Optical spectroscopy and population behavior between 4 I 11 / 2 and 4 I 13 / 2 levels of erbium doped germanate glass

In this paper, mid-infrared emission properties and energy transfer mechanism were investigated in Er doped germanate glass pumped by 980 nm diode laser. Spontaneous radiative transition probability and emission cross section at 2.7 μm were calculated to be as high as 36.45 s and 1.61 × 10 cm, respectively. Corresponding upconversion emission spectra and radiative lifetimes of I13/2 level were determined to elucidate the mid-infrared luminescent characteristics. Moreover, population behaviors of Er: I11/2 and I13/2 level were analyzed numerically via Inokuti-Hirayama model, rate equations and Dexter’s theory. In addition, DSC curves of developed samples were measured and thermal stabilities were studied to evaluate the ability of resisting thermal damage and crystallization. The results indicate that erbium activated germanate glass is a promising candidate for mid-infrared applications. This work may provide beneficial guide for investigation of population behaviors of Er ions at 2.7 μm emissions. ©2014 Optical Society of America OCIS codes: (160.5690) Rare-earth-doped materials; (250.5230) Photoluminescence; (260.2160) Energy transfer; (300.6340) Spectroscopy, infrared. References and links 1. O. Henderson-Sapir, J. Munch, and D. J. Ottaway, “Mid-infrared fiber lasers at and beyond 3.5 μm using dualwavelength pumping,” Opt. Lett. 39(3), 493–496 (2014). 2. J. Hu, J. Meyer, K. Richardson, and L. Shah, “Feature issue introduction: mid-IR photonic materials,” Opt. Mater. Express 3(9), 1571 (2013). 3. M. C. Pierce, S. D. Jackson, M. R. Dickinson, T. A. King, and P. Sloan, “Laser-tissue interaction with a continuous wave 3-μm fibre laser: Preliminary studies with soft tissue,” Lasers Surg. Med. 26(5), 491–495 (2000). 4. J. Yang, Y. Tang, and J. Xu, “Development and applications of gain-switched fiber lasers,” Photon. Res. 1(1), 52–57 (2013). 5. B. Wu, T. Chen, J. Wang, P. 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Introduction
The strong interest in the generation of light at mid-infrared region (2-5 μm) is being driven by applications in optical sensors, trace gas detection, military countermeasures, spectroscopy and medical diagnosis [1][2][3][4][5].With the fast development of mid-infrared photonics, the search for efficient and cost-effective light sources at wavelength approaching 3 μm is more and more urgent.
To date, fluoride fibers doped with Er 3+ , Ho 3+ and Dy 3+ et al. have been successfully utilized to develop high power radiation at ~3 μm [6][7][8].For example, in 2010, a diodepumped tunable 3 μm laser with a output power of the order of 10 W was realized in Er 3+ doped ZBLAN fiber [9].In 2011, a maximum output power of 20.6 W at 2.825 μm in singlemode operation from erbium doped all-fiber was reported and the slope efficiency was up to 35.4% in passively cooled condition [10].In addition, a 24 W liquid-cooled CW 3 μm laser with a multimode-core Er-doepd ZBLAN fiber was also developed along with an optical-tooptical efficiency of 14.5% [11].On the other hand, 3 μm laser with output power of 0.77 W at a slope efficiency of 12.4% was achieved from Ho 3+ doped fluoride fiber pumped by 1150 nm laser diodes (LDs) in 2011 [12].Dy 3+ doped ZBLAN fiber laser was also reported for 3 μm laser operation and its output power was ~0.1 W with a slope efficiency of 23% [8].The laser was pumped by an Yb 3+ doped silica fiber laser centered at 1088 nm [8].Although 3 μm laser can be obtained from fluoride fibers doped Ho 3+ and Dy 3+ , the higher output power was restrained due to the lack of high-efficient and high-power pump sources.Furthermore, complex design is needed to obtain 3 μm laser output and optical-optical coupling efficiency is relatively low for Ho 3+ and Dy 3+ doped fiber [7,8,10].On the contrary, Er 3+ doped fluoride fiber is currently the most convenient ~3 μm fiber laser since high power LDs are readily available for the 980 nm absorption band of Er 3+ .However, higher and more stable power output from Er 3+ doped fluoride fiber is difficult to be achieved without efficient and adequate cooling technique [10,11].Hence, the search for an appropriate glass host with excellent thermal stability and chemical durability is urgent since high thermal stability can efficiently resist the thermal damage and improve output power when incident pumping power is enhanced.
Recent decades have witnessed the great development of optical glasses, including fluoride, fluorophosphate, tellurite, bismuthate, germanate glass, etc [13][14][15][16][17].Among all kinds of glasses mentioned above, germanate glass has robust mechanical quality, low maximum phonon energy of 900 cm −1 and large solubility of rare earth ions [18,19].Moreover, the combination of high infrared transmittance in a wide wavelength region (~6.5 μm), superior thermal stability and chemical durability makes it an attractive infrared material [20,21].In the family of germanate glasses, the glasses based on barium gallogermanate glass (BGG) system possess good optical properties and glass-forming ability [22].Previous work has reported optical characteristics of BGG glass acting as a window for high energy laser system in the near-infrared wavelength range [22].Unfortunately, germanate glass has some disadvantages, such as high melting temperature, high viscosity and a high concentration of hydroxyl groups that cause a strong absorption band around 2.7 μm and depress the transmittance in 2.5-5 μm region [23].Fortunately, it has been reported that fluoride cannot only reduce glass viscosity for the purpose of energy conservation, but also decrease the content of OH -of glass and improve fluorescence efficiency with an efficient energy transfer of rare earth ions.It has been demonstrated that the properties of BGG glass can also be modified by adding other components such as La 2 O 3 and Y 2 O 3 [24].Besides, germanate glass containing Y 2 O 3 has been investigated for the purpose of structure and nearinfrared emissions [25,26].However, population dynamics for mid-infrared radiation, to our knowledge, have less been reported in Er 3+ doped germanate glass.Previous studies mainly focused on qualitative analysis of mid-infrared emission spectra [27][28][29].
The aim of this paper is to investigate mid-infrared spectroscopic properties and energy transfer mechanism in Er 3+ doped germanate glasses with the substitution of Y 2 O 3 for La 2 O 3 .Population dynamics of upper and lower levels for Er 3+ : 4 I 11/2 → 4 I 13/2 transition have been analyzed in detail based on I-H model, rate equation and Dexter's theory.It is expected that this work can provide useful guide for investigating population dynamics of mid-infrared emissions.

Experimental procedures
The investigated glasses have the following compositions in mol %: 65GeO 2 -15Ga 2 O 3 -5BaO-(10-x) La 2 O 3 -xY 2 O 3 -5NaF-0.5Er 2 O 3 (x = 0, 5, 10), denoted as GLY1, GLY2 and GLY3, respectively.The raw materials were prepared from the high purity GeO 2 , Ga 2 O 3 , BaO, La 2 O 3 , Y 2 O 3 , NaF and Er 2 O 3 powder.Well mixed raw materials (10 g) were placed in an alumina crucible and melted at 1400 °C for 50 min in air atmosphere.The melts were quickly poured on preheated stainless steel mold and annealed for 6 h near the temperature of glass transition (T g ).Subsequently, the annealed samples were fabricated and polished to the size of 10 × 10 × 1.5 mm 3 for optical performance measurements.
The glass transition temperature (T g ), crystallization onset temperature (T x ) and crystallization peak temperature (T p ) were characterized by a NetzschSTA449/C differential scanning calorimeter (DSC) at a heating rate of 10 K/min.The sample refractive indices and densities were measured by means of the prism minimum deviation method and the Archimedes principle using distilled water as immersion liquid, respectively.The absorption spectra from 350 to 1640 nm were recorded with a Perkin-Elmer Lambda 900UV/VIS/NIR spectrophotometer with the resolution of 1 nm.The fluorescence spectra in the range of 500-700 nm and 2600-2800 nm were measured by TRIAX550 spectrophotometer pumped at 980 nm LD with the output power of 600 mW.The decay curves at 1.53 μm fluorescence were obtained with light pulses of the 980 nm LD with the same power and HP546800B 100-MHz oscilloscope.The same conditions for different samples were maintained so as to get comparable results.All the measurements were performed at room temperature.

Absorption spectra
Figure 1 depicts absorption spectra of Er 3+ doped germanate glasses in the range of 360-1640 nm.It can be seen that ten absorption bands centered at 1530 nm, 980 nm, 800 nm, 652 nm, 542 nm, 521 nm, 488 nm, 451 nm, 407 nm and 378 nm corresponding to the ground state 4 I 15/2 to higher levels 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 + 4 F 3/2 ), 2 H 9/2 and 4 G 11/2 are labeled.The shape and the peak positions of each transition for Er 3+ doped germanate glass are very similar to those in other Er 3+ -doped glasses [13,16,30].It is indicated that Er 3+ ions are homogeneously incorporated into the germanate glassy network without obvious cluster in the local ligand field.The observed minor divergence may be attributed to the difference of ligand field strength [27].It is noted that no evident changes about the absorption intensity and peak positions occur with the replacement of Y 2 O 3 for La 2 O 3 , suggesting the similar glassy nature.In addition, apparent absorption band at 980 nm can be observed, which coincides with the commercially available and cost-effective 980 nm laser diode.The inset of Fig. 1 shows the enlarged 980 nm absorption band of Er 3+ ions for clear comparisons.It is revealed that the absorption coefficients at 980 nm are very similar for the three prepared samplers.Thus, efficient mid-infrared emission is expected to be achieved by 980 nm pumping.

J-O intensity parameters and radiative properties
The absorption spectra of Er 3+ ions serve as a basis for understanding their spectroscopic properties.The Judd-Ofelt (J-O) theory has been widely used to derive J-O parameters from the absorption spectra.Various radiative properties of fluorescent levels of Er 3+ ions in the present glasses can be calculated based on J-O parameters by the procedure described elsewhere [31][32][33].According to J-O theory, the measured and calculated oscillator strengths of Er 3+ ions for various levels are obtained and listed in Table 1.Besides, the results are also compared with other glass systems.The oscillator strengths for present samples are higher than those of fluoride and germanate glass, while are lower than those of tellurite glass [27,30,34].The divergence is due to the different glass compositions and ligand field environment around Er 3+ ions.Furthermore, 4 I 15/2 → 2 H 11/2 and 4 I 15/2 → 4 G 11/2 transitions have significantly higher oscillator strengths compared to other transitions, which are well-known hypersensitive transitions.They are sensitive to small changes of environment around Er 3+ ions [35].From Table 1, the calculated oscillators are in good agreement with the measured ones.The root mean square deviation δ r.m.s is calculated to be 0.3 × 10 −6 , indicating the reality and validity of the results.The calculated J-O intensity parameters of Er 3+ in present samples and other glasses are tabulated in Table 2.The intensity parameters follow the trend of Ω 2 >Ω 4 >Ω 6 .This trend is similar to those observed for tellurite, germanate and bismuthate glass [16,34,36], but is different from fluoride glass [27].It is noticed that the J-O parameters do not show the obvious changes with the substitution of Y 2 O 3 for La 2 O 3 .According to the previous researches, parameter Ω 2 is closely related to the hypersensitive transitions [17].The higher the oscillator strength of the hypersensitive transition is, the larger the value of Ω 2 becomes.It is well known that the hypersensitivity is related to the covalency parameter through the nephelauxetic effect and it can be attributed to the increasing polarizability of the ligands around Er 3+ ions [17].The Ω 2 value of present work is larger than those of fluoride and bismuthate glass [16,27], while is comparable to those of tellurite and germanate glass [34,36].It is suggested that the prepared glasses possess higher polarizability and covalency.Furthermore, the Ω 2 is also affected by the asymmetry of Er 3+ ions sites that is reflected in the crystal field parameter [37].The larger Ω 2 means higher asymmetry in crystal field environment around Er 3+ ions.On the other hand, Ω 6 depends less on the local environment nearby Er 3+ ions than Ω 2 but is more dependent on the overlap integrals of the 4f and 5d orbits [38].The Ω 6 of prepared glass is higher than those of germanate and bismuthate glass whereas a little lower than those of fluoride and tellurite glass as shown in Table 2.As a result, the developed germanate glasses possess higher covalency and overlap integrals of the 4f and 5d orbits.[16] Based on the J-O intensity parameters, the spontaneous radiative transition probability (A rad ), branching ratios (β) and radiative lifetimes (τ rad ) have been determined and listed in Table 3.It can be seen that the calculated A rad for Er 3+ : 4 I 11/2 → 4 I 13/2 transition is as high as 36.45s −1 , which is evidently larger than that of fluoride glass (29.04 s −1 ) [27] and comparable to that of tellurite glass (34.4 s −1 ) [39].Higher radiative transition probability provides larger opportunity to achieve better laser action [27,35].It is expected that efficient mid-infrared radiations can be achieved in prepared glasses.As is shown in Fig. 2, the 2.7 μm emission band is asymmetric in Er 3+ doped glasses.In order to evaluate the 2.7 μm broadband emission property, it is more reasonable to choose the effective emission bandwidth (Δλ eff ) rather than the full width at half maximum (FWHM).According to fluorescence spectra, the effective emission bandwidth Δλ eff can be defined as max ( ) where I max is the peak emission intensity and I(λ) is the emission intensity at wavelength λ.The Δλ eff is calculated to be 61 nm, which is higher than that of Ge-Ga-S glass [35].It makes germanate glass a potential candidate for broadband amplifier around 2.7 μm.In an effort to further understand the 2.7 μm radiative performance, the stimulated absorption (σ abs (λ)) and emission cross sections (σ em (λ)) have been computed derived from Füchtbauer-Ladenburg equation [40] and McCumber theory [41] as follows: where λ is the emission wavelength.A rad is the radiative transition probability of Er 3+ : 4 I 11/2 → 4 I 13/2 transition as shown in Table 3. c is the velocity of light.n is the refractive index of glass.I(λ) is the 2.7 μm fluorescence intensity, and I(λ)dλ is the integrated fluorescence intensity.Z l and Z u are partition functions of the lower and upper manifolds, respectively.ε is the net free energy demanded to excite one Er 3+ from the 4 I 13/2 to 4 I 11/2 state at the temperature of T. Figure 3 displays the absorption and emission cross sections at 2.7 μm in Er 3+ doped germanate glass.It can be obtained that the peak absorption (σ peak abs ) and emission cross sections (σ peak em ) of the present sample are 1.36 × 10 −20 cm 2 and 1.61 × 10 −20 cm 2 , respectively.The σ peak em of the prepared glass is substantially higher than those of tellurite (0.486 × 10 −20 cm 2 ) [39], bismuthate (0.661 × 10 −20 cm 2 ) [16] and fluoride glass (0.898 × 10 −20 cm 2 ) [35], while it is comparable to those of fluorotellurite (1.82 × 10 −20 cm 2 ) [42] and ZBYA glass (1.66 × 10 −20 cm 2 ) [43].For a laser medium, it is generally desirable to ensure that the emission cross section is as large as possible to provide high gain [44].Hence, the developed germanate glass is a promising laser material for mid-infrared applications.Additionally, the gain characteristics of the amplifier depend on the product of σ em and Δλ eff [45].A larger product results in better amplification behavior.Hence, Er 3+ doped germanate glass is predicted to be an effective gain medium that can be applied to broadband amplifiers in mid-infrared region due to its bigger emission cross section and wider effective emission bandwidth at 2.7 μm.

Energy transfer mechanism analysis
In order to elucidate clearly the mid-infrared fluorescence behaviors, the energy level diagram and energy transfer mechanism are proposed based on previous investigations [27,46] and presented in Fig. 4.
When the sample is pumped by 980 nm LD, the Er 3+ ions in the ground state are excited to the 4   To enhance 2.7 μm emission, it is necessary to increase the ions of 4 I 11/2 level and reduce the population of 4 I 13/2 level simultaneously.In Fig. 4, the ESA1 and ETU1 processes can decrease the population accumulation in 4 I 11/2 level, while ESA2 and ETU2 can help to reduce ions in lower laser level of 2.7 μm emission.For the purpose of estimating the influence of these processes on 2.7 μm fluorescence, upconversion emission spectra and 1.53 μm lifetimes have been determined and discussed.

Evolution of upconversion fluorescence
In general, upconversion emission spectra can be used to elucidate the population behavior in 4 I 11/2 level.It is well known that the ESA1 and ETU1 processes benefit to the upconversion emissions and, however, limit the ions accumulation in 4 I 11/2 level.In order to enhance the Er 3+ : 4 I 11/2 → 4 I 13/2 transition for 2.7 μm radiation, it is necessary to restrict the ESA1 and ETU1 processes.
Figure 5 shows the visible upconversion emission spectra of Er 3+ doped germanate glass.Three intense emission bands centered at 524 nm, 547 nm and 648 nm can be observed, which correspond to the 2 H 11/2 → 4 I 15/2 , 4 S 3/2 → 4 I 15/2 and 4 F 9/2 → 4 I 15/2 transitions, respectively.Moreover, the intensities of green and red light emissions do not show the obvious divergence when La 2 O 3 is substituted by Y 2 O 3 in prepared samples.It is indicated that the ESA1 and ETU1 processes are not more active when Y 2 O 3 is used to substitute La 2 O 3 .Thus, ions accumulation of Er 3+ : 4 I 11/2 level could be achieved.To demonstrate the upconversion emission mechanism, the power dependence of the upconversion signals for present sample has been analyzed and the results are depicted in Ln-Ln plots of the inset of Fig. 5.In upconversion process, the upconversion emission intensity I up increases in proportion to the kth power infrared excitation intensity I IR , that is, where k is the number of IR photons absorbed per visible photon emitted [47].Values of 1.92, 1.75 and 1.77 in present samples were obtained for k corresponding to 524 nm, 547 nm and 648 nm emission bands, respectively.The results indicate that the green and red light emissions are all predominantly populated by a two-photon absorption process.Hence, the upconversion transition processes in Fig. 4 is reasonable.I-H model can be used to estimate the energy transfer processes among Er 3+ ions and their interaction mechanism, which is expressed as [48] 3 0 0 ( ) exp (0) where s is 6, 8 or 10 depending on whether the dominant mechanism of interaction is dipoledipole, dipole-quadrupole or quadrupole-quadrupole, respectively.τ 0 is the intrinsic lifetime of Er 3+ : 4 I 13/2 level.The energy transfer parameter (Q) is defined as where Γ(1-3/s) is the gamma function, which 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 quadrupolequadrupole 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.Then, the energy transfer rate (C DA ) can be given by ( ) Via fitting Eq. ( 4) to the decay curves at 1.53 μm emissions for s = 6, the lifetime (τ 0 ) and energy transfer parameter (Q) have been obtained.Then, energy transfer rate (C DA ) is calculated using Eq. ( 6) and the results are listed in Table 4.It can be concluded that the experimental data coincide well with the fitted curves as displayed in Fig. 6(a).This indicates that the energy transfer among Er 3+ ions takes place due to dipole-dipole interactions.Moreover, the calculated parameters are reliable.It can be seen from Table 4 that the lifetime, energy transfer rate and energy transfer parameter all increase with the substitution of Y 2 O 3 for La 2 O 3 .The increased Q and C DA values indicate that population inversion between 4 I 11/2 and 4 I 13/2 level is achieved more easily when Y 2 O 3 is added to glasses and, therefore, 2.7 μm emission is improved as demonstrated in Fig. 2.Although I-H model has been utilized to prove the population evolution of Er 3+ : 4 I 13/2 level, the concrete energy transfer upconversion process of 4 I 13/2 level (ETU2: 4 I 13/2 + 4 I 13/2 → 4 I 9/2 + 4 I 15/2 ) requires to be analyzed in detail for further understanding 2.7 μm fluorescence behaviors.Therefore, rate equation is developed to estimate the population of 4 I 13/2 level [49].It is assumed that the Er 3+ ions are only distributed in 4 I 15/2 (n 1 (t)) and 4 I 13/2 (n 2 (t)) levels.Moreover, the ions in 4 I 13/2 level can either decay radiatively to ground state or undergo ETU process and no apparent ESA process.According to energy level diagram shown in Fig. 4, the expressions can be obtained as follows where R 0 is the pump rate of Er 3+ ions, which is defined as Pσ abs /Ahv, here, P is pump power.σ abs is the absorption cross section at the pump wavelength.A is the area of a pump light beam and hν is the pump photon energy.τ 0 is the measured lifetime of 4 I 13/2 level.C ETU is the energy transfer upconversion coefficient, and n Er is the concentration of Er 3+ ions.To fit the decay curves of 4 I 13/2 level and determine the C ETU values, we have to solve the rate equations mentioned above.It is assumed that other processes have no effects on the population of 4 I 13/2 level after the pump power is switched off (R 0 = 0) and then Eq. ( 8) can be rewritten as By solving the differential Eq. ( 10), the fitting function can be calculated as where n 2 (0) is the excited Er 3+ ion concentration after the pump source turns off (t = 0).By solving the Eq. ( 8) and ( 9) in the steady state condition (dn 2 (t)/dt = 0), n 2 (0) can be determined as follows ( ) ( ) By way of fitting Eq. ( 11) combined with Eq. ( 12) to the normalized decay curves of 1.53 μm emissions as shown in Fig. 6 The energy transfer microscopic parameter derived from Dexter's theory has been widely utilized to investigate the energy transfer process among rare earth ions, which can be evaluated by the calculations of the absorption and emission cross sections of rare earth ions [13,50,51].The dipole-dipole interaction among Er 3+ ions has been proved by I-H model.For a dipole-dipole interaction, the microscopic energy transfer probability between donor (D) and acceptor (A) ions can be denoted as [51,52] 6 ( ) where R is the distance between donor and acceptor.The C D-A is the energy transfer constant that can be expressed as follows [52] 6 where R C is the critical radius of the interaction and τ D is the intrinsic lifetime of the donor excited level.When phonons participate in the considered process, the energy transfer coefficient (C D-A ) can be determined by the following equation [52] ( ) where c is the light speed.n is the refractive index.g D low and g D up is the degeneracy of the lower and upper levels of the donor, respectively.0 ω  is the maximum phonon energy.kT n e ω − = −  is the wavelength with m phonon creation.In present work, the donor and acceptor both are Er 3+ ions.
To calculate the energy transfer microscopic parameters of Er 3+ , we firstly determined the absorption and emission cross sections of Er 3+ at 1.53 μm and 980 nm as displayed in Fig. 7.It can be found that the absorption cross section overlaps well with emission cross section for Er 3+ : 4 I 11/2 → 4 I 15/2 transition, as is the same with 1530 nm radiations.Therefore, efficient energy transfer among Er 3+ ions can be realized with hardly assistance of phonons.Table 5 summarized the energy transfer microscopic parameters of Er 3+ : 4 I 11/2 → 4 I 11/2 and 4 I 13/2 → 4 I 13/2 processes in germanate glass and the number of phonons assisted energy transfer as well as percentage of phonons.It is found that zero phonon is necessary to assist energy transfer from Er 3+ to adjacent Er 3+ ions.Besides, the energy transfer microscopic parameter for 4 I 13/2 level is more than ten times larger than that of 4 I 11/2 level, indicating that 4 I 13/2 level has more opportunity to transfer its ions to the same level nearby compared to 4 I 11/2 level.Thus, the population inversion for 2.7 μm emission is readily realized for Er 3+ doped germanate glass and efficient mid-infrared radiation can be determined.acts as a network former in the structure and make the island shape network unit repolymerisation by forming Ge-O-Y bond [25].In order to evaluate the thermal stability of prepared samples, the glass forming ability criterion, ΔT (T x -T g ) is obtained, which is usually used to measure the glass stability [35].A large ΔT means the strong inhibition of nucleation and crystallization.To estimate more comprehensively the thermal stability of developed samples, the parameter S is employed and defined by [53] ( ) The thermal stability parameter S reflects the resistance to devitrification after the formation of the glass.(T p -T x ) is related to the rate of devitrification transformation of the glassy phases.Besides, the high value of (T x -T g ) delays the nucleation process.The obtained glass transition temperature (T g ), onset crystallization temperature (T x ), top crystallization temperature (T p ), thermal stability ΔT and the parameter S in various glasses are summarized in Table 6.It can be seen that the ΔT and S are both higher than those of fluorophosphate [54], bismuthate [16] and ZBLAN glass [29].It is suggested that the prepared glasses possess better thermal stability and the ability of anticrystallization.In addition, T g is also an important factor for laser glass.High glass transition temperature provides good thermal stability to resist thermal damage at high pumping intensities [29].The prepared samples have much higher T g compared with other glass systems as shown in Table 6.Therefore, Er 3+ doped germanate glass along with excellent thermal performance might have potential applications in lasers and amplifiers.

Conclusion
In summary, Er 3+ activated germanate glasses were prepared.Thermal stability, optical absorption and mid-infrared spectroscopic properties were investigated.The prepared glass has high spontaneous radiative transition probability (36.45 s −1 ) and large stimulated emission cross section (1.61 × 10 −20 cm 2 ) at 2.7 μm.Moreover, upconversion emission spectra and fluorescence decay of 4 I 13/2 level were determined to unravel the mid-infrared emission behaviors.Decay curves of 4 I 13/2 level were fitted well to I-H model with s = 6, signifying that the energy transfer among Er 3+ ions was dominated by dipole-dipole interactions.Via the developed rate equation model, energy transfer upconversion process of Er 3+ : 4 I 13/2 level was investigated numerically.Furthermore, Dexter's theory was utilized to calculate the population evolution of upper and lower levels of the 2.7 μm transition.Population behaviors of Er 3+ : 4 I 11/2 → 4 I 13/2 transition demonstrate that the prepared germanate glass is a promising candidate applied in mid-infrared laser and amplifier.This work may provide helpful guide for the investigation of population behaviors of mid-infrared radiations.

Fig. 4 .
Fig. 4. Energy level diagram and energy transfer sketch of Er 3+ pumped at 980 nm.

Fig. 5 .
Fig. 5. Visible upconversion emission spectra of Er 3+ doped germanate glass.The inset is the power dependence of upconversion emission intensity in Ln-Ln scale.3.4.2.Luminescence decay from the 4 I 13/2 level Figure 6 displays the decay curves of 4 I 13/2 level in Er 3+ doped germanate glass pumped by 980 LD.It is found that the decay tendency becomes slower with the replacement of Y 2 O 3 for La 2 O 3 .To shed light on the population behaviors of 4 I 13/2 level, the energy transfer processes of this energy level have been analyzed quantitatively on the basis of Inokuti-Hirayama (I-H) model and rate equations [48, 49].

Fig. 6 .
Fig. 6.Decay data (dash line) of 4 I 13/2 level monitored at 1530 nm in Er 3+ doped germanate glass together with fitting curves (solid line) via (a) I-H model and (b) rate equation model.
occupancy of the phonon mode at the temperature of T. m is the number of the phonons that participate in the energy transfer.S 0 is the Huang-Rhys factor (here is 0.31

Fig. 7 .
Fig. 7. Absorption and emission cross sections at 978 nm and 1530 nm in Er 3+ doped germanate glass.Table 5.The energy transfer microscopic parameters (C D-A ) of Er 3+ : 4 I 11/2 → 4 I 11/2 and 4 I 13/2 → 4 I 13/2 processes in germanate glass and the number of phonons assisted energy transfer as well as percentage of phonons.

Table 3 . The energy gap (ΔE), predicted spontaneous transition probability (A rad ), branching ratios (β) and calculated lifetime (τ rad ) in studied glasses for various selected levels of Er 3+ .
3.3.Mid-infrared fluorescence spectra and cross sectionsFigure 2 presents the mid-infrared fluorescence spectra in the range of 2600-2800 nm by 980 nm pumping.Obviously, an emission band centered at 2.7 μm can be observed, which can be ascribed to Er 3+ : 4 I 11/2 → 4 I 13/2 transition.Moreover, the emission intensity increases gradually with the substitution of Y 2 O 3 for La 2 O 3 , indicating that Y 2 O 3 component is more beneficial for mid-infrared fluorescence than La 2 O 3 .

Table 4 . Lifetime (τ 0 ), energy transfer upconversion coefficient (C ETU ), pumping rate (R 0 ), energy transfer rate (C DA ) and energy transfer parameter (Q) of Er 3+ : 4 I 13/2 level in prepared samples.
(b), the C ETU parameter can be obtained and the fitting results #217655 -$15.00USDReceived29Jul2014;revised 11 Sep 2014; accepted 11 Sep 2014; published 22 Sep 2014are also summarized in Table4.In Fig.6(b), it can be found that the fitted curves are well matched with the measured data, indicating the validity and reliability of the results.From Table 4, it can be obtained that the C ETU value increases with La 2 O 3 is substituted by Y 2 O 3 , proving that ETU2 process becomes stronger.The result is in good agreement with that calculated from I-H model.The stronger ETU process makes population inversion between 4 I 13/2 and 4 I 15/2 level easier and therefore, the 2.7 μm radiations are improved greatly.In addition, we have noted that the calculated lifetimes via rate equation differ slightly from those by I-H model.This may result from the divergence of fitted procedures between the two models.3.4.3.Population evolution of upper and lower level at 2.7 μm emission The energy transfer from one Er 3+ to other Er 3+ ions nearby is another important factor to affect the efficiency of 2.7 μm emissions except for energy transfer upconversion and excited state absorption processes mentioned above.To quantitatively evaluate the energy transfer process and verify the efficiency of 2.7 μm emission, the energy transfer microscopic parameters for Er 3+ : 4 I 11/2 and 4 I 13/2 levels have been calculated via Dexter theory.
Figure 8 depicts the measured DSC curves in Er 3+ doped germanate glasses.It is observed that the glass transition temperature (T g ) and crystallization peak temperature (T p ) significantly increase with the replacement of Y 2 O 3 for La 2 O 3 .It can be explained that Y 2 O 3