R2O3 (R = La, Y) modified erbium activated germanate glasses for mid-infrared 2.7 μm laser materials

Er3+ activated germanate glasses modified by La2O3 and Y2O3 with good thermal stability were prepared. 2.7 μm fluorescence was observed and corresponding radiative properties were investigated. A detailed discussion of J–O parameters has been carried out based on absorption spectra and Judd–Ofelt theory. The peak emission cross sections of La2O3 and Y2O3 modified germanate glass are (14.3 ± 0.10) × 10−21 cm2 and (15.4 ± 0.10) × 10−21 cm2, respectively. Non-radiative relaxation rate constants and energy transfer coefficients of 4I11/2 and 4I13/2 levels have been obtained and discussed to understand the 2.7 μm fluorescence behavior. Moreover, the energy transfer processes of 4I11/2 and 4I13/2 level were quantitatively analyzed according to Dexter’s theory and Inokuti–Hirayama model. The theoretical calculations are in good agreement with the observed 2.7 μm fluorescence phenomena. Results demonstrate that the Y2O3 modified germanate glass, which possesses more excellent spectroscopic properties than La2O3 modified germanate glass, might be an attractive candidate for mid-infrared laser.

Experimental processes. Er 3+ doped germanate glasses were synthesized by conventional melting method, which has the following molar compositions: 65GeO 2 -15Ga 2 O 3 -5BaO-(10-x)La 2 O 3 -x Y 2 O 3 -5NaF-0.5Er 2 O 3 , (x = 0, 10), denoted as GL, GY, respectively. Samples were synthesized by using high-purity of GeO 2 , Ga 2 O 3 , BaO, La 2 O 3 , Y 2 O 3 , NaF and Er 2 O 3 powders. The stoichiometric chemicals were well-mixed and melted at 1400 °C for 30 min in a covered alumina crucible. The melts were poured onto a preheated steel plate and pressed by another plate for shaping. After annealing at around glass transition temperature, all samples were cut and polished into 10 × 10 × 1.5 mm 3 for further measurement.
Refractive indexes of samples were measured by prism minimum deviation method at the wavelength of 1053 nm. The resolution of the instrument was ± 0.5 × 10 −4 . The densities were tested by Archimedes principle using distilled water as an immersion liquid with error limit of ± 0.05%. Differential scanning calorimeter (DSC) curve is measured using NETZSCH DTA 404 PC at the heating rate of 10 K/min with maximum error of ± 5 °C. Absorption spectra were recorded with a Perkin-Elmer-Lambda 900UV/ VIS/NIR spectrophotometer in the range of 350-1640 nm. Photoluminescence spectra in the ranges of 2600-2800 nm and 1400-1700 nm were determined via a combined fluorescence lifetime and steady state spectrometer (FLSP 920) (Edingburg Co., England), which was detected with a liquid-nitrogen-cooled PbS detector using an 808 nm laser diode (LD) as an excitation source. The 808 nm LD with the same power was also utilized to measure the lifetimes of Er 3+ : 4 I 11/2 and 4 I 13/2 levels. The lifetimes were calculated by fitting a single exponential function to the measured data. The same experimental conditions for different samples were maintained so as to get comparable results. All the measurements were performed at ambient temperature.

Results and Discussion
Thermal stability and density. Figure 1 shows the differential DSC curves for the prepared glasses.
The glass transition temperature T g , onset crystallization temperature T x , and thermal stability Δ T( = T x -T g ) in various glasses are displayed in Table 1. It is found that the Δ T of GL and GY samples are 190 °C and 175 °C, respectively. Compared with ∆T, the glass formation factor, K gl = (T x -T g )/(T m -T g ), where T m is the glass melting temperature, is more suitable to estimate the glass thermal stability. It is clear that K gl of GL and GY can reach 0.26 and 0.25, respectively. Both Δ T and K gl of prepared samples are larger than those of tellurite 20 , bismuth 21 and germanate glass 22 , while is comparable to BGG glass 19 . The result suggests that the prepared germanate glasses have good glass forming ability and thermal stability.
T g is an important factor for laser glass, which gives glass good thermal stability to resist thermal damage at high pumping intensities. The values of T g of both prepared samples are substantially larger than the other glasses in Table 1. It is interesting to find that the T g of GY is larger than GL, which is in accordance with the work of John M. Jewell 19 . The importance of the density for describing the structure of a glass is evident. The density of glass is mainly influenced by the molecular weight of glass components, the integration and the compactness of the glass network. The density of GL (4.76) is larger than GY (4.47), and a most possible reason for the decrement in density is ascribed to the smaller molecular weight of Y 2 O 3 compared to La 2 O 3 . Both of the prepared glasses have a smaller density than BGG glass (4.85) 13 . Figure 2 reveals the absorption spectra of Er 3+ activated germanate glasses modified with La 2 O 3 (GL) and Y 2 O 3 (GY) at room temperature in wavelength region of 380-1600 nm. Absorption bands in this figure are labeled, which correspond to the transitions starting from the 4 I 15/2 ground state to higher 4 I 13/2 , 4 I 11/2 , 4 I 9/2 , 4 F 9/2 , 4 S 3/2 , 2 H 11/2 , 4 F 7/2 , 4 F 5/2,3/2 , 2 H 9/2 and 4 G 11/2 levels 23 . The shape and peak positions of each transition in present glasses are very similar to those of other Er 3+ doped glasses 24,25 , except for some tiny divergences that originated from the different ligand field strength of host glasses. It is observed that two absorption peaks ( 4 G 11/2 → 4 I 15/2 and 2 H 11/2 → 4 I 15/2 ) are much stronger than other bands. They are sensitive to small changes of local environment around Er 3+ ions, called hypersensitive transitions (HSTs) 5 . The inset of Fig. 2 displays the enlarged absorption spectrum in the range of 770-830 nm. Obvious absorption peaks around 808 nm manifested the prepared glasses can be pumped by low-cost 808 nm laser diodes (LDs).   Some important spectroscopic and laser parameters of rare earth doped glasses have been commonly analyzed by way of Judd-Ofelt (J-O) theory based on absorption data [26][27][28] . Details of the theory and method have been well described elsewhere [29][30][31] . Thus, only results will be presented here. The J-O intensity parameters Ω t (t = 2, 4, 6) of GL and GY glass were determined in Table 1. The root-mean-square deviation (δ rms ) in GL and GY glass is as low as 0.49 × 10 −6 , 0.29 × 10 −6 , respectively, proving the validity of the results and the reliable calculations.

Absorption spectra and J-O analysis.
It can be seen from Table 2 that the value of Ω 2 in GY glass is higher than those of other Er 3+ doped glasses. It is well known that Ω 2 is strongly dependent on the RE 3+ local environment and it is directly related to the symmetry or polarization of local structure and the covalence of chemical bonds formed by the RE 3+ with its ligands. Based on this idea, the higher Ω 2 in GY glass indicates the larger polarization of Y 2 O 3 and asymmetry around Er 3+ 32 . Thus, the chemical bonds associated with the Er 3+ ions is more covalent than those of silicate 33 , tellurite 34 , fluoride 6 glasses as shown in Table 2. In addition, in this work, the Ω 2 value of GL glass is lower than that of GY glass. According to the electronegativity theory, the covalency of the bond will become stronger with the decrease of the difference of electronegativity between cation and anion 35 . Since the values of electronegativity, for La, Y and O elements, are 1.1, 1.22, 3.5, respectively, the covalency of Y-O bond is stronger than that of La-O bond. This behavior will lead to the larger polarization of Y 2 O 3 component than that of La 2 O 3 and the asymmetry of the site occupied by Er 3+ in GL glass is lower than that of GY glass. On the other hand, the Ω 6 parameter is related to the overlap integrals of 4f and 5d orbit 36 . The Ω 6 of GY is larger than those of GL, germanate 37 , tellurite 34 , silicate 33 glasses, smaller than that of fluoride glass 6 .
Radiative properties. Since S md is independent of ligand fields and S ed is a function of glass structure and composition 38 , in order to get flat emission spectrum, it can be effective to increase the relative contribution of the electric-dipole transition 39  According to Eq. (1), the S ed is mainly dominated by Ω 6 . From Table 2 it is noted that Ω 6 in GY glass is higher than those of other various glasses except fluoride glass. Therefore, compared to GL glass, GY glass is more expected to be an appropriate host material that gets flat emission spectrum from the Er 3+ : 4 I 11/2 → 4 I 13/2 transitions. Further calculation about spontaneous radiative transition probability (A rad ), fluorescence lifetime (τ rad ), and branching ratios (β ) of Er 3+ various transition in prepared glasses are listed in Table 3. As is shown in Table 3, the GY glass possesses a larger A rad (36.21 s −1 ) than that of GL glass (35.03 s −1 ) for Er 3+ : 4 I 11/2 → 4 I 13/2 respectively 40 . It is worth noting that both of prepared glasses possess evidently larger A rad than BGG glass (19 s −1 ) 41 . Furthermore, the values of β in both samples are comparable to those germanate glasses 37,41 .
Since multiphonon relaxation rate has a substantial impact on 2.7 μ m emissions, a low nonradiative decay rate is required to achieve strong 2.7 μ m fluorescence. The multiphonon relaxation rate constant (k mp ) from a given excited state can be estimated from the energy-gap law 42 . The multiphonon relaxation rate constant (k mp ) can be defined as, where ΔE is the energy gap between the emitting level and the adjacent lower level. α and β are positive-definite constants depending on glasses. ћω max is the highest phonon energy of the glass. Where ω = Δ / p E max is the minimum number of phonons required to bridge the energy gap Δ E 43 . In this work, k mp is calculated using the parameters α = 4.6 × 10 −3 cm, β = 6.1 × 10 7 s −1 and T = 300 K reported for germanate glass 44 . Via Eq. (2), the k mp values for Er 3+ : 4 I 11/2 → 4 I 13/2 and 4 I 9/2 → 4 I 11/2 transitions of GL glass and GY glass are determined as shown in Table 3. The transition of 4 I 9/2 → 4 I 11/2 is proposed to be a multiphonon decay process compared to 4 I 11/2 → 4 I 13/2 transition. In addition, the k mp of 4  Fluorescence spectra at 2.7 μm. Figure 3 illustrates the mid-infraed emission spectra and cross sections of Er 3+ doped GL and GY glasses pumped at 808 nm laser diode(LD). As shown in Fig. 3(a),    where λ is the emission wavelength, A rad is the spontaneous radiative transition probability of Er 3+ : 4 I 11/2 → 4 I 13/2 transition, c is the velocity of light in vacuum, n is the refractive index of glass host (GL:1.76 and GY: 1.73), I(λ ) is the 2.7 μ m fluorescence intensity, and ∫I(λ )dλ is the integrated fluorescence intensity. Based on emission cross section, σ em , absorption cross section (σ abs ) can be obtained by [51], where Z l and Z u are the partition functions for the lower and the upper levels involved in the considered optical transition, respectively. T is the temperature (here is 300 K), k is the Boltzmann constant and λ ZL is the wavelength for the transition between the lower Stark sublevels of the emitting multiplets and the lower Stark sublevels of the receiving multiplets. As shown in Fig. 3(b), the absorption and emission cross sections can be calculated by Eq. (3) and (4). It can be seen that the peak absorption cross sections at 2.7 μ m of GL and GY glass are (10.3 ± 0.10) × 10 −21 cm 2 and (10.1 ± 0.10) × 10 −21 cm 2 , respectively, the peak emission cross section are (14.3 ± 0.10) × 10 −21 cm 2 and (15.4 ± 0.10) × 10 −21 cm 2 , respectively. Higher emission cross section means that better laser gain can be achieved in glass. It is found that the obtained σ em for both glasses are higher than those of fluoride (9.16 × 10 −21 cm 2 ) 6 , bismuthate (7.73 × 10 −21 cm 2 ) 21 and tungsten-tellurite glass (6.05 × 10 −21 cm 2 ) 46 .
In addition, according to Eq. (5), the effective emission bandwidths (Δ λ eff ) have been obtained. where σ em peak is the peak emission cross section at 2.7 μ m. Since the 2.7 μ m emission band of Er 3+ ions in glass is asymmetric, it is more reasonable to select effective emission bandwidth other than the full width at half maximum as presented in Fig. 3(b). For broadband amplifier, it is required that effective emission bandwidth is as wide as possible to provide multiple channels for signal transmission. It is calculated from Fig. 3(a) that the Δλ eff of GL and GY glass can reach 58.4 and 59.3 nm, which is larger than that of chalcogenide glass (56 nm) 5 . High effective emission bandwidth means that the prepared glasses have potential applications in broadband amplifier operating at 2.7 μ m.
According to the σ em (λ ) and σ abs (λ ), the gain spectra (G(λ )) at 2.7 μ m can be calculated by the report 18 . Figure 4 indicates the gain spectra of 2.7 μ m of prepared glasses. Evidently, both GL and GY, when the population inversion P > 0.4, the gain cross sections in range of 2683-2772 nm become positive. It is suggested that Er 3+ activated GL and GY glass is an attractive candidate for mid-infrared laser with low pump threshold.
The product of λ Δ eff × σ em peak , defined as gain bandwidth, is another important parameter to evaluate the gain performances of prepared samples 47 . Larger gain bandwidth means better gain property of the material. Due to higher emission cross section and larger emission bandwidth, the GY glass has higher gain performance (9.13 × 10 −26 cm 3 ) than GL glass (8.35 × 10 −26 cm 3 ). From the above comparsion, it is roundly expected that GY glass have a better gain properties than GL glass at 2.7 μ m, which is also in good with the 2.7 fluorescence intensity as shown in Fig. 3(a).
Energy transfer mechanism and microparameters. Figure 5 reveals the energy transfer process of Er 3+ pumped by 808 nm LD. Under 808 nm pumping, the ions in Er 3+ : 4 I 15/2 level are excited to the 4 I 9/2 state by ground state absorption process (GSA). Then the ions in 4 I 9/2 level non-radiatively decay to 4 I 11/2 state by multiphonon relaxation process due to small energy gap between 4 I 9/2 and 4 I 11/2 level. The ions in 4 I 11/2 state are populated to 4 F 7/2 level owing to excited state absorption (ESA: 4 I 11/2 + a photon → 4 F 7/2 ) or energy transfer upconversion (ETU1: 4 I 11/2 + 4 I 11/2 → 4 I 15/2 + 4 F 7/2 ). Afterwards, ions in 4 F 7/2 level relax non-radiatively to 2 H 11/2 state due to multiphonon relaxation process. Due to small energy gaps among 2 H 11/2 , 4 S 3/2 and 4 F 9/2 levels, ions in 2 H 11/2 state decay nonradiatively to 4 S 3/2 and 4 F 9/2 level. On the other hand, ions in 4 I 11/2 level can decay to lower 4 I 13/2 level by radiative or nonradiative process and radiative process generates 2.7 μ m fluorescence. Finally, ions in 4 I 13/2 state relax radiatively to the ground state and 1.53 μ m fluorescence occurs. Besides, ions in 4 I 13/2 level can also undergo ETU2 process ( 4 I 13/2 + 4 I 13/2 → 4 I 15/2 + 4 I 9/2 ), thus resulting in the further population accumulations of 4 I 9/2 level. The nonradiative rate of 4 I 9/2 → 4 I 11/2 transition is so large that ions in 4 I 9/2 level decay quickly to 4 I 11/2 level, which is beneficial to populations of the 4 I 11/2 level and 2.7 μ m emissions. Moreover, as is discussed in above, for Er 3+ : 4 I 11/2 → 4 I 15/2 transition, GY has a higher multiphonon relaxation rate constant than GL, which makes it have a more active energy transfer process mentioned above. It is worth mentioning that the residual OH − of glass is to the disadvantage of mid-infrared emission. It can quench the 2.7 μ m fluorescence via the following processes ( 4 I 11/2 + 0 → 4 I 13/2 + 1) in prepared glasses as depicted in Fig. 5. These energy transfer processes are harmful for mid-infrared emissions. Hence, it is necessary to minimize OH − content and weaken unwanted energy transfer from Er 3+ to OH − .
To make clear of mid-infrared emission mechanism, a quantitative understanding of energy transfer process about Er 3+ : 4 I 11/2 level in present glasses is required. According to FÖster 48 and Dexter 49 , the probability rate of energy transfer between donor and acceptor can be estimated as 50,51 Where H DA is the matrix element of the perturbation Hamiltonian between initial and final states in energy transfer process, N is the total phonons in the transfer process m + k = N, S DA N is the integral   In this work, both the donor and acceptor are Er 3+ ions. Energy transfer properties of 4 I 11/2 and 4 I 13/2 level in GL and GY have been calculated using Eqs (6)- (11) and listed in Table 4. The results show that the energy transfer processes of Er 3+ : 4 I 11/2 and 4 I 13/2 level are scarcely phonon dependent. The energy transfer coefficient C D-A in GL and GY of Er 3+ : 4 I 13/2 level are as high as 50 × 10 −40 and 52 × 10 −40 cm 6 /s, respectively, but 4 I 11/2 level is 4.61 × 10 −40 and 4.63 × 10 −40 cm 6 /s, respectively. This suggests the energy of 4 I 13/2 level in present glasses can more efficiently transfer to the same level nearby compared with 4 I 11/2 level, which is helpful to deplete the populations of 4 I 13/2 level and promote population inversion between 4 I 11/2 and 4 I 13/2 level. Figure 6 displays the decay curves of 4 I 11/2 and 4 I 13/2 level in both glasses pumped by 808 LD. It is found that the decay tendency of GY is slower than GL at both 975 and 1530 nm. To shed new light on the population behavior of 4 I 11/2 level and 4 I 13/2 level, the energy transfer processes of these energy levels were analyzed quantitatively on the basis of Inokuti-Hirayama (I-H) model. I-H model can also be used to estimate the energy transfer process among Er 3+ ions, which is expressed as 52,53   where s is 6, 8 or 10 depending on whether the dominant mechanism of interaction is dipole-dipole, dipole-quadrupole or quadrupole-quadrupole, respectively. τ 0 is the intrinsic lifetime. The energy transfer parameter (Q) is defined as

GL GY
Er c 3 where Γ (1-3/s) is equal to 1.77 for dipole-dipole interactions (s = 6), 1.43 for dipole-quadrupole interactions (s = 8) and 1.3 in the case of quadrupole-quadrupole interactions (s = 10). N Er is the concentration of Er 3+ ions (in ions cm −3 ) and R c is the critical transfer distance defined as the donor-acceptor separation for which the energy transfer rate is equal to the rate of intrinsic decay of the donors. The decay curves of present samples have been well fitted by I-H model for s = 6 and the results are listed in Table 5. This indicates that the energy transfer among Er 3+ ions takes place due to dipole-dipole interactions. From Table 5, it can be found that the energy transfer parameter Q for GY sample is lower than that of GL sample in 4 I 11/2 level while the Q value of GY sample is higher than that of GL sample in 4 I 13/2 level. The higher the value Q is, the stronger the energy transfer process becomes. It is indicated that higher Q of 4 I 13/2 level and lower Q of 4 I 11/2 level for GY sample are more beneficial for the population inversion between them and enhancing 2.7 μ m emissions. It is in accordance with the result of Fig. 3(a).