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Dual function of Nd3+ in Nd,Er:LuYSGG crystal for LD pumped ~3.0 μm mid-infrared laser

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Abstract

Enhanced ~3.0 μm emission corresponding to Er3+:4I11/24I13/2 was achieved in Nd3+/Er3+ co-doped Lu0.15Y2.85Sc2Ga3O12 (abbr. as Nd,Er:LuYSGG) crystal under 808nm pumping. As compared with Er:YSGG crystal, the absorption pump efficiency of Nd,Er:LuYSGG crystal is greatly improved and thus ~3.0 μm emission is enhanced by 2.2 times owing to the sensitization of Nd3+, at the same time, Nd3+ as deactivator quenches ~1.5 μm emission from Er3+:4I13/2 level and thus inhibit the self-termination effect successfully. The energy transfer efficiencies of Nd: 4F3/2→Er: 4I11/2 and Er: 4I13/2→Nd:4I15/2 are estimated to be 91.6% and nearly 100%, respectively. These results indicate that the introduction of Nd3+ is very helpful for achieving ~3.0 μm laser in Nd,Er:LuYSGG crystal.

© 2015 Optical Society of America

1. Introduction

In recent years, solid state lasers operating around ~3.0 μm based on the 4I11/24I13/2 transition of Er3+ have attracted much attention, due to their wide utilization in many fields, such as laser surgery, dentistry, remote sensing etc [1–3]. Moreover, ~3.0 μm laser is also attractive as a pump source for a far-infrared waveband optical parametric oscillation (OPO) or optical parametric generation (OPG) laser system, which have broad applications in spectroscopy, radar, atmospheric detection and defense etc [4, 5].

Even so, there are still mainly two challenging obstacles to prevent the improvement and development of Er3+-activated ~3.0 µm lasers: one is the low absorption efficiency of laser diode (LD) pumping energy for Er3+ doped laser crystals, which are usually pumped by commercial 980 or 800 nm LDs, owing to the weak intensity and narrow bandwidth of the intrinsic absorption bands of Er3+ with peaks around 980 or 800 nm corresponding to 4I11/24I15/2 or 4I9/24I15/2, respectively. In order to solve this problem, Yb3+ or Nd3+ ions with strong and broad absorption bands around 980 nm or 808 nm have usually been introduced as the sensitizer to improve the absorption [6–8]. The other main obstacle preventing the development of Er3+-doped laser is the self-terminating “bottleneck” effect, which results from the much shorter lifetime of the laser upper level 4I11/2 than the lower level 4I13/2, and thus might cause the ~3.0 μm laser to terminate owing to the populations in upper level unable to transform to the lower level quickly. To overcome this negative effect, one solution is to reduce the lifetime of the lower level 4I13/2 of Er3+ by co-doping with depopulation ions such as Nd3+ [8], Pr3+ [9], Ho3+ [10–12], Eu3+ [11,12] or Tm3+ [12] etc. These ions can decrease the lower-level populations effectively, and thus lower ~3.0 µm laser threshold and increase laser output power. Therefore, interests in studying the spectroscopy of the depopulation ions co-doped, Er3+-activated laser crystals and ~3.0 µm solid-state lasers have increased recently [2,3,6–12]. Among all the rare earth ions, Nd3+ is the only one able to act as sensitization and depopulation ions simultaneously, therefore, we chose Nd3+ as the co-dopant ions in Er3+ activated bulk laser crystal in this work.

To date, most of the researches of erbium ~3.0 µm lasers have focused on garnet crystal hosts due to their outstanding physicochemical, optical and laser properties [2,3,6,10,12–20], such as Y3Al5O12 (YAG), Gd3Ga5O12 (GGG), Y3Sc2Ga3O12 (YSGG), GSGG (Gd3Sc2Ga3O12) etc., among which Er:YSGG/YSGG composite crystal has achieved the highest laser output power and efficiency [15]. YSGG crystal belongs to cubic system and Ia3d space group, with the same garnet structure as famous and commercial YAG crystal. The mean ion radius of Sc, Ga is 0.696 Å and the lattice parameter is 12.4584 Å [21]. Its density is 5.643 g/cm3 and the melting point is 1877°C [21]. As it melts congruently, large size single crystals can be obtained by the Czochralski (CZ) method. Compared with YAG crystal, YSGG crystals has lower phonon energy which could result in the decrement of the nonradiative transition ratio between the two energy levels (4I11/2 and 4I13/2) of Er3+ ions, and thus decrease the laser threshold and improve the laser output power and efficiency [17,21]. Recently, a new hybrid crystal with formula Er:GYSGG (Gd1.17Y1.83Sc2Ga3O12) was invented which has superior optical and laser properties than Er:YSGG [2,10,14]. Owing to the big gap of the radius between Gd3+ (93.8 pm) and Y3+ (88 pm), it might be difficult for GYSGG crystal to accept high concentration Er3+ (88.1 pm), while the radius of Lu3+ (84.8 pm) is smaller than that of Gd3+ and more close to Y3+, we think there will possibly be an effect of compensation when Lu3+ was co-doped into the YSGG crystal [22], therefore, we design a new hybrid crystal written as Lu0.15Y2.85Sc2Ga3O12 (abbr. as LuYSGG below) by substituting a fraction of Y3+ ions with Lu3+ ions in the YSGG crystal, and in Nd,Er:LuYSGG crystal three ions Nd3+, Er3+ and Lu3+ ions have the chance to enter the dodecahedral site of Y3+, which makes the crystal structure more complex and more disordered. As a result, the emission bands of Er3+ in the Nd,Er:LuYSGG crystal might be broadened dramatically as compared with that in Er:YSGG crystal, and the newly mixed Nd,Er:LuYSGG crystal might be suitable for Q-switching and mode-locking operation because of its broader fluorescence line width. Due to Nd3+/Er3+ multi-center distribution and the more complex structure of host material, we believe that Nd,Er:LuYSGG crystal could possess wider inhomogeneously broadened spectra, which would be suitable for mode-locking operation. However, the growth of mixed single crystal Nd,Er:LuYSGG has not yet been reported up till now.

The choice of dopant concentrations of Er3+ and Nd3+ in LuYSGG crystal is based on theoretical analyses and our previous serial work [3,6,8,12]: in theory, the high concentration of Er3+ doped systems (at least≥10at%) can help to improve the absorption intensity and line width of Er3+ and thus increase the pumping energy, also, it can help to suppress the self-saturation problem since high concentration Er ions are proposed to induce upconversion from 4I11/2 and 4I13/2, as well as cross-relaxation from 4S3∕2, and thus aids the establishment of a continuous-wave gain at ~3.0 µm in Er3+ activated crystals [10]; as for Nd3+, its doping concentration shouldn’t be too high (at least ≤5at%), in order to prevent a sharp decrease of the fluorescence lifetimes of laser upper and lower levels of Er3+ and restrain strong infrared waveband emissions. From another perspective, the doping of too high concentration of rare earth ions might make it difficult to obtain high-optical-quality crystal and usually decrease its thermal conductivity. In our previous work [8], the concentrations of Nd3+ and Er3+ in SrGdGa3O7 crystal were chosen to be 5 at% and 30 at% respectively, but we found that the grown crystal had some scatter particles, and the fluoresence lifetime of Er3+:4I11/2 level was extremely short (0.164 ms), hence afftected the output of the target 2.5~3µm laser, therefore, the choice of dopant ions’ concentrations should be reasonable based on the consideration of every possible problems. In this job, we have synthetized a serial of different concentration Nd3+ and Er3+ codoped Nd,Er:LuYSGG polycrystalline powders and measured their absorption, fluorescence spectra and fluorescence decay curves carefully, after a careful comparison of their optical properties, finally the concentration of Nd3+ is adjusted to be 5 at% and Er3+ to be 20 at% in the title crystal host.

In this work, we have grown the Nd3+ and Er3+ codoped LuYSGG crystal successfully for the first time by using Czochralski (CZ) method. Its absorption spectra, near-infrared and mid-infrared fluorescence spectra as well as the fluorescence decay curves were measured at room temperature. The ~3.0 μm emission properties and the energy transfer mechanism of Nd,Er:LuYSGG crystal were discussed. Nd3+ was demonstrated to greatly facilitate the Er3+:4I11/24I13/2 ~3.0 μm emission by efficient mutual energy transfers between Nd3+ and Er3+ ions. The spectroscopy investigation of ~3.0 μm emission has been made for potential high power laser output in practical operation.

2. Experimental details

The 5 at% Nd3+ and 20 at% Er3+-codoped LuYSGG single crystal was grown by the CZ technique, 20 at% Er3+ singly doped YSGG crystal was also grown for spectral comparison. 99.99% purity Y2O3, Ga2O3, Sc2O3 and 99.999% purity Lu2O3, Er2O3 and Nd2O3 commercial powders (Haipuri Rare Earth Materials Company, China) were dried and then weighed out according to the compositional formula, with an extra 1wt% Ga2O3 to compensate Ga loss owing to its evaporation. The mixtures were ground, mixed and pressed into tablets, then heated up in a Muffle furnace till 1200 °C at the rate of 100°C/h, and maintaining at this temperature for 48h to react completely. Then the tablets were taken out and the calcined powders were milled and pressed into tablets again, sintered at 1450°C for 18 h. The above procedures were repeated twice to confirm the finally synthesized polycrystalline compounds by using X-ray diffraction (Dmax2500, Rigaku) method. The crystals were grown with <111> direction YSGG seeds and carried out in DJL-400 furnace (NCIREO, China) with rotation speed of 12.0~20.0 rpm, pulling rate of 1.0~3.0 mm/h and annealing rate of 8.0~30.0 °C/h, finally two good optical quality crystals were obtained for the next spectral measurements.

The concentrations of Nd3+, Er3+, Lu3+, Y3+, Sc3+ and Ga3+ in the grown crystals were measured by inductively coupled plasma atomic emission spectrometry (ICP-AES) analysis.

Two samples in random direction were cut from the as-grown Nd,Er:LuYSGG and Er:YSGG crystals with dimensions of 5.0 × 5.0 × 1.0 mm3, respectively. The two 5.0 × 5.0 mm2 faces were polished for spectral experiments. Absorption spectra of Nd,Er:LuYSGG and Er:YSGG crystals were measured by Perkin-Elmer UV-Vis-NIR Spectrometer (Lambda-900). The near-infrared (NIR) wavelength fluorescence spectra and decay curves were recorded in Edinburgh Instruments FLS920 spectrophotometer, by using 808 LD pump source. The mid-infrared (MIR) fluorescence spectra and decay curves were recorded by Edinburgh Instruments FSP920 spectrophotometer, under 808 nm pumping with a 5 ns pulse of an optical parametric oscillator. All the measurements were carried out at room temperature (RT), and the two samples were measured under the exactly same experimental conditions.

3. Results and discussion

The doping concentrations of Nd3+ and Er3+ in doubly-doped LuYSGG crystal were measured to be 3.51 × 1020 and 2.24 × 1021 ions⋅cm−3, respectively. The doping concentration of Er3+ in singly-doped YSGG crystal was measured to be 2.21 × 1021 ions⋅cm−3. According to the effective segregation coefficient equation keff = c1/c2, where c1 and c2 are the respective concentrations of the ions in the crystal and raw materials, keff values of Nd3+ and Er3+ in Nd,Er:LuYSGG crystal were determined to be 0.58 and 0.98, respectively, and keff value of Er3+ in Er:YSGG crystal were determined to be 0.93. Figure 1 shows the XRD pattern of the Nd,Er:LuYSGG crystal powder, and it is well consistent with the standard JCPDF file [No.25-1246] for YSGG crystal, which means that there is no phase transformation even after Lu3+, Nd3+ and high concentration Er3+ are doped into YSGG crystal.

 figure: Fig. 1

Fig. 1 The XRD pattern of Nd,Er:LuYSGG single crystal.

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Absorption spectra of Nd,Er:LuYSGG and Er:YSGG crystals are shown in Fig. 2. As seen in Er:YSGG crystal, ten characteristic absorption bands of Er3+ centered at the wavelengths of 377, 407, 451, 488, 524, 542, 654, 790, 967, 1469 (1533) nm have been revealed, which are assigned to the transitions from the ground state (4I15/2) to 4G11/2, 2H9/2, 4F5/2 + 4F3/2, 4F7/2, 2H11/2, 4S3/2, 4F9/2, 4I9/2, 4I11/2 and 4I13/2, respectively. While in Nd,Er:LuYSGG crystal, besides the characteristic absorption bands of Er3+, we also observe the absorption bands of Nd3+: the main peaks centered at 364, 570, 589, 748, 808, 878 nm are assigned to the transitions from Nd3+: 4I9/2 to 4D3/2, 4G7/2 + 4G9/2, 4G5/2 + 2G7/2, 4F7/2 + 4S3/2, 4F5/2 + 2H9/2 and 4F3/2, respectively.

 figure: Fig. 2

Fig. 2 Absorption spectra of Nd,Er:LuYSGG and Er:YSGG crystals at RT.

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The absorption cross-section σa can be determined by the following equation [3]:

σa=αNc=ANcL×lge.
Here α is the absorption coefficient, A is the absorbance, L is the thickness of the polished sample, and Nc is the dopant ions concentration in the crystal. Thereby, the absorption cross-section of Nd,Er:LuYSGG with peak at 808 nm is calculated to be 5.25 × 10−20 cm2, meanwhile, the absorption cross-section of Er:YSGG with peak at 790 nm is calculated to be 1.56 × 10−21 cm2, and the full width at half maximum (FWHM) of them are 8 nm and 3 nm, respectively. The absorption cross section of Nd,Er:LuYSGG crystal is more than 33 times of Er:YSGG crystal.

Apparently, the Nd3+/Er3+ co-doped crystal exhibits much more intense and wider absorption than that of Er3+ doped crystal at around 808 nm, thus indicating that Nd3+/Er3+ co-doped sample can absorb the pump energy of 808 nm more effectively, which makes it very suitable for AlGaAs laser diode pumping. The absorption at around 808 nm in the co-doped sample involves both the contributions from Er3+ and Nd3+ ions owing to the transitions Er3+:4I15/24I9/2 and Nd3+: 4I9/24F5/2 + 2H9/2, respectively. Owing to the small energy gap between Nd3+:4F5/2 + 2H9/2 (approximately 12500 cm−1) and Er3+:4I11/2 (approximately 10000 cm−1), it is expected that efficient resonance energy transfer could occur from Nd3+ to Er3+ and thus improve the MIR emission greatly.

Figure 3 shows the 850~1700 nm wavelength near-infrared (NIR) emission spectra of Er:YSGG and Nd,Er:LuYSGG crystals under 808 nm excitation. The weak emission around 1002 nm and the much strong emission around 1534 nm were observed in Er:YSGG crystal due to the transition of Er3+:4I11/24I15/2 and Er3+:4I13/24I15/2, respectively. However, as seen in Nd,Er:LuYSGG crystal, 1.5-μm emission is quenched obviously as compared with the Er3+ single doped sample, and the strongest emissions with peaks at 1061 and 1104 nm are caused by Nd3+, corresponding to 4F3/24I11/2. Also, we can observe the other several peaks at round 882 (936) and 1335 nm, which are caused by Nd3+ ions too, corresponding to 4F3/24I9/2 and 4F3/24I13/2, respectively. The 1.5-μm emission quenching phenomenon indicates that the depopulation of Er3+:4I13/2 level by Nd3+ in Nd,Er:LuYSGG crystal is very effective, and thus beneficial to the ~3.0 μm emission in Er3+ activated LuYSGG crystal.

 figure: Fig. 3

Fig. 3 NIR emission spectra of Er:YSGG and Nd,Er:LuYSGG crystals excited by 808 nm.

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The MIR emission spectra of Er:YSGG and Nd,Er:LuYSGG crystals pumped by 808 nm and measured under the same experimental conditions are presented in Fig. 4. The observed strongest emission bands around 2640 and 2820 nm are assigned to Er3+:4I11/24I13/2 in both crystals. It is found that more intense emission is detected in Nd, Er:LuYSGG crystal than in Er:YSGG crystal, and the introduction of Nd3+ ions enhance the emission intensity by nearly 2.2 times.

 figure: Fig. 4

Fig. 4 MIR emission spectra of Er: YSGG and Nd, Er: LuYSGG crystals under 808 nm pumping.

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In order to explain the above-mentioned absorption and emission spectra, the energy level diagram of Nd3+ and Er3+ is presented in Fig. 5. The possible mechanisms of the energy transfer processes between Nd3+ and Er3+ ions were explained as follows: in Er:YSGG, Er3+ ions are excited by 808 nm photons from ground state 4I15/2 to 4I9/2 state, then relaxed to 4I11/2 and 4I13/2 levels, and thus ~1.5 µm emission (4I13/24I15/2) and ~3.0 μm emission (4I11/24I13/2) can be observed as seen in Fig. 3 and Fig. 4, respectively. The weaker intensity of ~3.0 μm emission in Er:YSGG crystal indicates that nonradiative transition is the main route for depopulating 4I11/2. However, once Nd3+ ions are introduced into Er3+ activated LuYSGG crystal, the 808 nm pump energy is mainly absorbed by Nd3+ via the transition 4I9/24F5/2 + 2H9/2. On one hand, a part of the excited Nd3+ ions at 4F5/2 + 2H9/2 relax nonradiatively to 4F3/2 and give a well-known emission with peak at 1061 nm corresponding to 4F3/24I11/2 transition as seen in Fig. 3. On the other hand, Nd3+ ions in the 4F5/2, 2H9/2 and 4F3/2 levels transferred their energy to Er3+:4I9/2 and 4I11/2 via the processes:

 figure: Fig. 5

Fig. 5 The energy level diagram of Nd3+ and Er3+ ions for Nd,Er:LuYSGG crystal.

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(Nd3+:4F5/2,2H9/2+Er3+:4I15/2)(Nd3+:4I9/2+Er3+:4I9/2),(Nd3+:4F5/2,2H9/2+Er3+:4I15/2)(Nd3+:4I9/2+Er3+:4I11/2),and(Nd3+:4F3/2+Er3+:4I15/2)(Nd3+:4I9/2+Er3+:4I11/2).

These energy transfer processes (named as ET1) from Nd3+ to Er3+ increased the population of Er3+:4I11/2, which led to enhanced ~3.0 μm emission corresponding to 4I11/24I13/2 as observed in Fig. 4. Meanwhile, an obvious quench phenomenon was observed in the 1.5- μm emission as shown in Fig. 3 in Nd,Er:LuYSGG crystal, which is due to the presence of energy transfer channel ET2, that is (Er3+:4I13/2, Nd3+:4I9/2)→(Er3+:4I15/2, Nd3+:4I15/2). The introduction of Nd3+ depopulates 4I13/2 level of Er3+, which is helpful to the population inversion for ~3.0 μm laser operation.

To further explore the energy interaction mechanism, the fluorescence decay curves of Er3+:4I13/2 and 4I11/2 multiplets of Er:YSGG and Nd,Er:LuYSGG crystals were measured at 1534 and 2640 nm excited by 808 nm, respectively, as shown in Fig. 6. And the decay curves from the 4I13/2 and 4I11/2 levels of Er:YSGG crystal both show singly-exponential decay behavior, while the decay curve from Er3+:4I11/2 level of Nd,Er:LuYSGG crystal is doubly-exponential decaying. The fluorescence lifetimes were fitted and presented in Fig. 6. It is noticed that the fluorescence lifetime of 4I11/2 state (0.57 ms) is shorter than that of 4I13/2 state (2.06 ms) in Er:YSGG crystal. As we pointed previously, the shorter lifetime of laser upper level 4I11/2 than lower level 4I13/2 will make the accumulated population in the 4I11/2 levels unable to relax quickly enough to maintain the necessary population inversion, and then cause the ~3.0 µm lasing transition to self-terminate automatically. In this work, the codopant Nd3+ quenched the emission corresponding to 4I13/24I15/2 and decreased the lifetime of 4I11/2 state from 0.57 to 0.38 ms, thus suppressed the self-termination bottleneck effect successfully.

 figure: Fig. 6

Fig. 6 Fluorescence decay curves of Er3+:4I11/2, 4I13/2 and Nd3+:4F3/2 levels in Nd,Er:LuYSGG and Er:YSGG crystals.

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The energy transfer efficiency of Nd3+→Er3+ via ET1 in Nd,Er:LuYSGG crystal can be estimated by the following equation [23]:

ηT=1τNdErτNd.
Where τNdEr is the lifetime of Nd3+:4F3/2 of Nd,Er:LuYSGG crystal, τNd is the lifetime of Nd3+:4F3/2 of Nd:YSGG crystal with same Nd3+ concentration as in Nd,Er:LuYSGG crystal. The fluorescence decay curve of the Nd3+:4F3/2 multiplets of Nd,Er:LuYSGG crystal was measured at 1061 nm excited by 808 nm, as shown in Fig. 6 too. By linear fitting, the fluorescence lifetime is fitted to be 20.26 µs, which is much shorter than that of Nd:YSGG crystal (240 µs) [21]. Therefore, the energy transfer efficiency of Nd3+→Er3+ via ET1 is calculated to be 91.6%. Similarly, the energy transfer efficiency of Er3+→Nd3+ via ET2 in Nd,Er:LuYSGG crystal can be estimated. Since the 1.5 µm emission of Er3+ is quenched in Nd Er:LuYSGG crystal, we can think the energy transfer efficiency via ET2 is close to 100%.

The emission cross sections are calculated by the F-L equation [14]:

σem(λ)=βλ58πcn2τrI(λ)λI(λ)dλ.
Where I(λ)/λI(λ)dλ is the normalized line shape function of the experimental emission spectrum, β is the fluorescence branching ratio, c is the speed of light, n is the refractive index and τr is the radiative lifetime. The maximum emission cross section of Nd,Er:LuYSGG crystal is estimated to be 1.84 × 10−19 cm2 at 2640 nm, which is larger than that of Er:YSGG crystal (1.02 × 10−19 cm2), ascribing to the shorter radiative lifetime and higher fluorescence branching ratio of the 4I11/24I13/2 transition for the Nd,Er:LuYSGG crystal.

Herein, we list the spectral properties of several erbium activated garnet crystals in Table 1. As seen in these data, the absorption cross-section and emission cross-section of Nd, Er: LuYSGG crystal are much bigger than the other similar crystals.

Tables Icon

Table 1. The spectral parameters of several erbium activated garnet crystals

4. Conclusions

The spectroscopic properties of Nd,Er:LuYSGG crystal were studied systematically. Compared with Er:YSGG crystal, the ~1.5 µm emission is quenched in Nd,Er:LuYSGG crystal, meanwhile, the intensity of the target ~3.0 μm emission enhances 2.2 times owing to the presence of Nd3+ ions. Furthermore, the lifetimes of the Er3+:4I11/2 upper laser level fall from 0.57 ms to 0.38 ms, and that of 4I13/2 level decreases sharply from 2.06 ms to quenching, which indicating that the self-saturation effect for the Er3+ ~3.0 μm laser is effectively suppressed. The energy transfer efficiency of Nd3+→Er3+ (ET1) in Nd,Er:LuYSGG crystal is estimated to be 91.6%, and that of Er3+→Nd3+ (ET2) is almost 100%. These results indicate that Nd3+ codoping is beneficial in achieving ~3.0 μm laser in Nd,Er:LuYSGG crystal, and this crystal can be acted as an excellent candidate for MIR lasers.

Acknowledgments

This work is supported by National Nature Science Foundation of China (51472240, 91122033 and 11304313), Knowledge Innovation Program of Chinese Academy of Sciences (KJCX2-EW-H03), Key Laboratory of Functional Crystal Materials and Device (No. JG1403, Shandong University, Ministry of Education), State Key Laboratory of Rare Earth Resource Utilization (No. RERU2015018, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences), Science and Technology Plan Cooperation Project of Fujian Province (2015I0007) and Nature Science Foundation of Fujian Province (2015J05134).

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Figures (6)

Fig. 1
Fig. 1 The XRD pattern of Nd,Er:LuYSGG single crystal.
Fig. 2
Fig. 2 Absorption spectra of Nd,Er:LuYSGG and Er:YSGG crystals at RT.
Fig. 3
Fig. 3 NIR emission spectra of Er:YSGG and Nd,Er:LuYSGG crystals excited by 808 nm.
Fig. 4
Fig. 4 MIR emission spectra of Er: YSGG and Nd, Er: LuYSGG crystals under 808 nm pumping.
Fig. 5
Fig. 5 The energy level diagram of Nd3+ and Er3+ ions for Nd,Er:LuYSGG crystal.
Fig. 6
Fig. 6 Fluorescence decay curves of Er3+:4I11/2, 4I13/2 and Nd3+:4F3/2 levels in Nd,Er:LuYSGG and Er:YSGG crystals.

Tables (1)

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Table 1 The spectral parameters of several erbium activated garnet crystals

Equations (4)

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σ a = α N c = A N c L×lge .
( Nd 3+ : 4 F 5/2 , 2 H 9/2 + Er 3+ : 4 I 15/2 )( Nd 3+ : 4 I 9/2 + Er 3+ : 4 I 9/2 ), ( Nd 3+ : 4 F 5/2 , 2 H 9/2 + Er 3+ : 4 I 15/2 )( Nd 3+ : 4 I 9/2 + Er 3+ : 4 I 11/2 ), and ( Nd 3+ : 4 F 3/2 + Er 3+ : 4 I 15/2 )( Nd 3+ : 4 I 9/2 + Er 3+ : 4 I 11/2 ).
η T =1 τ NdEr τ Nd .
σ em (λ)= β λ 5 8πc n 2 τ r I(λ) λI(λ)dλ .
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