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Dy: BaLaGa3O7 crystals
Journal of Luminescence 208 (2019) 259–266
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Spectroscopic analyses and laser properties simulation of Er/Yb, Er/Nd, Er/ Dy: BaLaGa3O7 crystals
T
Wei Zhanga,b, Yan Wanga, , Jian-fu Lia, Zhao-jie Zhua, Zhen-yu Youa, Chao-yang Tua, ⁎
⁎
a
Key Laboratory of Optoelectronic Materials Chemistry and Physics, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou City, Fujian Province 350002, PR China b College of Chemistry, Fuzhou University, Fuzhou City, Fujian Province 350116, PR China
ARTICLE INFO
ABSTRACT
Keywords: BaLaGa3O7 Crystal growth Spectroscopic properties Mid-infrared laser
The Er3+/Yb3+, Er3+/Nd3+ and Er3+/Dy3+ co-doped BaLaGa3O7 crystals were grown by the Czochralski method. The absorption spectra, up-conversion emission spectra, near-infrared and mid-infrared emission spectra, as well as the fluorescence decay curves of them were measured at room temperature. Detailed spectroscopic analyses were carried out and the spectral parameters of them were compared. Furthermore, the energy transfer processes among Er3+-Yb3+, Er3+-Nd3+ and Er3+-Dy3+ were investigated and the rate-equation theory models were built and discussed. The results demonstrate that Er/Nd: BaLaGa3O7 crystal is a best candidate for obtainment of ~2.7 µm laser among the three doping kinds, since the introduction of Nd3+ not only increases the absorption efficiency of pump energy, but also inhibits the self-termination bottleneck effect, which are both beneficial to the output of the mid-infrared ~2.7 µm laser.
1. Introduction Recently, mid-infrared lasers in the range of 2.7–3 µm have received extensive attention due to their important potential applications in remote sensing, laser medical surgery, environmental detection and military field [1–5]. In addition, 2.7–3.0 µm laser is also attractive as pump source for far-infrared waveband optical parametric oscillation or optical parametric generation laser system [6,7]. It is worth noting that 2.7–3 µm lasers can be achieved by Er3+ ions through its 4I11/2 → 4I13/2 transition. However, on the one hand, the output power and efficiency of ~2.7 µm erbium lasers are not high enough owing to the low absorption efficiency of 980 or 808 nm laser pumping energy. In order to solve the problem of weak intensity and narrow band width in the absorption bands near 980 or 808 nm, it is a good choice to co-dope with sensitive ions such as Yb3+ [8] or Nd3+ [9] to improve the absorption properties. On the other hand, there exists a detrimental selftermination “bottleneck” effect in this transition owing to the lifetime of upper laser level (4I11/2) much shorter than that of the lower one (4I13/2) [10]. Therefore, some effective measures should be taken to suppress the self-termination problem. Previous studies have shown that some deactive ions appropriately co-doping into the Er3+ activated materials can inhibit the self-termination effect by depopulating the 4 I13/2 state, such as Er/Pr co-doped GGG [11], GYSGG [12] and CaGdAlO4 crystals [13], Er/Eu co-doped YAP crystal [14], Er/Tm co-doped ⁎
KCaF3 crystal [15], Er/Tm co-doped Y3Al5O12 nanocrystals–tellurate glass composites [16], and Er/Ho co-doped fluoride glass [17]. In this work, BaLaGa3O7 (abbr. as BLGO) crystal is chosen as host material. It belongs to the ABC3O7 family with tetragonal symmetry and melilite structure in the space group P4¯ 21m. The cell parameters are a=b= 8.145 Å, c= 5.382 Å, Z = 2 and d= 5.568 g/cm3 [18]. The refractive index of the crystal is 1.85 [19]. BLGO is a congruently melting compound with a melting point of 1560 °C [20], which makes it suitable to obtain large-sized and high quality crystals by using the Czochralski (CZ) method. BLGO crystal doesn’t have a center of symmetry [21], and owns good physicochemical stability, simple synthesis condition, and disordered structure [22,23]. Therefore, it is a wise choice to choose BLGO as host crystal in this work, and to the best of our knowledge, for the first time Yb3+, Nd3+ and Dy3+ as co-dopant ions are introduced into Er3+ activated BLGO crystal to improve the absorption or/and suppress the self-termination effect. The dopant rare earth ions are substituted for La3+, and occupy the same position (4e) with Ba and La ions [18]. Thus these rare earth ions, La3+ and Ba2+ are located in one crystal lattice, leading to a different crystal lattice field, further causing inhomogeneous broadening in the absorption and emission spectra. In this paper, Er3+/Yb3+, Er3+/Nd3+ and Er3+/Dy3+ co-doped BaLaGa3O7 (abbr. as Er/Yb: BLGO, Er/Nd: BLGO, Er/Dy: BLGO) crystals were grown by the Czochralski method successfully. The spectroscopic
Corresponding authors. E-mail addresses: [email protected] (Y. Wang), [email protected] (C.-y. Tu).
https://doi.org/10.1016/j.jlumin.2018.12.061 Received 19 October 2018; Received in revised form 27 December 2018; Accepted 27 December 2018 Available online 28 December 2018 0022-2313/ © 2018 Published by Elsevier B.V.
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properties based on the measured absorption, emission spectra and fluorescence decay curves in these three crystals were investigated. The absorption/emission cross sections were calculated to further compare their spectral properties. The energy transfer mechanisms were analysed and the energy transfer efficiencies were calculated. In addition, the rate-equation models of them were built and discussed carefully to estimate the upper limit of quantum efficiency.
were measured to be 2.18 at% and 0.38 at%, respectively. The concentrations of Er3+ and Nd3+ in Er/Nd: BLGO crystal were measured to be 2.34 at% and 1.25 at%, respectively. In Er/Dy: BLGO crystal, the doping concentrations of Er3+ and Dy3+ were measured to be 2.95 at% and 0.69 at%, respectively. The effective segregation coefficient K for Er3+, Yb3+, Nd3+ and Dy3+ in all the three crystals are performed by the following equation: (1)
K = C / C0
2. Experimental
Where C and C0 are the respective concentrations of ions in the crystal and raw material. The K values of Er3+ and Yb3+ in Er/Yb: BLGO crystal are determined to be 0.145 and 0.076, respectively. In Er/ Nd: BLGO crystal, the K values of Er3+ and Nd3+ are determined to be 0.156 and 0.625, respectively. In Er, Dy: BLGO crystal, the K values of Er3+ and Dy3+ are determined to be 0.197 and 0.345, respectively.
The Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals were grown by Czochralski method. According to our previous work [8–10,24], the initial concentrations of Er3+ were 15 at% in these three crystals, and the concentrations of Yb3+, Nd3+ and Dy3+ ions were 5 at %, 2 at% and 2 at%, respectively. 15 at% Er: BLGO single crystal was also grown for spectral comparison. High purity BaCO3 (Alfa Aesar Chemical Reagent Co., Ltd., A.R. grade), La2O3 (Changchun Highpurity Chemical Reagent Co., Ltd., 5N purity), Ga2O3 (Chengdu Jinhu New Materials Co., Ltd., 5N purity), Er2O3 (Changchun Highpurity Chemical Reagent Co., Ltd., 5N purity), Yb2O3 (Changchun Highpurity Chemical Reagent Co., Ltd., 5N purity), Nd2O3 (Changchun Institute of Applied Chemistry, 6N purity) and Dy2O3 (Changchun Institute of Applied Chemistry, 4N purity) powders were used. The raw materials were weighed accurately according to the stoichiometric ratio, with an excess of Ga2O3 (1.0 wt%) added for compensating the evaporation in crystal growth. The stoichiometric amounts of chemicals were mixed, ground thoroughly and suppressed into pellets, then placed into the muffle furnace (MXX1700-30, Shanghai Weixing Furnace Co., Ltd.) sintering at 1300 °C for 48 h to assure the complete reaction. Afterwards, the sintered tablets were milled carefully, and repeated the previous procedures until the measured powder diffraction peaks by Xray diffraction match the standard PDF card. The three crystals were grown respectively in a Czochralski instrument (China Electronics Technology Group Co., Ltd.) with nitrogen atmosphere protection containing 2% oxygen. During the growth process, the pulling rate varied from 0.5 to 2 mm/h and the crystal rotation speed was kept 10–15 r.p.m. After the growth was completed, the crystal was cooled slowly to room temperature at a rate of 5–35 K/h. The grown crystals were performed on X-ray diffraction (XRD, Miniflex 600) in the 2θ range of 10–80° at room temperature. The concentrations of Er3+, Yb3+, Nd3+ and Dy3+ in the grown crystals were measured by inductively coupled plasma atomic emission spectrometry (ICP-AES) analyses. The a-cut samples with dimensions of 5.0 × 5.0 × 1.0 mm3 were cut from the as-grown Er: BLGO, Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals and polished for spectral experiments, respectively. Absorption spectra were measured by Perkin-Elmer UV–VIS–NIR Spectrometer (Lambda-950). The up-conversion (UC) fluorescence spectra were measured by using Edinburgh Instruments FLS920 spectrophotometer. The near-infrared (NIR) fluorescence spectra and the decay curves were recorded in Edinburgh Instruments FLS980 spectrophotometer. The mid-infrared (MIR) fluorescence spectra and the fluorescence decay curves for the samples were recorded by Edinburgh Instruments FSP920 spectrophotometer. All the measurements were carried out at room temperature. For each kind of spectral measurement, the four samples were maintained under same conditions.
3.2. Absorption spectroscopy The room temperature absorption spectra of Er: BLGO, Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals were recorded in the range of 320–1700 nm, as shown in Fig. 2. In the three codopant samples, the spectra include the typical characteristic absorption peaks of both Er3+ and the co-dopant ion (Yb3+/Nd3+/Dy3+): the main seven absorption characteristic peaks of Er3+ are located at 379, 488, 523, 650, 802, 978 and 1536 nm, corresponding to Er3+ transitions from the 4I15/2 ground state to 4G11/2 + 2K15/2, 4F7/2, 2H11/2, 4F9/2, 4I9/2, 4I11/2 and 4I13/2, respectively. In Er/Yb: BLGO crystal, the absorption spectrum shows a much stronger band located near 980 nm, which involves both the contributions from Yb3+ and Er3+, assigned to Er3+: 4I15/2 → 4I11/2 and Yb3+: 2F7/2 → 2F5/2 transitions. The absorption bands of Nd3+ are observed in Er/Nd: BLGO crystal: the six main peaks centered at 360, 523, 589, 752, 808 and 882 nm correspond to the transitions from Nd3+: 4I9/2 to 4D3/2, 4G9/2 + 2G7/2, 2G5/2, 4F7/2 + 4S3/2, 4F5/2 + 2H9/2 and 4F3/2, respectively. The absorption band centered at 808 nm involves both the contributions from Nd3+ and Er3+. Also, there are six main absorption peaks of Dy3+ ions in Er/Dy: BLGO crystal, with the peaks centered at 345, 365, 452, 879, 1046 and 1234 nm, which are assigned to the transitions from Dy3+: 6H15/2 to 6P7/2, 6P5/2, 4I15/2, 6F7/2, 6H7/2 + 6F9/2 and 6H9/2 + 6F11/2, respectively. The absorption cross-section σa can be determined by the following equation [25]: a
=
Nm
=
2.303OD lNm
(2) 3+
Here α is the absorption coefficient, Nm is the Er concentration in the crystal, l is the thickness of the polished sample (l= 0.10 cm) and OD is the optical density. In Er/Yb: BLGO and Er/Dy: BLGO crystal, the absorption cross-sections σa are calculated to be 6.68 × 10−21 cm2 at 980 nm and 1.41 × 10−21 cm2 at 978 nm, with full width at half maximum (FWHM) of 10.3 and 27.8 nm, respectively. The absorption cross-section σa at 808 nm in Er/Nd: BLGO crystal is calculated to be 1.90 × 10−20 cm2, with full width at half maximum of 8.9 nm. Therefore, Yb3+ and Nd3+ can act as sensitizer for Er3+ to improve the absorption efficiency, thus making the Er/Yb: BLGO crystal more suitable for 980 nm InGaAs and Er/Nd: BLGO crystal for 808 nm AlGaAs LD pumping, respectively.
3. Results and discussion
3.3. Fluorescence spectroscopy
3.1. XRD analyses and ion concentrations
Fig. 3 shows the up-conversion emission spectra of Er: BLGO, Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals within the range of 450–750 nm under pumping of 978, 980, 808 and 978 nm, respectively. The green up-conversion emission bands centered at around 548 nm correspond to the transition: Er3+: 2H11/2 + 4S3/2 → 4I15/2, and the red up-conversion emission bands with peak around 669 nm can be assigned to Er3+: 4F9/2 → 4I15/2 transition. It is obvious that the green
Fig. 1 shows the photographs and XRD patterns of the as-grown Er/ Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals. The diffraction peaks are well consistent with the standard PDF file [No. 50–1800], which indicates the formation of pure phase in all the three crystals. The doping concentrations of Er3+ and Yb3+ in Er/Yb: BLGO crystal 260
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W. Zhang et al.
Fig. 1. Photographs and XRD patterns of Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals.
emission is much stronger than the red emission. As compared with Er: BLGO crystal, the green up-conversion emissions are reduced significantly in Er/Yb:BLGO and Er/Nd: BLGO crystals, while increased in Er/Dy: BLGO crystal. It can also be found that: the samples all exhibit weaker intensity in the red emission band, and Er/Nd: BLGO crystal almost can’t detect the red emission. The up-conversion emission as a negative factor for MIR laser output which needs to be suppressed, so
the introduction of Nd3+ is most favorable to the ~2.7 µm emission. As seen in Fig. 4, the near-infrared emission spectra of Er: BLGO, Er/ Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals within 1450–1650 nm are obtained when pumped by 978, 980, 808 and 978 nm, respectively. There are two strong emissions with peaks around at 1535 nm and 1548 nm, which are assigned to the transition of Er3+: 4 I13/2 → 4I15/2. Er: BLGO crystal shows the strongest intensity among the four samples. As compared with Er: BLGO crystal, the near-infrared
Fig. 2. Absorption spectra of Er: BLGO, Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals at room temperature.
Fig. 3. UC emission spectra of Er: BLGO, Er/Yb: BLGO, Er/Nd: BLGO and Er/ Dy: BLGO crystals. 261
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refractive index and τr is the radiative lifetime. β and τr are calculated to be 0.14 and 2.55 ms by Judd-Ofelt theory [24,29,30]. The maximum emission cross sections of Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals are estimated to be 4.26 × 10−20 cm2 at 2735 nm, 4.08 × 10−20 cm2 at 2700 nm and 4.12 × 10−20 cm2 at 2730 nm, respectively. 3.4. Fluorescence decay curve and fluorescence lifetime The decay curves of Er3+: 4I11/2 level in Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals are shown in Fig. 6(a), which are measured at 2735, 2700 and 2730 nm excited by 980, 808 and 978 nm, respectively. Fig. 6(b) displays the decay curves of Er3+: 4I13/2 level in Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals under pumping of 980, 808 and 978 nm, respectively, the detection wavelength is 1535 nm. Fig. 6(c) shows the decay curve of Yb3+: 2F5/2 level in Er/Yb: BLGO crystal, which is measured at 1003 nm excited by 980 nm. The decay curve of Nd3+: 4F3/2 level in the Er/Nd: BLGO crystal measured at 1059 nm excited by 808 nm is shown in Fig. 6(d). After being fitted, the decay curves of Er3+ : 4I11/2 level in Er/Yb: BLGO crystal and Er3+: 4I13/2 level in Er/Nd: BLGO crystal show singly exponential decaying behavior and the fluorescence lifetime can be fitted with
Fig. 4. NIR emission spectra of Er: BLGO, Er/Yb: BLGO, Er/Nd: BLGO and Er/ Dy: BLGO crystals.
emission spectra of Er/Yb: BLGO and Er/Nd: BLGO crystals exhibit weaker intensity while that of Er/Dy: BLGO crystal shows the weakest intensity. Near-infrared emission is a hindering factor for ~2.7 µm laser output. Owing to the existence of Dy3+, near-infrared emission can be inhibited and thus beneficial to the ~2.7 µm emission. The mid-infrared fluorescence spectra of Er: BLGO, Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals in the wavelength range from 2500 to 3000 nm are shown in Fig. 5. The Er: BLGO, Er/Yb: BLGO and Er/Dy: BLGO crystals are excited by 978, 980 and 978 nm, respectively, and Er/Nd: BLGO crystal is excited by 808 nm. The MIR emission band centered at 2735 nm is attributed to Er3+: 4I11/2 → 4I13/2 transition in Er/Yb: BLGO crystal, while the strong emission bands with peaks at 2700 and 2730 nm can be observed in Er/Nd: BLGO and Er/Dy: BLGO crystals, respectively. Er/Yb: BLGO crystal shows the strongest intensity and its intensity is over 4 times than that in Er/Nd: BLGO crystal. This is the objective emission which would lead to the achievement of ~2.7 µm laser. The emission cross-section is an important parameter influencing the potential laser performance [26]. The stimulated emission crosssection can be estimated from the fluorescence spectrum by using the Füchtbauer–Ladenburg (F–L) formula [27,28]: em (
)=
5
8 cn2
r
I( ) I ( )d
I (t ) = I0 exp
t
(4)
The decay curves of 4I11/2 level in Er/Nd: BLGO, Er/Dy: BLGO crystals and 4I13/2 level in Er/Yb: BLGO, Er/Dy: BLGO crystals exhibit multi-exponential decaying behavior, the decay curves of Yb3+: 2F5/2 level in Er/Yb: BLGO crystal and Nd3+: 4F3/2 level in the Er/Nd: BLGO crystal also show multi-exponential decaying behavior and the fluorescence lifetimes can be fitted by the following formula:
I (t ) = A + B1 exp
=
t 1
+ B2 exp
B1 12 + B2 22+ + Bn n 2 B1 1 + B2 2+ + Bn n
t 2
+
+ Bn exp
t n
(5) (6)
Where τ is the fluorescence lifetime. The fluorescence lifetimes of Er3+: 4I11/2 and 4I13/2 levels in Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals are fitted and presented in Table 1. To analyze the energy transfer in these three crystals, the energy transfer efficiency can be calculated by using the following formula [11–13]:
(3)
=1
DA A
I ( ) d is the normalized line shape function of the WhereI ( )/ experimental emission spectrum, β is the fluorescence branching ratio, λ is the emission peak wavelength, c is the speed of light, n is the
(7)
Where τDA is the lifetime of the donor in the existence of the acceptor, and τA is the lifetime of the donor in the absence of the acceptor. The fluorescence lifetimes of Yb3+: 2F5/2 level in Er/Yb: BLGO crystal is fitted to be 0.254 ms, and the lifetime of 2F5/2 of Yb3+ singly doped BLGO crystal is 0.522 ms [31]. Thus the energy efficiency of Yb3+: 2F5/2 → Er3+: 4I11/2 is calculated to be 51.3%, which means half of the pump energy absorbed by Yb3+ can transfer to Er3+, thereby increasing the utilization of Er ions for 980 nm pump energy. Similarly, the fluorescence lifetimes of Nd3+: 4F3/2 level in the Er/ Nd: BLGO crystal is fitted to be 0.211 ms, and the lifetime of 4F3/2 of Nd3+ singly doped BLGO crystal is 0.340 ms [32]. The energy efficiency of Nd3+: 4F3/2 → Er3+: 4I11/2 is calculated to be 38.1%, and the energy efficiency of Er3+: 4I13/2 + Nd3+: 4I9/2 → Er3+: 4I15/2 + Nd3+: 4I15/2 is calculated to be 52.5%. Co-dopant Nd3+ can transform a part of the pump energy to Er3+ to improve the absorption efficiency, and more than half of the ions on Er3+: 4I13/2 level can be transferred to the Nd3+: 4I9/2 level through energy transfer process and thus to suppress the self-termination problem. The lifetimes of 4I11/2 and 4I13/2 energy levels of Er3+ singly doped BLGO crystal can be obtained from Table 1. So the energy efficiencies of Er3+: 4I11/2 → Dy3+: 6H5/2 and Er3+: 4I13/2 → Dy3+: 6H11/2 are
Fig. 5. MIR emission spectra of Er: BLGO, Er/Yb: BLGO, Er/Nd: BLGO and Er/ Dy: BLGO crystals. 262
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W. Zhang et al.
Fig. 6. Decay curves of Er3+: 4I11/2 level (a), Er3+: 4I13/2 level (b), Yb3+: 2F5/2 level (c) and Nd3+: 4F3/2 level (d) of Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals.
relaxation (abbr. as CR) processes 4I13/2 + 4I13/2 → 4I9/2 + 4I15/2 (CR1) and 4I11/2 + 4I11/2 → 4F7/2 + 4I15/2 (CR2), respectively. The populations on 4F7/2 level relax to the (2H11/2, 4S3/2) and 4F9/2 energy level quickly. Then, the green emission is produced through the transition 2 H11/2 + 4S3/2 → 4I15/2 and the red emission is generated through the transition: 4F9/2 → 4I15/2. The CR1 process can decrease the ions on 4 I13/2 level and contributes to ~2.7 µm emission. But the CR2 process is adverse to obtain ~2.7 µm emission since it can reduce the populations on Er3+: 4I11/2. Fig. 7(b) shows that the Nd3+ and Er3+ ions are transformed from the ground states Nd3+: 4I9/2 and Er3+: 4I15/2 to the excited states Nd3+: 4F5/2 + 2H9/2 and Er3+: 4I9/2 when excited by 808 nm in Er/Nd: BLGO crystal. On one hand, part of the ions on Nd3+: 4F5/2 + 2H9/2 level can non-radiatively relax to Nd3+: 4F3/2 energy level and produce 1059 nm emission corresponding to 4F3/2 → 4I11/2 transition. On the other hand, the energy transfer processes Nd3+: 4F5/2 + 2H9/2 → Er3+: 4 I9/2 (ET1) and Nd3+: 4F3/2 + Er3+: 4I15/2 → Nd3+: 4I9/2 + Er3+: 4I11/2 (ET2) occur, which increase the ions on Er3+: 4I11/2 and then enhance ~2.7 µm emission, as shown in Fig. 5. The ~1.5 µm emission as seen in Fig. 4 is reduced as compared with Er:BLGO, which is due to the
calculated to be 27.5% and 47.6%, respectively. Nearly half of the populations in Er3+: 4I13/2 level can be transferred to Dy3+: 6H11/2 level, which proves that the co-dopant Dy3+ is helpful to suppress the self-termination effect, and thus the accumulated population on the 4 I13/2 level can be quickly relaxed to maintain the required population inversion to achieve ~2.7 µm laser output. 3.5. Energy transfer mechanism The energy transfer mechanism among Er3+ and Yb3+ in Er/Yb: BLGO crystal can be interpreted by the energy level diagram in Fig. 7(a). The ions on Yb3+: 2F7/2 and Er3+: 4I15/2 states are excited to Yb3+: 2F5/2 and Er3+: 4I11/2 levels by the ground state absorption when crystal is pumped by 980 nm. Then, the energy transfer (abbr. as ET) process Yb3+: 2F5/2 → Er3+: 4I11/2 occurs, which increases the populations on Er3+: 4I11/2 level and contributes to ~2.7 µm emission, as shown in Fig. 5. The ~2.7 µm emission is generated efficiently through the transition: 4I11/2 → 4I13/2 and ~1.5 µm emission is also obtained via Er3+: 4I13/2 → 4I15/2. Meanwhile, populations on Er3+: 4I13/2 and Er3+: 4 I11/2 levels can be excited to the 4I9/2 and 4F7/2 levels through cross-
Table 1 Spectroscopic parameters of Er: BLGO, Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals. Crystals
σa (10−21 cm2)
Er: 4I11/2 σe (10
Er: BLGO Er/Yb: BLGO Er/Nd: BLGO Er/Dy: BLGO
1.74@978 nm 0.75@808 nm 6.68@980 nm 19.0@808 nm 1.41@978 nm
4.20 3.54 4.26 4.08 4.12
−20
2
cm )
Er: 4I11/2
Er: 4I13/2
FWHM (nm)
τ (ms)
τ (ms)
190.17 180.46 183.90 188.26 182.44
0.703 0.263 0.982 0.174 0.510
9.760 8.959 8.476 4.256 5.119
263
Ref.
[24] This work This work This work
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W. Zhang et al.
Fig. 7. The energy transfer diagram of Er3+ and Yb3+ (a), Er3+ and Nd3+ (b), Er3+ and Dy3+ (c) in Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals.
presence of Er3+: 4I13/2 + Nd3+: 4I9/2 → Er3+: 4I15/2 + Nd3+: 4I15/2 (ET3). So, the introduction of Nd3+ not only increases the absorption efficiency of pump energy, but also depopulates the ions on Er3+: 4I13/2 level, which is helpful to the population inversion for ~2.7 µm laser operation. In Er, Dy co-dopant system, as shown in Fig. 7(c), part of the energy of the Er3+: 4I11/2 level generates ~2.7 µm emission while the other part relaxes to Dy3+: 6H5/2 level (ET1) due to small energy gap between these two energy levels. The energy transfer process Er3+: 4I13/2 → Dy3+: 6H11/2 (ET2) occurs, which decreases the populations on Er3+: 4 I13/2 and thus contributes to the 4I11/2 → 4I13/2 transition. The ions on Dy3+: 6H11/2 level can relax to the lower 6H13/2 level through multiphonon relaxation. Then the ions on Dy3+: 6H13/2 level will radiate to the 6H15/2 ground state and result in ~2.8 µm emission [33]. The energy efficiency of ET2 is higher than that of ET1, indicating that the ions on 4I13/2 level has more opportunity to transfer its energy to the same level nearby as compared with 4I11/2 level. Thus, the co-dopant Dy3+ is helpful to suppress the self-termination effect, and maintain the required population inversion to achieve ~2.7 µm laser output.
d c = [ ( N2 dt (n 1 + l /l)
dN6 = dt
N6 + T6
dN5 = dt
N5 N + 6 T5 T6
dN4 = dt
N4 N + 5 + Rp4 N0 T4 T5
dN3 = dt
N3 N + 4 + T3 T4
dN2 = dt
N2 N + 3 T2 T3
KNE1 N0 + K NE 0 N2 + Rp0 NE 0 22 (N2
2
R NE1
N0 N6) + Rp6 N0
50 (N5 N0
2 11 (N1
N0
50 (N5 N0
2 22 (N2
N0 N6)
( N2
(8)
i
(10)
dN1 = dt +
N1 N + 2 T1 T2
2
( N2
N1)
2 11 (N1
N1) + KNE1 N0
+ Rp1 N0
50 (N5 N0
22 11
(16)
. R1 = Rp1 + Rp5 + Rp6 , R2 = Rp2 + Rp3 + Rp4
= [R2 + (R1 + R2 )(1
p2 )]/ Rpi
(17)
3.6.2. Rate equations of Er/Nd: BLGO crystal The rate equations of energy level transitions in Er/Nd: BLGO crystal are similar to that of Er/Yb: BLGO crystal except for the formula (8), (12)–(14), which are presented as follows:
(13)
N0 N3) +
4
The excitation rates of Er3+ energy levels except for 4I11/2 energy level could be omitted since the 980 nm pumping source is applied to achieve 2.7 µm laser in Er doped BLGO crystal, that means Rp1 = Rp3 = Rp4 = Rp5 = Rp6 = 0. For pumping in 4I11/2, R1 = 0, R2 = Rp2 0, thus, the upper limit of the quantum efficiency can be abbreviated to η = 2-p2.
N3 N1) + Rp3 N0
K NE 0 N2 + Rp2 N0
4
+ Rp5 + Rp6. The 2.7 µm laser quantum efficiency is defined as the ratio between the number of quanta generated in the laser cavity and the number of absorbed pump quanta [35], and the upper limit of the quantum efficiency for pumping performed in the level i is [35]
(12)
2
[R2 + (R1 + R2 )(1 p2 )]
Herein, p =
(11)
N0 N3) +
(15) 4
Where N0 to N6 are the populations of Er : I15/2, I13/2, I11/2, I9/2, F9/2, 4S3/2 and 4F7/2 levels, respectively. NE1 and NE0 are the populations of Yb3+ on the levels of 2F5/2 and 2F7/2, respectively. K and K′ are the energy transfer coefficient and reverse energy transfer coefficient of Yb3+: 2F5/2 to Er: 4I11/2 respectively. Ti (i = 1,2,3···6) is the lifetime each energy levels of Er3+. T0 is the lifetime of Yb3+: 2F5/2. Rpi is the transition rate of Er3+ from ground energy level to several excited energy levels. Rp0 is the pumping rate of Yb3+ from 2F7/2 to 2F5/2 energy level.R is rate of stimulated emission transitions 2F5/2 → 2F7/2. The cross-relaxation processes are represented by ω50 (from 4S3/2). ω11 and ω22 are the energy transfer rates of up-conversion of 4I13/2 and 4I11/2, respectively. φ is the photon flux density inside the laser resonator. l is the length of active medium, l′ is the length of the laser resonator. σ is the emission cross-section. α and β are the Boltzmann distribution coefficients of stark energy levels of 4I11/2 and 4I13/2, respectively. ρ is the total losses for a round trip and CN2/T2 represents the contribution of spontaneous radiation to the photon flux density inside resonant cavity. The rate equation system can be further simplified owing to T1, T2 > > T3, T4, T5, T6, the CN2/T2 could be omitted, and in the steady d dN states dt = 0 , dt i = 0 . When the pumping ratio is large enough, the photon flux density is abbreviated as follows:
(9)
N3 N1) + Rp5 N0
N2 T2
4
3.6.1. Rate equations of Er/Yb: BLGO crystal The mathematical rate equation model is proved to be a very valuable tool to analyze and simulate 2.7–3 µm erbium lasers [14,24,34,35]. In this paper, we explain the main energy transfer processes that take place in the three crystals, and the rate equations of energy level transitions in Er/Yb: BLGO crystal are presented as follows:
NE1 T0
]+C
3+ 4
3.6. Rate equations and upper limit of quantum efficiency
dNE1 = dt
N1)
N3 N1)
dNn3 = dt
(14) 264
Nn3 T
K1 Nn3 N0 + K1 Nn0 N3 + Rp0 Nn0
(18)
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Fig. 8. Stark splitting of the 4I11/2 and 4I13/2 levels with the observed laser transitions and their tentative assignments in Er/Yb: BLGO (a), Er/Nd: BLGO (b) and Er/ Dy: BLGO (c) crystals.
dN3 = dt
N3 N + 4 + T3 T4 + K1 Nn3 N0
dN2 = dt
N2 N + 3 T2 T3 + K2 Nn2 N0
dN1 = dt
N1 N + 2 T1 T2 + ( N2
2
11 (N1
N0 N3) +
50 (N5 N0
are shown in Table 1. α and β can be calculated by the following equation [8]:
N3 N1)
K1 Nn0 N3 + Rp3 N0 2
22 (N2
2
N0 N6)
(19)
( N2
N1)
K2 Nn0 N2 + Rp2 N0 2 N1)
2 11 (N1
N0 N3) +
Ni = N
N3 N1)
K3 Nn0 N1 + K3 Nn1 N0 + Rp1 N0
(21)
3+ 4
4
Where Nn0, Nn1, Nn2 and Nn3 are the populations of Nd : I9/2, I15/2, F3/2 and 4F5/2 + 2H9/2, respectively. T is the lifetime of Nd3+: 4F5/2 + 2H9/2. Rp0 is the pumping rate of Nd3+ from 4I9/2 to 4F5/2 + 2H9/2 energy level. K1/K2/K3 and K1′/K2′/K3′ are the energy transfer coefficients and reverse energy transfer coefficients of ET1/ET2/ET3 ( as shown in Fig. 7(b)), respectively. When pumped by 808 nm, the excitation rates of Er3+ energy levels except for 4I9/2 energy level could be omitted. Rp1 = Rp2 = Rp4 = Rp5 = Rp6 = 0, then R1 = 0, R2 = Rp3 0. So according to formula (17), the upper limit of quantum efficiency is also abbreviated as η = 2-p2. 4
4. Conclusion The Er3+/Yb3+, Er3+/Nd3+ and Er3+/Dy3+ co-doped BaLaGa3O7 crystals were grown by Czochralski method successfully. The detailed spectroscopic analyses based on the measured absorption spectra and emission spectra, as well as the fluorescence decay curves of them were carried out and compared carefully. The rate-equation theory model was built to estimate and compare the upper limit of quantum efficiency. Yb3+ can act as sensitizer for Er3+ to improve absorption efficiency and contribute to the mid-infrared emission. The co-dopant Dy3+ makes nearly half of the populations on Er3+: 4I13/2 level move to Dy3+: 6H11/2 level by efficient energy transfer, which is helpful to suppress the self-termination effect and achieve the mid-infrared laser output. The introduction of Nd3+ not only increases the absorption efficiency of pump energy, but also reduces the ions on Er3+: 4I13/2 level, which is favorable to the population inversion for ~2.7 µm laser operation. These results indicate that the three title crystals can be promising candidates for mid-infrared laser, and among them Er3+/ Nd3+: BaLaGa3O7 crystal demonstrates the most excellent spectral properties.
3.6.3. Rate equations of Er/Dy: BLGO crystal The rate equations of energy level transitions in Er/Dy: BLGO crystal are similar to the other two crystals, except for the Eqs. (13) and (14), which are presented as follows:
dN2 = dt
N2 N + 3 T2 T3
2
22 (N2
2
N0 N6)
( N2
N1)
K a Ny0 N2 + K a Ny2 N0 + Rp2 N0 dN1 = dt
N1 N + 2 T1 T2 + ( N2
2 N1)
2 11 (N1
N0 N3) +
(22) 50 (N5 N0
N3 N1)
Kb Ny0 N1 + Kb Ny1 N0 + Rp1 N0 3+
6
(24)
Where Ni is the number of particles on Stark sublevels and N is the total number of particles. Ni and N as shown in Fig. 8 can be obtained according to the Table 1 in Ref. [36] and the measured low temperature absorption spectra, the values of α and β are obtained by using their ratios. Thus α and β are calculated to be 0.212 and 0.167, 0.213 and 0.166, 0.211 and 0.167 in Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals, respectively. And the values of ω11 and ω22 are 1.3 × 10−15 cm3/s and 3.7 × 10−15 cm3/s, respectively [8]. So the upper limit of quantum efficiencies of Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals are approximately equal to 0.234, 0.271 and 0.217, respectively. It can be seen that Er/Nd: BLGO crystal owns the highest laser quantum efficiency among the three kinds of co-dopant crystals, which makes it as a best candidate for obtaining mid-infrared laser.
(20) 50 (N5 N0
exp( Ei / kT ) exp( Ei / kT )
(23) 6
Ny0, Ny1 and Ny2 are the populations of Dy : H15/2, H11/2 and H5/2, respectively. Ka and Ka′ are the energy transfer coefficients of Er3+: 4I11/2 → Dy3+: 6H5/2 and Dy3+: 6H5/2 → Er3+: 4I11/2, respectively. Kb and Kb′ are the energy transfer coefficients of Er3+: 4I13/2 → Dy3+: 6H11/2 and Dy3+: 6H11/2 → Er3+: 4I13/2, respectively. The rate equations of Er/Dy: BLGO crystal under 980 nm pumped are similar to the Er/Yb: BLGO crystal, thus, the upper limit of the quantum efficiency can be abbreviated to η = 2-p2.
6
Acknowledgments This work is supported by National Natural Science Foundation of China (Grant nos. 51472240, 51872286, 51832007 and 61675204), The National Key Research and Development Program of China (Grant no. 2016YFB0701002), the Strategic Priority Research Programs of the Chinese Academy of Science (Grant no. XDB20010200), Science and Technology Plan Industry Leading Project of Fujian Province (Grant no.
3.6.4. Upper limit of quantum efficiency As for Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals, the fluorescence lifetimes of Er: 4I13/2, Er: 4I11/2 and emission cross-sections 265
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2018H0046), and State Key Laboratory of Rare Earth Resources Utilization (Grant no. RERU2018004, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences).
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266
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Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin
Spectroscopic analyses and laser properties simulation of Er/Yb, Er/Nd, Er/ Dy: BaLaGa3O7 crystals
T
Wei Zhanga,b, Yan Wanga, , Jian-fu Lia, Zhao-jie Zhua, Zhen-yu Youa, Chao-yang Tua, ⁎
⁎
a
Key Laboratory of Optoelectronic Materials Chemistry and Physics, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou City, Fujian Province 350002, PR China b College of Chemistry, Fuzhou University, Fuzhou City, Fujian Province 350116, PR China
ARTICLE INFO
ABSTRACT
Keywords: BaLaGa3O7 Crystal growth Spectroscopic properties Mid-infrared laser
The Er3+/Yb3+, Er3+/Nd3+ and Er3+/Dy3+ co-doped BaLaGa3O7 crystals were grown by the Czochralski method. The absorption spectra, up-conversion emission spectra, near-infrared and mid-infrared emission spectra, as well as the fluorescence decay curves of them were measured at room temperature. Detailed spectroscopic analyses were carried out and the spectral parameters of them were compared. Furthermore, the energy transfer processes among Er3+-Yb3+, Er3+-Nd3+ and Er3+-Dy3+ were investigated and the rate-equation theory models were built and discussed. The results demonstrate that Er/Nd: BaLaGa3O7 crystal is a best candidate for obtainment of ~2.7 µm laser among the three doping kinds, since the introduction of Nd3+ not only increases the absorption efficiency of pump energy, but also inhibits the self-termination bottleneck effect, which are both beneficial to the output of the mid-infrared ~2.7 µm laser.
1. Introduction Recently, mid-infrared lasers in the range of 2.7–3 µm have received extensive attention due to their important potential applications in remote sensing, laser medical surgery, environmental detection and military field [1–5]. In addition, 2.7–3.0 µm laser is also attractive as pump source for far-infrared waveband optical parametric oscillation or optical parametric generation laser system [6,7]. It is worth noting that 2.7–3 µm lasers can be achieved by Er3+ ions through its 4I11/2 → 4I13/2 transition. However, on the one hand, the output power and efficiency of ~2.7 µm erbium lasers are not high enough owing to the low absorption efficiency of 980 or 808 nm laser pumping energy. In order to solve the problem of weak intensity and narrow band width in the absorption bands near 980 or 808 nm, it is a good choice to co-dope with sensitive ions such as Yb3+ [8] or Nd3+ [9] to improve the absorption properties. On the other hand, there exists a detrimental selftermination “bottleneck” effect in this transition owing to the lifetime of upper laser level (4I11/2) much shorter than that of the lower one (4I13/2) [10]. Therefore, some effective measures should be taken to suppress the self-termination problem. Previous studies have shown that some deactive ions appropriately co-doping into the Er3+ activated materials can inhibit the self-termination effect by depopulating the 4 I13/2 state, such as Er/Pr co-doped GGG [11], GYSGG [12] and CaGdAlO4 crystals [13], Er/Eu co-doped YAP crystal [14], Er/Tm co-doped ⁎
KCaF3 crystal [15], Er/Tm co-doped Y3Al5O12 nanocrystals–tellurate glass composites [16], and Er/Ho co-doped fluoride glass [17]. In this work, BaLaGa3O7 (abbr. as BLGO) crystal is chosen as host material. It belongs to the ABC3O7 family with tetragonal symmetry and melilite structure in the space group P4¯ 21m. The cell parameters are a=b= 8.145 Å, c= 5.382 Å, Z = 2 and d= 5.568 g/cm3 [18]. The refractive index of the crystal is 1.85 [19]. BLGO is a congruently melting compound with a melting point of 1560 °C [20], which makes it suitable to obtain large-sized and high quality crystals by using the Czochralski (CZ) method. BLGO crystal doesn’t have a center of symmetry [21], and owns good physicochemical stability, simple synthesis condition, and disordered structure [22,23]. Therefore, it is a wise choice to choose BLGO as host crystal in this work, and to the best of our knowledge, for the first time Yb3+, Nd3+ and Dy3+ as co-dopant ions are introduced into Er3+ activated BLGO crystal to improve the absorption or/and suppress the self-termination effect. The dopant rare earth ions are substituted for La3+, and occupy the same position (4e) with Ba and La ions [18]. Thus these rare earth ions, La3+ and Ba2+ are located in one crystal lattice, leading to a different crystal lattice field, further causing inhomogeneous broadening in the absorption and emission spectra. In this paper, Er3+/Yb3+, Er3+/Nd3+ and Er3+/Dy3+ co-doped BaLaGa3O7 (abbr. as Er/Yb: BLGO, Er/Nd: BLGO, Er/Dy: BLGO) crystals were grown by the Czochralski method successfully. The spectroscopic
Corresponding authors. E-mail addresses: [email protected] (Y. Wang), [email protected] (C.-y. Tu).
https://doi.org/10.1016/j.jlumin.2018.12.061 Received 19 October 2018; Received in revised form 27 December 2018; Accepted 27 December 2018 Available online 28 December 2018 0022-2313/ © 2018 Published by Elsevier B.V.
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properties based on the measured absorption, emission spectra and fluorescence decay curves in these three crystals were investigated. The absorption/emission cross sections were calculated to further compare their spectral properties. The energy transfer mechanisms were analysed and the energy transfer efficiencies were calculated. In addition, the rate-equation models of them were built and discussed carefully to estimate the upper limit of quantum efficiency.
were measured to be 2.18 at% and 0.38 at%, respectively. The concentrations of Er3+ and Nd3+ in Er/Nd: BLGO crystal were measured to be 2.34 at% and 1.25 at%, respectively. In Er/Dy: BLGO crystal, the doping concentrations of Er3+ and Dy3+ were measured to be 2.95 at% and 0.69 at%, respectively. The effective segregation coefficient K for Er3+, Yb3+, Nd3+ and Dy3+ in all the three crystals are performed by the following equation: (1)
K = C / C0
2. Experimental
Where C and C0 are the respective concentrations of ions in the crystal and raw material. The K values of Er3+ and Yb3+ in Er/Yb: BLGO crystal are determined to be 0.145 and 0.076, respectively. In Er/ Nd: BLGO crystal, the K values of Er3+ and Nd3+ are determined to be 0.156 and 0.625, respectively. In Er, Dy: BLGO crystal, the K values of Er3+ and Dy3+ are determined to be 0.197 and 0.345, respectively.
The Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals were grown by Czochralski method. According to our previous work [8–10,24], the initial concentrations of Er3+ were 15 at% in these three crystals, and the concentrations of Yb3+, Nd3+ and Dy3+ ions were 5 at %, 2 at% and 2 at%, respectively. 15 at% Er: BLGO single crystal was also grown for spectral comparison. High purity BaCO3 (Alfa Aesar Chemical Reagent Co., Ltd., A.R. grade), La2O3 (Changchun Highpurity Chemical Reagent Co., Ltd., 5N purity), Ga2O3 (Chengdu Jinhu New Materials Co., Ltd., 5N purity), Er2O3 (Changchun Highpurity Chemical Reagent Co., Ltd., 5N purity), Yb2O3 (Changchun Highpurity Chemical Reagent Co., Ltd., 5N purity), Nd2O3 (Changchun Institute of Applied Chemistry, 6N purity) and Dy2O3 (Changchun Institute of Applied Chemistry, 4N purity) powders were used. The raw materials were weighed accurately according to the stoichiometric ratio, with an excess of Ga2O3 (1.0 wt%) added for compensating the evaporation in crystal growth. The stoichiometric amounts of chemicals were mixed, ground thoroughly and suppressed into pellets, then placed into the muffle furnace (MXX1700-30, Shanghai Weixing Furnace Co., Ltd.) sintering at 1300 °C for 48 h to assure the complete reaction. Afterwards, the sintered tablets were milled carefully, and repeated the previous procedures until the measured powder diffraction peaks by Xray diffraction match the standard PDF card. The three crystals were grown respectively in a Czochralski instrument (China Electronics Technology Group Co., Ltd.) with nitrogen atmosphere protection containing 2% oxygen. During the growth process, the pulling rate varied from 0.5 to 2 mm/h and the crystal rotation speed was kept 10–15 r.p.m. After the growth was completed, the crystal was cooled slowly to room temperature at a rate of 5–35 K/h. The grown crystals were performed on X-ray diffraction (XRD, Miniflex 600) in the 2θ range of 10–80° at room temperature. The concentrations of Er3+, Yb3+, Nd3+ and Dy3+ in the grown crystals were measured by inductively coupled plasma atomic emission spectrometry (ICP-AES) analyses. The a-cut samples with dimensions of 5.0 × 5.0 × 1.0 mm3 were cut from the as-grown Er: BLGO, Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals and polished for spectral experiments, respectively. Absorption spectra were measured by Perkin-Elmer UV–VIS–NIR Spectrometer (Lambda-950). The up-conversion (UC) fluorescence spectra were measured by using Edinburgh Instruments FLS920 spectrophotometer. The near-infrared (NIR) fluorescence spectra and the decay curves were recorded in Edinburgh Instruments FLS980 spectrophotometer. The mid-infrared (MIR) fluorescence spectra and the fluorescence decay curves for the samples were recorded by Edinburgh Instruments FSP920 spectrophotometer. All the measurements were carried out at room temperature. For each kind of spectral measurement, the four samples were maintained under same conditions.
3.2. Absorption spectroscopy The room temperature absorption spectra of Er: BLGO, Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals were recorded in the range of 320–1700 nm, as shown in Fig. 2. In the three codopant samples, the spectra include the typical characteristic absorption peaks of both Er3+ and the co-dopant ion (Yb3+/Nd3+/Dy3+): the main seven absorption characteristic peaks of Er3+ are located at 379, 488, 523, 650, 802, 978 and 1536 nm, corresponding to Er3+ transitions from the 4I15/2 ground state to 4G11/2 + 2K15/2, 4F7/2, 2H11/2, 4F9/2, 4I9/2, 4I11/2 and 4I13/2, respectively. In Er/Yb: BLGO crystal, the absorption spectrum shows a much stronger band located near 980 nm, which involves both the contributions from Yb3+ and Er3+, assigned to Er3+: 4I15/2 → 4I11/2 and Yb3+: 2F7/2 → 2F5/2 transitions. The absorption bands of Nd3+ are observed in Er/Nd: BLGO crystal: the six main peaks centered at 360, 523, 589, 752, 808 and 882 nm correspond to the transitions from Nd3+: 4I9/2 to 4D3/2, 4G9/2 + 2G7/2, 2G5/2, 4F7/2 + 4S3/2, 4F5/2 + 2H9/2 and 4F3/2, respectively. The absorption band centered at 808 nm involves both the contributions from Nd3+ and Er3+. Also, there are six main absorption peaks of Dy3+ ions in Er/Dy: BLGO crystal, with the peaks centered at 345, 365, 452, 879, 1046 and 1234 nm, which are assigned to the transitions from Dy3+: 6H15/2 to 6P7/2, 6P5/2, 4I15/2, 6F7/2, 6H7/2 + 6F9/2 and 6H9/2 + 6F11/2, respectively. The absorption cross-section σa can be determined by the following equation [25]: a
=
Nm
=
2.303OD lNm
(2) 3+
Here α is the absorption coefficient, Nm is the Er concentration in the crystal, l is the thickness of the polished sample (l= 0.10 cm) and OD is the optical density. In Er/Yb: BLGO and Er/Dy: BLGO crystal, the absorption cross-sections σa are calculated to be 6.68 × 10−21 cm2 at 980 nm and 1.41 × 10−21 cm2 at 978 nm, with full width at half maximum (FWHM) of 10.3 and 27.8 nm, respectively. The absorption cross-section σa at 808 nm in Er/Nd: BLGO crystal is calculated to be 1.90 × 10−20 cm2, with full width at half maximum of 8.9 nm. Therefore, Yb3+ and Nd3+ can act as sensitizer for Er3+ to improve the absorption efficiency, thus making the Er/Yb: BLGO crystal more suitable for 980 nm InGaAs and Er/Nd: BLGO crystal for 808 nm AlGaAs LD pumping, respectively.
3. Results and discussion
3.3. Fluorescence spectroscopy
3.1. XRD analyses and ion concentrations
Fig. 3 shows the up-conversion emission spectra of Er: BLGO, Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals within the range of 450–750 nm under pumping of 978, 980, 808 and 978 nm, respectively. The green up-conversion emission bands centered at around 548 nm correspond to the transition: Er3+: 2H11/2 + 4S3/2 → 4I15/2, and the red up-conversion emission bands with peak around 669 nm can be assigned to Er3+: 4F9/2 → 4I15/2 transition. It is obvious that the green
Fig. 1 shows the photographs and XRD patterns of the as-grown Er/ Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals. The diffraction peaks are well consistent with the standard PDF file [No. 50–1800], which indicates the formation of pure phase in all the three crystals. The doping concentrations of Er3+ and Yb3+ in Er/Yb: BLGO crystal 260
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Fig. 1. Photographs and XRD patterns of Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals.
emission is much stronger than the red emission. As compared with Er: BLGO crystal, the green up-conversion emissions are reduced significantly in Er/Yb:BLGO and Er/Nd: BLGO crystals, while increased in Er/Dy: BLGO crystal. It can also be found that: the samples all exhibit weaker intensity in the red emission band, and Er/Nd: BLGO crystal almost can’t detect the red emission. The up-conversion emission as a negative factor for MIR laser output which needs to be suppressed, so
the introduction of Nd3+ is most favorable to the ~2.7 µm emission. As seen in Fig. 4, the near-infrared emission spectra of Er: BLGO, Er/ Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals within 1450–1650 nm are obtained when pumped by 978, 980, 808 and 978 nm, respectively. There are two strong emissions with peaks around at 1535 nm and 1548 nm, which are assigned to the transition of Er3+: 4 I13/2 → 4I15/2. Er: BLGO crystal shows the strongest intensity among the four samples. As compared with Er: BLGO crystal, the near-infrared
Fig. 2. Absorption spectra of Er: BLGO, Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals at room temperature.
Fig. 3. UC emission spectra of Er: BLGO, Er/Yb: BLGO, Er/Nd: BLGO and Er/ Dy: BLGO crystals. 261
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refractive index and τr is the radiative lifetime. β and τr are calculated to be 0.14 and 2.55 ms by Judd-Ofelt theory [24,29,30]. The maximum emission cross sections of Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals are estimated to be 4.26 × 10−20 cm2 at 2735 nm, 4.08 × 10−20 cm2 at 2700 nm and 4.12 × 10−20 cm2 at 2730 nm, respectively. 3.4. Fluorescence decay curve and fluorescence lifetime The decay curves of Er3+: 4I11/2 level in Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals are shown in Fig. 6(a), which are measured at 2735, 2700 and 2730 nm excited by 980, 808 and 978 nm, respectively. Fig. 6(b) displays the decay curves of Er3+: 4I13/2 level in Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals under pumping of 980, 808 and 978 nm, respectively, the detection wavelength is 1535 nm. Fig. 6(c) shows the decay curve of Yb3+: 2F5/2 level in Er/Yb: BLGO crystal, which is measured at 1003 nm excited by 980 nm. The decay curve of Nd3+: 4F3/2 level in the Er/Nd: BLGO crystal measured at 1059 nm excited by 808 nm is shown in Fig. 6(d). After being fitted, the decay curves of Er3+ : 4I11/2 level in Er/Yb: BLGO crystal and Er3+: 4I13/2 level in Er/Nd: BLGO crystal show singly exponential decaying behavior and the fluorescence lifetime can be fitted with
Fig. 4. NIR emission spectra of Er: BLGO, Er/Yb: BLGO, Er/Nd: BLGO and Er/ Dy: BLGO crystals.
emission spectra of Er/Yb: BLGO and Er/Nd: BLGO crystals exhibit weaker intensity while that of Er/Dy: BLGO crystal shows the weakest intensity. Near-infrared emission is a hindering factor for ~2.7 µm laser output. Owing to the existence of Dy3+, near-infrared emission can be inhibited and thus beneficial to the ~2.7 µm emission. The mid-infrared fluorescence spectra of Er: BLGO, Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals in the wavelength range from 2500 to 3000 nm are shown in Fig. 5. The Er: BLGO, Er/Yb: BLGO and Er/Dy: BLGO crystals are excited by 978, 980 and 978 nm, respectively, and Er/Nd: BLGO crystal is excited by 808 nm. The MIR emission band centered at 2735 nm is attributed to Er3+: 4I11/2 → 4I13/2 transition in Er/Yb: BLGO crystal, while the strong emission bands with peaks at 2700 and 2730 nm can be observed in Er/Nd: BLGO and Er/Dy: BLGO crystals, respectively. Er/Yb: BLGO crystal shows the strongest intensity and its intensity is over 4 times than that in Er/Nd: BLGO crystal. This is the objective emission which would lead to the achievement of ~2.7 µm laser. The emission cross-section is an important parameter influencing the potential laser performance [26]. The stimulated emission crosssection can be estimated from the fluorescence spectrum by using the Füchtbauer–Ladenburg (F–L) formula [27,28]: em (
)=
5
8 cn2
r
I( ) I ( )d
I (t ) = I0 exp
t
(4)
The decay curves of 4I11/2 level in Er/Nd: BLGO, Er/Dy: BLGO crystals and 4I13/2 level in Er/Yb: BLGO, Er/Dy: BLGO crystals exhibit multi-exponential decaying behavior, the decay curves of Yb3+: 2F5/2 level in Er/Yb: BLGO crystal and Nd3+: 4F3/2 level in the Er/Nd: BLGO crystal also show multi-exponential decaying behavior and the fluorescence lifetimes can be fitted by the following formula:
I (t ) = A + B1 exp
=
t 1
+ B2 exp
B1 12 + B2 22+ + Bn n 2 B1 1 + B2 2+ + Bn n
t 2
+
+ Bn exp
t n
(5) (6)
Where τ is the fluorescence lifetime. The fluorescence lifetimes of Er3+: 4I11/2 and 4I13/2 levels in Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals are fitted and presented in Table 1. To analyze the energy transfer in these three crystals, the energy transfer efficiency can be calculated by using the following formula [11–13]:
(3)
=1
DA A
I ( ) d is the normalized line shape function of the WhereI ( )/ experimental emission spectrum, β is the fluorescence branching ratio, λ is the emission peak wavelength, c is the speed of light, n is the
(7)
Where τDA is the lifetime of the donor in the existence of the acceptor, and τA is the lifetime of the donor in the absence of the acceptor. The fluorescence lifetimes of Yb3+: 2F5/2 level in Er/Yb: BLGO crystal is fitted to be 0.254 ms, and the lifetime of 2F5/2 of Yb3+ singly doped BLGO crystal is 0.522 ms [31]. Thus the energy efficiency of Yb3+: 2F5/2 → Er3+: 4I11/2 is calculated to be 51.3%, which means half of the pump energy absorbed by Yb3+ can transfer to Er3+, thereby increasing the utilization of Er ions for 980 nm pump energy. Similarly, the fluorescence lifetimes of Nd3+: 4F3/2 level in the Er/ Nd: BLGO crystal is fitted to be 0.211 ms, and the lifetime of 4F3/2 of Nd3+ singly doped BLGO crystal is 0.340 ms [32]. The energy efficiency of Nd3+: 4F3/2 → Er3+: 4I11/2 is calculated to be 38.1%, and the energy efficiency of Er3+: 4I13/2 + Nd3+: 4I9/2 → Er3+: 4I15/2 + Nd3+: 4I15/2 is calculated to be 52.5%. Co-dopant Nd3+ can transform a part of the pump energy to Er3+ to improve the absorption efficiency, and more than half of the ions on Er3+: 4I13/2 level can be transferred to the Nd3+: 4I9/2 level through energy transfer process and thus to suppress the self-termination problem. The lifetimes of 4I11/2 and 4I13/2 energy levels of Er3+ singly doped BLGO crystal can be obtained from Table 1. So the energy efficiencies of Er3+: 4I11/2 → Dy3+: 6H5/2 and Er3+: 4I13/2 → Dy3+: 6H11/2 are
Fig. 5. MIR emission spectra of Er: BLGO, Er/Yb: BLGO, Er/Nd: BLGO and Er/ Dy: BLGO crystals. 262
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Fig. 6. Decay curves of Er3+: 4I11/2 level (a), Er3+: 4I13/2 level (b), Yb3+: 2F5/2 level (c) and Nd3+: 4F3/2 level (d) of Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals.
relaxation (abbr. as CR) processes 4I13/2 + 4I13/2 → 4I9/2 + 4I15/2 (CR1) and 4I11/2 + 4I11/2 → 4F7/2 + 4I15/2 (CR2), respectively. The populations on 4F7/2 level relax to the (2H11/2, 4S3/2) and 4F9/2 energy level quickly. Then, the green emission is produced through the transition 2 H11/2 + 4S3/2 → 4I15/2 and the red emission is generated through the transition: 4F9/2 → 4I15/2. The CR1 process can decrease the ions on 4 I13/2 level and contributes to ~2.7 µm emission. But the CR2 process is adverse to obtain ~2.7 µm emission since it can reduce the populations on Er3+: 4I11/2. Fig. 7(b) shows that the Nd3+ and Er3+ ions are transformed from the ground states Nd3+: 4I9/2 and Er3+: 4I15/2 to the excited states Nd3+: 4F5/2 + 2H9/2 and Er3+: 4I9/2 when excited by 808 nm in Er/Nd: BLGO crystal. On one hand, part of the ions on Nd3+: 4F5/2 + 2H9/2 level can non-radiatively relax to Nd3+: 4F3/2 energy level and produce 1059 nm emission corresponding to 4F3/2 → 4I11/2 transition. On the other hand, the energy transfer processes Nd3+: 4F5/2 + 2H9/2 → Er3+: 4 I9/2 (ET1) and Nd3+: 4F3/2 + Er3+: 4I15/2 → Nd3+: 4I9/2 + Er3+: 4I11/2 (ET2) occur, which increase the ions on Er3+: 4I11/2 and then enhance ~2.7 µm emission, as shown in Fig. 5. The ~1.5 µm emission as seen in Fig. 4 is reduced as compared with Er:BLGO, which is due to the
calculated to be 27.5% and 47.6%, respectively. Nearly half of the populations in Er3+: 4I13/2 level can be transferred to Dy3+: 6H11/2 level, which proves that the co-dopant Dy3+ is helpful to suppress the self-termination effect, and thus the accumulated population on the 4 I13/2 level can be quickly relaxed to maintain the required population inversion to achieve ~2.7 µm laser output. 3.5. Energy transfer mechanism The energy transfer mechanism among Er3+ and Yb3+ in Er/Yb: BLGO crystal can be interpreted by the energy level diagram in Fig. 7(a). The ions on Yb3+: 2F7/2 and Er3+: 4I15/2 states are excited to Yb3+: 2F5/2 and Er3+: 4I11/2 levels by the ground state absorption when crystal is pumped by 980 nm. Then, the energy transfer (abbr. as ET) process Yb3+: 2F5/2 → Er3+: 4I11/2 occurs, which increases the populations on Er3+: 4I11/2 level and contributes to ~2.7 µm emission, as shown in Fig. 5. The ~2.7 µm emission is generated efficiently through the transition: 4I11/2 → 4I13/2 and ~1.5 µm emission is also obtained via Er3+: 4I13/2 → 4I15/2. Meanwhile, populations on Er3+: 4I13/2 and Er3+: 4 I11/2 levels can be excited to the 4I9/2 and 4F7/2 levels through cross-
Table 1 Spectroscopic parameters of Er: BLGO, Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals. Crystals
σa (10−21 cm2)
Er: 4I11/2 σe (10
Er: BLGO Er/Yb: BLGO Er/Nd: BLGO Er/Dy: BLGO
1.74@978 nm 0.75@808 nm 6.68@980 nm 19.0@808 nm 1.41@978 nm
4.20 3.54 4.26 4.08 4.12
−20
2
cm )
Er: 4I11/2
Er: 4I13/2
FWHM (nm)
τ (ms)
τ (ms)
190.17 180.46 183.90 188.26 182.44
0.703 0.263 0.982 0.174 0.510
9.760 8.959 8.476 4.256 5.119
263
Ref.
[24] This work This work This work
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Fig. 7. The energy transfer diagram of Er3+ and Yb3+ (a), Er3+ and Nd3+ (b), Er3+ and Dy3+ (c) in Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals.
presence of Er3+: 4I13/2 + Nd3+: 4I9/2 → Er3+: 4I15/2 + Nd3+: 4I15/2 (ET3). So, the introduction of Nd3+ not only increases the absorption efficiency of pump energy, but also depopulates the ions on Er3+: 4I13/2 level, which is helpful to the population inversion for ~2.7 µm laser operation. In Er, Dy co-dopant system, as shown in Fig. 7(c), part of the energy of the Er3+: 4I11/2 level generates ~2.7 µm emission while the other part relaxes to Dy3+: 6H5/2 level (ET1) due to small energy gap between these two energy levels. The energy transfer process Er3+: 4I13/2 → Dy3+: 6H11/2 (ET2) occurs, which decreases the populations on Er3+: 4 I13/2 and thus contributes to the 4I11/2 → 4I13/2 transition. The ions on Dy3+: 6H11/2 level can relax to the lower 6H13/2 level through multiphonon relaxation. Then the ions on Dy3+: 6H13/2 level will radiate to the 6H15/2 ground state and result in ~2.8 µm emission [33]. The energy efficiency of ET2 is higher than that of ET1, indicating that the ions on 4I13/2 level has more opportunity to transfer its energy to the same level nearby as compared with 4I11/2 level. Thus, the co-dopant Dy3+ is helpful to suppress the self-termination effect, and maintain the required population inversion to achieve ~2.7 µm laser output.
d c = [ ( N2 dt (n 1 + l /l)
dN6 = dt
N6 + T6
dN5 = dt
N5 N + 6 T5 T6
dN4 = dt
N4 N + 5 + Rp4 N0 T4 T5
dN3 = dt
N3 N + 4 + T3 T4
dN2 = dt
N2 N + 3 T2 T3
KNE1 N0 + K NE 0 N2 + Rp0 NE 0 22 (N2
2
R NE1
N0 N6) + Rp6 N0
50 (N5 N0
2 11 (N1
N0
50 (N5 N0
2 22 (N2
N0 N6)
( N2
(8)
i
(10)
dN1 = dt +
N1 N + 2 T1 T2
2
( N2
N1)
2 11 (N1
N1) + KNE1 N0
+ Rp1 N0
50 (N5 N0
22 11
(16)
. R1 = Rp1 + Rp5 + Rp6 , R2 = Rp2 + Rp3 + Rp4
= [R2 + (R1 + R2 )(1
p2 )]/ Rpi
(17)
3.6.2. Rate equations of Er/Nd: BLGO crystal The rate equations of energy level transitions in Er/Nd: BLGO crystal are similar to that of Er/Yb: BLGO crystal except for the formula (8), (12)–(14), which are presented as follows:
(13)
N0 N3) +
4
The excitation rates of Er3+ energy levels except for 4I11/2 energy level could be omitted since the 980 nm pumping source is applied to achieve 2.7 µm laser in Er doped BLGO crystal, that means Rp1 = Rp3 = Rp4 = Rp5 = Rp6 = 0. For pumping in 4I11/2, R1 = 0, R2 = Rp2 0, thus, the upper limit of the quantum efficiency can be abbreviated to η = 2-p2.
N3 N1) + Rp3 N0
K NE 0 N2 + Rp2 N0
4
+ Rp5 + Rp6. The 2.7 µm laser quantum efficiency is defined as the ratio between the number of quanta generated in the laser cavity and the number of absorbed pump quanta [35], and the upper limit of the quantum efficiency for pumping performed in the level i is [35]
(12)
2
[R2 + (R1 + R2 )(1 p2 )]
Herein, p =
(11)
N0 N3) +
(15) 4
Where N0 to N6 are the populations of Er : I15/2, I13/2, I11/2, I9/2, F9/2, 4S3/2 and 4F7/2 levels, respectively. NE1 and NE0 are the populations of Yb3+ on the levels of 2F5/2 and 2F7/2, respectively. K and K′ are the energy transfer coefficient and reverse energy transfer coefficient of Yb3+: 2F5/2 to Er: 4I11/2 respectively. Ti (i = 1,2,3···6) is the lifetime each energy levels of Er3+. T0 is the lifetime of Yb3+: 2F5/2. Rpi is the transition rate of Er3+ from ground energy level to several excited energy levels. Rp0 is the pumping rate of Yb3+ from 2F7/2 to 2F5/2 energy level.R is rate of stimulated emission transitions 2F5/2 → 2F7/2. The cross-relaxation processes are represented by ω50 (from 4S3/2). ω11 and ω22 are the energy transfer rates of up-conversion of 4I13/2 and 4I11/2, respectively. φ is the photon flux density inside the laser resonator. l is the length of active medium, l′ is the length of the laser resonator. σ is the emission cross-section. α and β are the Boltzmann distribution coefficients of stark energy levels of 4I11/2 and 4I13/2, respectively. ρ is the total losses for a round trip and CN2/T2 represents the contribution of spontaneous radiation to the photon flux density inside resonant cavity. The rate equation system can be further simplified owing to T1, T2 > > T3, T4, T5, T6, the CN2/T2 could be omitted, and in the steady d dN states dt = 0 , dt i = 0 . When the pumping ratio is large enough, the photon flux density is abbreviated as follows:
(9)
N3 N1) + Rp5 N0
N2 T2
4
3.6.1. Rate equations of Er/Yb: BLGO crystal The mathematical rate equation model is proved to be a very valuable tool to analyze and simulate 2.7–3 µm erbium lasers [14,24,34,35]. In this paper, we explain the main energy transfer processes that take place in the three crystals, and the rate equations of energy level transitions in Er/Yb: BLGO crystal are presented as follows:
NE1 T0
]+C
3+ 4
3.6. Rate equations and upper limit of quantum efficiency
dNE1 = dt
N1)
N3 N1)
dNn3 = dt
(14) 264
Nn3 T
K1 Nn3 N0 + K1 Nn0 N3 + Rp0 Nn0
(18)
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Fig. 8. Stark splitting of the 4I11/2 and 4I13/2 levels with the observed laser transitions and their tentative assignments in Er/Yb: BLGO (a), Er/Nd: BLGO (b) and Er/ Dy: BLGO (c) crystals.
dN3 = dt
N3 N + 4 + T3 T4 + K1 Nn3 N0
dN2 = dt
N2 N + 3 T2 T3 + K2 Nn2 N0
dN1 = dt
N1 N + 2 T1 T2 + ( N2
2
11 (N1
N0 N3) +
50 (N5 N0
are shown in Table 1. α and β can be calculated by the following equation [8]:
N3 N1)
K1 Nn0 N3 + Rp3 N0 2
22 (N2
2
N0 N6)
(19)
( N2
N1)
K2 Nn0 N2 + Rp2 N0 2 N1)
2 11 (N1
N0 N3) +
Ni = N
N3 N1)
K3 Nn0 N1 + K3 Nn1 N0 + Rp1 N0
(21)
3+ 4
4
Where Nn0, Nn1, Nn2 and Nn3 are the populations of Nd : I9/2, I15/2, F3/2 and 4F5/2 + 2H9/2, respectively. T is the lifetime of Nd3+: 4F5/2 + 2H9/2. Rp0 is the pumping rate of Nd3+ from 4I9/2 to 4F5/2 + 2H9/2 energy level. K1/K2/K3 and K1′/K2′/K3′ are the energy transfer coefficients and reverse energy transfer coefficients of ET1/ET2/ET3 ( as shown in Fig. 7(b)), respectively. When pumped by 808 nm, the excitation rates of Er3+ energy levels except for 4I9/2 energy level could be omitted. Rp1 = Rp2 = Rp4 = Rp5 = Rp6 = 0, then R1 = 0, R2 = Rp3 0. So according to formula (17), the upper limit of quantum efficiency is also abbreviated as η = 2-p2. 4
4. Conclusion The Er3+/Yb3+, Er3+/Nd3+ and Er3+/Dy3+ co-doped BaLaGa3O7 crystals were grown by Czochralski method successfully. The detailed spectroscopic analyses based on the measured absorption spectra and emission spectra, as well as the fluorescence decay curves of them were carried out and compared carefully. The rate-equation theory model was built to estimate and compare the upper limit of quantum efficiency. Yb3+ can act as sensitizer for Er3+ to improve absorption efficiency and contribute to the mid-infrared emission. The co-dopant Dy3+ makes nearly half of the populations on Er3+: 4I13/2 level move to Dy3+: 6H11/2 level by efficient energy transfer, which is helpful to suppress the self-termination effect and achieve the mid-infrared laser output. The introduction of Nd3+ not only increases the absorption efficiency of pump energy, but also reduces the ions on Er3+: 4I13/2 level, which is favorable to the population inversion for ~2.7 µm laser operation. These results indicate that the three title crystals can be promising candidates for mid-infrared laser, and among them Er3+/ Nd3+: BaLaGa3O7 crystal demonstrates the most excellent spectral properties.
3.6.3. Rate equations of Er/Dy: BLGO crystal The rate equations of energy level transitions in Er/Dy: BLGO crystal are similar to the other two crystals, except for the Eqs. (13) and (14), which are presented as follows:
dN2 = dt
N2 N + 3 T2 T3
2
22 (N2
2
N0 N6)
( N2
N1)
K a Ny0 N2 + K a Ny2 N0 + Rp2 N0 dN1 = dt
N1 N + 2 T1 T2 + ( N2
2 N1)
2 11 (N1
N0 N3) +
(22) 50 (N5 N0
N3 N1)
Kb Ny0 N1 + Kb Ny1 N0 + Rp1 N0 3+
6
(24)
Where Ni is the number of particles on Stark sublevels and N is the total number of particles. Ni and N as shown in Fig. 8 can be obtained according to the Table 1 in Ref. [36] and the measured low temperature absorption spectra, the values of α and β are obtained by using their ratios. Thus α and β are calculated to be 0.212 and 0.167, 0.213 and 0.166, 0.211 and 0.167 in Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals, respectively. And the values of ω11 and ω22 are 1.3 × 10−15 cm3/s and 3.7 × 10−15 cm3/s, respectively [8]. So the upper limit of quantum efficiencies of Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals are approximately equal to 0.234, 0.271 and 0.217, respectively. It can be seen that Er/Nd: BLGO crystal owns the highest laser quantum efficiency among the three kinds of co-dopant crystals, which makes it as a best candidate for obtaining mid-infrared laser.
(20) 50 (N5 N0
exp( Ei / kT ) exp( Ei / kT )
(23) 6
Ny0, Ny1 and Ny2 are the populations of Dy : H15/2, H11/2 and H5/2, respectively. Ka and Ka′ are the energy transfer coefficients of Er3+: 4I11/2 → Dy3+: 6H5/2 and Dy3+: 6H5/2 → Er3+: 4I11/2, respectively. Kb and Kb′ are the energy transfer coefficients of Er3+: 4I13/2 → Dy3+: 6H11/2 and Dy3+: 6H11/2 → Er3+: 4I13/2, respectively. The rate equations of Er/Dy: BLGO crystal under 980 nm pumped are similar to the Er/Yb: BLGO crystal, thus, the upper limit of the quantum efficiency can be abbreviated to η = 2-p2.
6
Acknowledgments This work is supported by National Natural Science Foundation of China (Grant nos. 51472240, 51872286, 51832007 and 61675204), The National Key Research and Development Program of China (Grant no. 2016YFB0701002), the Strategic Priority Research Programs of the Chinese Academy of Science (Grant no. XDB20010200), Science and Technology Plan Industry Leading Project of Fujian Province (Grant no.
3.6.4. Upper limit of quantum efficiency As for Er/Yb: BLGO, Er/Nd: BLGO and Er/Dy: BLGO crystals, the fluorescence lifetimes of Er: 4I13/2, Er: 4I11/2 and emission cross-sections 265
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