min, the two rods were sintered in air at 1700 °C for 24 h. One was used as the feed rod and the other was used as the seed rod. The two rods should be placed on a same vertical axis during the growth process. The crystal was grown in high-purity argon gas atmosphere with a rotation rate of 8–10 rpm and growth rate of 1–2 mm h⁻¹ for both rods. Then the grown Er:Lu₂O₃ was cooled to room temperature. The samples of Er:Lu₂O₃ crystal were cut and polished on both sides. The samples are transparent and crack-free with the dimensions of 5 mm × 5 mm × 1.22 mm is shown in figure 1.

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2.2. Spectra measurements

The XRD pattern of the 1.5 at% Er:Lu₂O₃ crystal is shown in figure 2. All the diffraction peaks of Er:Lu₂O₃ are sharp and consistent well with the standard pattern of JCPDS#86–2475 of Lu₂O₃. The lattice parameters of 1.5 at% Er:Lu₂O₃ crystal are a = b = c = 10.3709 Å, α = β = γ = 90°. The values are smaller that of pure Lu₂O₃ crystal (a = b = c = 10.390 Å). According to ICP analysis, the Er³⁺ concentration N_c was 4.3 × 10²⁰ cm³. The absorption spectrum of Er:Lu₂O₃ crystal at room temperature is shown in figure 3. Eleven absorption bands centered at 378, 410, 446, 455, 490, 523, 545, 657, 797, 976 and 1520 nm corresponding to the transitions the ground state ⁴I_15/2 to the excited states of ⁴G_11/2, ²H_9/2, ⁴F_3/2, ⁴F_5/2, ⁴F_7/2, ²H_11/2, ⁴S_3/2, ⁴F_9/2, ⁴I_9/2, ⁴I_11/2 and ⁴I_13/2, respectively. The 1.5 at% Er:Lu₂O₃ crystal exhibits two strong absorptions at 971 nm and 1536 nm. The absorption cross-section can be calculated by the following equation:

$$\begin{eqnarray}&&{\sigma }_{{\rm{abs}}}\left(\lambda \right)=\displaystyle \frac{2.303}{{N}_{c}\times L}OD\left(\lambda \right)\end{eqnarray} \tag{ 1 }$$

Where λ is the wavelength, L is the thickness of the crystal, OD is the optical density and N_c is concentration of Er³⁺ ions in Er:Lu₂O₃ crystal. The absorption cross-section at near 971 nm and 1536 nm are 0.15 × 10^–20 cm² and 1.07 × 10^–20 cm², and the FWHMs are 18.3 nm and 12.3 nm, respectively. The large absorption cross-section is beneficial to absorp the pumping sources. In addition, the broader FWHMs can decrease the temperature dependence of the diode laser and improve laser efficiency.

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The Judd-Ofelt theory [21, 22] is widely used for the calculation of spectroscopic parameters of rare earth ion-doped crystals. In this work, spectroscopic parameters of Er:Lu₂O₃ crystal were calculated with J-O theory. Eleven absorption bands in the visible and infrared spectra ranges correspondjing to the transition of Er³⁺ from the ground state ⁴I_15/2 to the excited states are utilized to fit the transition intensity parameters Ω_t (t = 2, 4, 6). All the final states are assigned and marked in figure 3. The main equations of J-O theory and the detailed reviews are applied in the following analysis procedure [23, 24]. The refractive index of cubic Er:Lu₂O₃ crystal is calculated with the Sellmeier equation as follows [25]:

$$\begin{eqnarray}&&{\rm{n}}=\sqrt{{D}_{1}+\displaystyle \frac{{D}_{2}}{\left({\lambda }^{2}-{D}_{3}\right)}-{D}_{4}{\lambda }^{2}}\end{eqnarray} \tag{ 2 }$$

where the values of D₁, D₂, D₃ and D₄ in the Sellmeier equation are 3.619 68, 0.041 31, 0.0238 and 0.008 56, respectively.

In this work, the calculated values of average wavelength λ, refractive index n, experimental oscillator strength f_exp , the experimental electric dipole line strength S_exp and the calculated electric dipole line strength S_cal are presented and summarized in table 1. The fitting quality, which is characterized by the relative square deviation between the measured and calculated electric-dipole oscillator strength, can be expressed by:

$$\begin{eqnarray}&&R=\displaystyle \frac{\sum {\left({S}_{\exp }-{S}_{{\rm{cal}}}\right)}^{2}}{\sum {{S}^{2}}_{\exp }}\end{eqnarray} \tag{ 3 }$$

Table 1.  The average wavelength $\left(\bar{\lambda }\right),$ refractive indices (n), experimental and calculated line strength of Er³⁺ in Er:Lu₂O₃ crystal.

Final states (ground state 4I15/2 )	λstart–λend	$\bar{\lambda }$ (nm)	ƒexp(×10−6 )	Sexp (×10–20 cm2)	Scal (×10–20 cm2)
4I13/2	1426–1609	1520	1.601	1.956	1.998
4I11/2	955–1004	976	0.423	0.329	0.647
4I9/2	789–807	797	0.351	0.222	0.179
4F9/2	643–672	657	1.768	0.914	1.088
4S3/2	537–559	545	0.772	0.327	0.274
2H11/2	501–536	523	8.862	3.595	4.461
4F7/2	468–500	489	1.502	0.568	0.919
4F5/2	450–466	455	0.263	0.092	0.277
4F3/2	440–450	446	0.096	0.033	0.158
2H9/2	402–421	409	0.776	0.240	0.298
4G11/2	346–400	377	21.850	6.157	5.741

The relative square deviation R is fitted to be 5.84%, which indicates a good consistency between the calculated and experimental values. By a least squared fitting to the experimental line strength S_exp, the three intensity parameters are fitted to be Ω₂ = 5.542 × 10^–20 cm², Ω₄ = 0.962 × 10^–20 cm² and Ω₆ = 1.241 × 10^{–2 0}cm². Normally, the Ω_t parameters depend on the doping ions and the crystalline field environment. The value of Ω₂ is proportional to the asymmetry. The higher value of Ω₂ indicates the lower local environment symmetry exists. However, Ω₄ and Ω₆ are not directly related to the ligand symmetry of rare-earth ions. Ω₆ usually increases with decreasing covalence between doping ions and the surrounding elements. Ω₄/Ω₆ is used as a spectroscopic quality factor and is a significant characteristic parameter for estimating the stimulated emission efficiency [26]. Intensity parameters in our work compared with other Er³⁺ doped crystals are shown in table 2. In this work, the value of Ω₂ is 5.54, which is smaller than that of GdTaO₄ [27] and BaLaGa₃O₇ [14], but higher than that of Gd₃Sc₂Ga₃O₁₂ [26], CaLaGa₃O₇ [15], CaF₂ [28] and YAlO₃ [29]. The results show that grade of contravalency in Lu₂O₃ is lower than that of GdTaO₄ and BaLaGa₃O₇ but higher than that of Gd₃Sc₂Ga₃O₁₂, CaF₂ and CaLaGa₃O₇ surrounding the Er³⁺ ions. The value of Ω₄/Ω₆ is 0.77 higher than CaF₂, which indicates the rigidity of Er:Lu₂O₃ higher than CaF₂.

By using the obtained transition intensity parameters, the calculated results of the radiative transition rate A_(J→J'), the fluorescence branching ratio β_(J→J'), and the radiative lifetime τ_rad are listed in table 3. As shown in table 3, the radiative transitions of ⁴I_13/2 → ⁴I_15/2 and ⁴I_11/2 → ⁴I_13/2corresponding to the wavelengths 1.5 μm and 2.8 μm, have larger fluorescence branching ratios in infrared wavelength regions. The fluorescence branching ratios of ⁴I_13/2 → ⁴I_15/2 and ⁴I_11/2 → ⁴I_13/2 are 100% and 48.4%. There are some effects of non-radiative processes in ⁴I_11/2 → ⁴I_13/2. Moreover, the radiative lifetimes of ⁴I_13/2 and ⁴I_11/2 is estimated to be 1.36 ms and 2.52 ms, which indicate excellent energy storage capability.

The emission spectra in 1.5 μm and 2.8 μm of 1.5 at% Er:Lu₂O₃ crystal are shown in figure 4. Figures 3(a) and (b) show the emission cross-section in near 1.5 μm and 2.8 μm. The emission cross-section is calculated by the Fuchtbauer–Ladenburg (F–L) formula [30]:

$$\begin{eqnarray}&&{\sigma }_{{\rm{em}}}\left(\lambda \right)=\displaystyle \frac{A(J\to {J}^{\mbox{'}}){\lambda }^{5}I\left(\lambda \right)}{8\pi {{\rm{cn}}}^{2}\int I\left(\lambda \right)\lambda {\rm{d}}\left(\lambda \right)}\end{eqnarray} \tag{ 4 }$$

Where A is transition probabilities correspond to radiative transitions, c is the velocity of light, n is the refractive index and I(λ) represents the experimental emission intensity as a function of the wavelength. The emission cross-sections of the 1.5 at% Er:Lu₂O₃ crystal at 1558 nm and 2742 nm were calculated to be 2.20 × 10^–20 cm² and 3.22 × 10^–20 cm², and the FWHMs are 64.9 nm and 178.1 nm, respectively.

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The fluorescence decay curves for ⁴I_11/2 (a and ⁴I_13/2 (b) are shown in figure 5. With a single exponential function, the lifetimes of ⁴I_11/2 and ⁴I_13/2 are fitted to be 1.59 ms and 12.43 ms. The fluorescence lifetime of ⁴I_11/2 (1.59 ms) is longer compared to other host materials, supplies a long and efficient radiative relaxation from the ⁴I_11/2 onto the ⁴I_13/2 level. Theoretically, the radiative lifetime should be longer than the fluorescence lifetime. The thin samples are used to measure because the reabsorption phenomenon would generate a longer measured fluorescence lifetime.

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The spectroscopic data in 2.8 μm between the Er:Lu₂O₃ crystal and other Er³⁺ doped crystals is listed in table 4. The 1.5 at% Er:Lu₂O₃ crystal has a larger spectral quality factors Q (Q = σ_emτ_up ) than CaF₂ and YAG. because it has higher emission cross-section and the lifetime of ⁴I_11/2. The result indicates that Er:Lu₂O₃ single crystal is a potential material for 2.8 μm laser operation.

The absorption cross-section of Er³⁺ in radiative transitions ⁴I_13/2 → ⁴I_15/2 and ⁴I_11/2 → ⁴I_13/2 can be derived from the calculated emission cross-section through the McCumber method [31]:

$$\begin{eqnarray}&&{\sigma }_{{\rm{abs}}}\left(\lambda \right)={\sigma }_{{\rm{em}}}\left(\displaystyle \frac{{Z}_{u}}{{Z}_{l}}\right)\exp \left[\displaystyle \frac{-\left({E}_{zl}-hc{\lambda }^{-1}\right)}{{K}_{B}T}\right]\end{eqnarray} \tag{ 5 }$$

where E_zl is the energy difference between the lowest Stark level of the lower and upper manifolds, h is Plancks constant, K_B is the Boltzmann constant, T is the temperature, and Z_u and Z_l are partition functionsand. Z_u/Z_l of ⁴I_13/2 → ⁴I_15/2 and ⁴I_11/2 → ⁴I_13/2 are 1.25 and 1.09, respectively [32, 33].

As the absorption and emission cross-section were calculated, the gain cross-section, which is used to evaluated laser performance, is commonly calculated according to the formula [34]:

$$\begin{eqnarray}&&{\sigma }_{{\rm{gain}}}\left(\lambda \right)=P{\sigma }_{em}-\left(1-p\right){\sigma }_{abs}\end{eqnarray} \tag{ 6 }$$

where p is the population inversion ratio, P = N_u/N₀, where N_u and N₀ are the numbers of ions in the upper laser level and overall number of ions, respectively. The calculated results of the gain cross-sections of the 1.5 at% Er:Lu₂O₃ crystal in 1.5 μm and 2.8 μm with the P various from 0 to 1 were estimated and illustrated in figure 6. The gain cross-sections in near 1.5 μm and 2.8 μm are displayed in figure 5(a) and (b). when inversion ratio P = 0.5, the positive gain cross-section was achieved at 1.5 μm and 2.8 μm. As inversion ratio increasing, the local peaks at 1.5 μm and 2.8 μm are also observed. The low inversion ratios indicate a great potential of Er:Lu₂O₃ crystal with good gain performance.

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A high-quality 1.5 at% Er:Lu₂O₃ single crystal was successfully grown by Fz method. The transition probabilities, line strength, fluorescence branch ratios were calculated. The J-O intensity parameters Ω_t (t = 2, 4, 6) were calculated to be Ω₂ = 5.542 × 10^–20 cm², Ω₄ = 0.962 × 10^–20 cm² and Ω₆ = 1.241 × 10^–20cm². The absorption cross-section at near 971 nm and 1536 nm are 0.15 × 10^–20 cm² and 1.07 × 10^–20 cm², and the FWHMs are 18.3 nm and 12.3 nm, respectively. The fluorescence lifetime of ⁴I_11/2 and ⁴I_13/2 at 2.8 μm are fitted to be 1.59 ms and 12.43 ms. In addition, the emission cross-section at 1558 nm and 2742 nm were calculated to be 2.20 × 10^–20 cm² and 3.22 × 10^–20 cm² , and the FWHMs are 64.85 nm and 178.1 nm, respectively. The longer fluorescence lifetime , larger σ_em, and the larger spectral quality factors Q of 1.5 at% Er:Lu₂O₃ crystal indicate that it has a great potential for 2.8 μm laser operation.

This work is partially supported by the National Key Research and Development Program of China (No. 2016YFB1102202), the Fundamental Research Funds for the Central Universities and MOE Key Laboratory of Advanced Micro-Structured Materials.