Growth, Thermal and Spectral Properties of Er3+-Doped and Er3+/Yb3+-Codoped Li3Ba2La3(WO4)8 Crystals

This paper reports the growth and spectral properties of Er3+-doped and Er3+/Yb3+-codoped Li3Ba2La3(WO4)8 crystals. The Er3+: Li3Ba2La3(WO4)8 crystal with dimensions of 56 mm×28 mm×9 mm and Er3+/Yb3+: Li3Ba2La3(WO4)8 crystal with dimensions of 52 mm×24 mm×8 mm were obtained by the top-seeded solution growth (TSSG) method. Thermal expansion coefficients and thermal conductivity of both crystals were measured. The spectroscopic characterizations of both crystals were investigated. The spectroscopic analysis reveals that the Er3+/Yb3+: Li3Ba2La3(WO4)8 crystal has much better optical properties than the Er3+: Li3Ba2La3(WO4)8 crystal, thus it may become a potential candidate for solid-state laser gain medium material.

Li 3 Ba 2 Ln 3 (WO 4 ) 8 (Ln = La-Lu, Y) belongs to the monoclinic system with space group C2/c, which was firstly discovered by our group [21]. Due to the existence of a statistical distribution of Ln and Li atoms, these crystals have a high structure disorder, which results in the absorption and emission lines broadening homogeneously when rare-earth ions are doped and occupy the positions of Ln 3+ ions [22]. Li 3 Ba 2 La 3 (WO 4 ) 8 (hereafter denoted as LBLW) is a member of this family. In this work, the thermal expansion coefficients and thermal conductivity of Er 3+ : LBLW and Er 3+ / Yb 3+ : LBLW single crystals grown by TSSG method were measured. The room-temperature polarized absorption and fluorescence spectra as well as the up-conversion mechanism of both kinds of crystals were reported and analyzed.

Crystal Growth
The Er 3+ : LBLW and Er 3+ /Yb 3+ : LBLW crystals were grown by the top-seeded solution growth (TSSG) method from a flux of Li 2 WO 4 . The crystal growth was carried out in a vertical tubular furnace. The schematic diagram of crystal growth apparatuses is same as that in Ref. [23]. The furnace temperature was controlled by an AL-708 controller with controlling accuracy of 60.1 K. The raw materials of Er 3+ : LBLW and Er 3+ /Yb 3+ : LBLW were synthesized by the solid-state reaction. The chemicals used were WO 3 , Li 2 CO 3 , BaCO 3 , La 2 O 3 , Er 2 O 3 and Y 2 O 3 with the purity of 99.99%. The solutions were composed of 25 mol% of solute (LBLW) and 75 mol% of solvent (Li 2 WO 4 ).The crystal growth procedure is similar to that in Ref [23]. When the growth ended, the crystals were drawn out of the solution and cooled down to room temperature at a cooled rate of 15 K/h. Fig. 1

Thermal Properties
The thermal expansion of crystal is an important thermal factor for the crystal growth [24,25]. The thermal expansion coefficients were measured using a thermal expansion dilatometer (NETZSCH DIL 402 PC). The linear thermal expansion coefficient is defined as: where L 0 is the initial length of the sample at room temperature, and DL is the change in length when the temperature changes DT.
Since the LBLW crystal with monoclinic is of anisotropy, the thermal expansion coefficient a ij is a second rank tensor with four nonzero components in the orthogonal crystallo-physical axes (a, b, c*) [26]. Thus, in order to obtain thermal expansion ellipsoid, the measurement should be carried out along at least four different directions. Therefore, four rectangular samples were cut from both the Er 3+ -doped and Er 3+ /Yb 3+ -codoped LBLW crystals, of which three were along the crystallographic a-, band c*-axis and the fourth, namely c', was cut with the anti-clockwise angle (w) 45u with respect to the c-axis. During the measurement, the samples were heated at a heating rate of 5 K/min in the range of 300,1100 K in the air atmosphere. The processes to determine the thermal expansion tensor in both crystals is similar, therefore here, for brevity, we mainly discuss the Er 3+ -doped one. The measured thermal expansion ratios DL=L 0 versus T are shown in Fig. 2 (a). It can be found that when the temperature is below 450 K, the value of DL=L 0 rise nonlinearly with the temperature. This may be due to the error caused by the thermal dilatometer at temperature below 450 K The next step is to find the values of the principal thermal expansion. For a monoclinic crystal, one of the principal axes (X II ) of the thermal expansion ellipsoid coincides with the crystallographic b-axis. The other two principle axes (X I , X III ) which can be calculated from the secular equation det(a ij -ld ij ) = 0 [29] are in the (0 1 0) plane. For Er 3+ -doped LBLW crystal, the eigenvalues are a' 11 = 11.33 K 21 and a' 33 = 8.80 K 21 , and the linear thermal expansion tensor in the principal axes is the angle r between the crystallo-physical c*-axis and principal X III axis can be evaluated by the minus value of r denotes the clockwise angle from c*-axis to the XIII axis (see Fig. 2 The values of the linear thermal expansion coefficients along the optical indicatrix axes are more important in practice because the laser elements are normally cut along these axes. The orientation   of the optical indicatrix axes (X, Y, Z) with respect to the crystallographic axes (a, b, c) is from that of Ref [30]: (a, X) = 19u and (c, Z) = 20u (see Fig. 2 (b)). Using the detailed procedure described in Ref. [26], the ellipsoid in the optical indicatrix axis can be determined as The linear thermal expansion coefficient for the both Er 3+doped and Er 3+ /Yb 3+ -doped crystals along the directions of crystallo-physical axes (a, b, c*), principal axes (X I , X II , X III ) and optical indicatrix axes (X, Y, Z) are included in Table 1. The values of a b /a a and a a /a c* are 0.71 and 0.78, respectively. The thermal expansion exhibits a larger anisotropy than Li 3 Ba 2 La 3 (MoO 4 ) 8 crystal [33], which means the LBLW crystal is easier to crack during the cooling process. Therefore, a slow annealing rate should be applied in the crystal growth procedure.
The thermal conductivity coefficient (k) of both Er 3+ -doped and Er 3+ /Yb 3+ -doped crystals were measured by the laser-flash method (Model NETZSCH LFA 457, Germany) in the temperature range 350-700 K. Four samples along a, b, c and c* crystallographic directions for each crystal were prepared for thermal conductivity measurements. The dimension of the samples was about 6 mm66 mm62 mm. Fig. 3

Spectral Properties
Two cubic samples with dimensions of 7.4 mm63.8 mm65.8 mm and 7.2 mm62.4 mm64.7 mm were cut from the Er 3+ : LBLW and Er 3+ /Yb 3+ : LBLW crystals, respectively. Each face of samples was perpendicular to one of the optical indicatrix axes. All the surfaces of these cuboids were polished for spectral experiments. The polarized absorption spectra from 300 nm to 1700 nm were measured using a Perkin-Elmer UV-VIS-NIR spectrometer (Lambda 900). The polarized fluorescence spectra were recorded by a spectrophotometer (FLS920, Edinburgh) equipped with a xenon lamp as the excitation source. Two photomultiplier tubes (PMT) (Hamamatsu R955 and R5509) were used as the detectors in the VIS and NIR regions, respectively. Furthermore, the up-conversion spectroscopic experiments were carried out by a monochromator (Triax550,  Jobin-Yvon) excited at 976 nm with a diode laser, and the power range of the diode emission was from 40 to 1400 mW. The signals were detected with a PMT (R943-02, Hamamasu). All measurements were performed at room temperature.
The absorption spectra of the Er 3+ : LBLW and Er 3+ /Yb 3+ : LBLW crystals at room temperature are shown in Fig. 4. These sharp absorption lines are attributed to the Er 3+ ions except the broad absorption band at 900-1050 nm, which is the overlap of the 4 I 15/2 R 4 I 11/2 transition of Er 3+ ions and the 2 F 7/2 R 2 F 5/2 transition of Yb 3+ ions. In comparison with Er 3+ : LBLW crystal, such broad and strong absorption band around 900-1050 nm was mainly attributed to the 2 F 7/2 R 2 F 5/2 transition of Yb 3+ ions. The absorption coefficients for Er 3+ /Yb 3+ : LBLW crystal are 1.76 cm 21 at 980 nm, 2.54 cm 21 at 974 nm and 1.80 cm 21 at 978 nm for E||X, E||Y and E||Z respectively. They are roughly ten times as large as those of the Er 3+ : LBLW crystal (0.15 cm 21 , 0.14 cm 21 and 0.22 cm 21 for E||X, E||Y and E||Z, respectively). Therefore, the crystal co-doped with Yb 3+ ions can signifi-cantly increase the absorption of the pump energy if pumped at around 980 nm. It should be also noted that the FWHMs of Er 3+ / Yb 3+ : LBLW crystal around 980 nm are 35 nm, 38 nm and 34 nm for E||X, E||Y and E||Z, respectively, and these values are larger than those of Er 3+ /Yb 3+ : YCa 4 O(BO 3 ) 3 and Er 3+ /Yb 3+ : GdCa 4 O(BO 3 ) 3 crystals [4,5]. The broad absorption bands which can relax the requirement of accurate temperature control of diode laser make Er 3+ /Yb 3+ : LBLW crystal suitable for diode laser pumping.
The Judd-Ofelt theory [36,37] has been widely used to analyze the spectroscopic properties of the rare earth ions except Yb 3+ ion in crystals. The oscillator strength parameters V t (t = 2, 4, 6) can be fitted from the room-temperature absorption spectra, then the spontaneous emission probabilities, radiative lifetime and fluorescence branching ratios can be obtained. The detailed calculation procedure is similar to that reported in Ref [38]. The reduced matrix elements values of unit tensor operators used in the calculation could be found in Ref [39,40]. Except for the two high  Table 3. Spontaneous emission probabilities A ed JJ' , fluorescence branching ratios b and radiative lifetimes t r for Er 3+ : LBLW crystal.  Fig. 4), all the other ones were chose to fit the oscillator strength parameters for E||X, E||Y and E||Z polarizations. Because those two transitions belong to hypersensitive transition [41,42], they are sensitive to the variation of local structure around Er 3+ ions. Here, only the spectrum of the Er 3+ : LBLW crystal was calculated for brevity. Table 2 lists the values of the measured (S mea ) and calculated (S cal ) line strengths, the intensity parameters V X,Y,Z for each polarization as well as the effective intensity parameters which are defined as V eff = (V X +V X +V X )/3. After obtaining the oscillator strength parameters V X,Y,Z for each polarization, the spontaneous emission probabilities of the electric-and magnetic-dipole transitions (named A ed JJ 0 and A md JJ 0 respectively), fluorescence branching ratio b and radiative lifetime t r of some typical transitions could be gained. The values of these spectroscopic parameters are all outlined in Table 3. The Er 3+ : LBLW crystal could not be efficiently excited by Xenon lamp because of the weak absorption at 976 nm. Moreover, considering the small phonon energy of the (WO 4 ) 22 groups (roughly 900 cm 21 ) [43], the multiphonon relaxation from the 4 I 11/2 to 4 I 13/2 multiplets of Er 3+ ions was slow. Therefore, the emission band surrounding 1550 nm ( 4 I 13/2 R 4 I 15/2 ) for Er 3+ : LBLW crystal is too weak to be distinguished. Thus, the fluorescence spectra of the Er 3+ /Yb 3+ : LBLW crystal were only recorded (see Fig. 5). The stimulated-emission cross-sections were calculated by the Füchtbauer-Ladenburg (F-L) formula [44,45], where A q is the spontaneous emission probability for q polarization, I q (l) is the fluorescence intensity as a function of wavelength. The peak emission cross-sections are about 0.81610 220 , 1.23610 220 and 0.84610 220 cm 2 for E||X, E||Y and E||Z respectively, which are comparable to other co-doped crystals, such as 1.89610 220 cm 2 for Er 3+ /Yb 3+ : KY(WO 4 ) 2 [46], 0.71610 220 cm 2 for Er 3+ /Yb 3+ : LaPO 4 [47] and 0.95610 220 cm 2 for Ce 3+ /Er 3+ NaLa(MoO 4 ) 2 [48].
The Er 3+ laser via the 4 I 13/2 R 4 I 15/2 transition operates in a quasi-three scheme, therefore the re-absorption losses should be considered. The useful laser wavelength could be evaluated by the so-called effective gain cross section [49].     Fig. 7 shows the up-conversion fluorescence spectra for Er 3+ : LBLW and Er 3+ /Yb 3+ : LBLW crystals in the range from 500 to 700 nm excited at 976 nm radiation of diode laser. Note that the fluorescence intensity of Er 3+ /Yb 3+ co-doped LBLW crystal is much larger than that of Er 3+ -doped LBLW. This means there existed fast and efficient Yb 3+ REr 3+ energy transfer in Er 3+ /Yb 3+ : LBLW crystal. Fig. 8 displays the up-conversion mechanisms and simplified energy levels of Er 3+ and Yb 3+ ions in Er 3+ /Yb 3+ : LBLW crystal. Two different mechanisms, namely Er 3+ excited state absorption (ESA) and a two-step Yb-Er energy transfer (ET), may exist in the up-conversion process [5,20,50].
For the Er 3+ /Yb 3+ crystal, the green emissions of 530 and 553 nm ( 2 H 11/2 R 4 I 15/2 and 4 S 3/2 R 4 I 15/2 , respectively) can be explained by the following steps: Firstly, the Er 3+ ions were excited from ground state to the excited state 4 I 11/2 by means of ground state absorption (GSA) and by ET process from 2 F 5/2 level of Yb 3+ to Er 3+ . The ET process is dominant because of the large absorption across-section around 980 nm of Yb 3+ ions. Secondly, some Er 3+ ions at the 4 I 11/2 level were promoted up to the higher 4 F 7/2 level by ET process from 2 F 5/2 level of Yb 3+ or by ESA of Er 3+ ions, then the ions at the 4 F 7/2 level relaxed non-radiatively to the lower levels 2 H 11/2 and 4 S 3/2 owning to the small energy gap between them. When the Er 3+ ions at the 2 H 11/2 and 4 S 3/2 levels transited to the ground state, they produced 530 and 553 nm green emissions, respectively. The green emissions of the Er 3+ : LBLW crystal also experienced the above processes except the lack of ET process. Because the lifetime of the 4 S 3/2 level is much longer than that of the 2 H 11/2 level [51], more ions would non-radiatively decay to the 4 S 3/2 level. As a consequence, the intensity of 553 nm is stronger than 530 nm.
For the red emission of 661 nm ( 4 F 9/2 R 4 I 15/2 ), population on the 4 F 9/2 might be accumulated by two ways: ESA and ET process. Both ways excited Er 3+ ions from 4 I 13/2 to 4 F 9/2 . Besides, the ions at the 4 S 3/2 level also relaxed rapidly to the 4 F 9/2 level. The red emission intensity is also significantly weaker than that of Er 3+ /Yb 3+ crystal because of lacking of ET process in the Er 3+ : LBLW crystal.
The dependence of integrated up-conversion fluorescence intensity on the excitation power at 976 nm for Er 3+ /Yb 3+ crystal is shown in Fig. 9. According to the relation I up !I n [52], where n is the number of photon involved in the up-conversion process and I is the excitation power. The slopes (for green and red light are all near 2) indicate that two photon processed populated the 2 H 11/2 , 4 S 3/2 and 4 F 9/2 levels. However, due to the competition between the linear decay and the depletion of the intermediate excited states, the values of n may be lower than 2 (see Fig. 9) [53].

Results and Discussion
The Er 3+ : LBLW and Er 3+ /Yb 3+ : LBLW have been successfully grown by the TSSG method from the flux of Li 2 WO 4 . The thermal expansion coefficients in the optical indicatrix axes were a X = 11.17610 26 K 21 , a Y = 8.07610 26 K 21 and a Z = 8.94610 26 K 21 for the Er 3+ : LBLW crystal, and a X = 11.18610 26 K 21 , a Y = 8.01610 26 K 21 and a Z = 9.22610 26 K 21 for the Er 3+ /Yb 3+ : LBLW crystal. The anisotropy of thermal expansion indicates that the LBLW crystals are easier to crack; thus, slow cooling rate should be adopted after the crystals were withdrawn from the melt. The Er 3+ /Yb 3+ : LBLW crystal has broad absorption bands near 980 nm (35 nm, 38 nm and 34 nm for E||X, E||Y and E||Z, respectively), which make it very suitable for diode pumping. The effective J-O intensity parameters of the Er 3+ : LBLW were calculated to be V eff 2 = 11.94610 220 cm 2 , V eff 4 = 1.60610 220 cm 2 , V eff 6 = 0.78610 220 cm 2 , respectively. Considering the re-absorp-tion losses of the quasi-three scheme, the effective emission crosssection around 1550 nm was also calculated. Under the 976 nm excitation, the up-conversion emissions of three visible optical bands, corresponding to the 2 H 11/2 R 4 I 15/2 , 4 S 3/2 R 4 I 15/2 and 4 F 9/2 R 4 I 15/2 , respectively, for Er 3+ /Yb 3+ : LBLW crystal were observed. The investigation of up-conversion spectra denotes that the energy transfer between Yb 3+ and Er 3+ is efficient. The spectroscopic analysis reveals that the Er 3+ /Yb 3+ : LBLW crystal has much better optical properties than the Er 3+ : LBLW crystal. Therefore, the Er 3+ /Yb 3+ : LBLW crystal may become a potential candidate for solid-state laser gain medium material.

Author Contributions
Conceived and designed the experiments: BX GW. Performed the experiments: BX ZL. Analyzed the data: BX GW. Contributed reagents/materials/analysis tools: YH LZ. Wrote the paper: BX GW.