In this paper, mid-infrared emission properties and energy transfer mechanism were investigated in Er3+ 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−1 and 1.61 × 10−20 cm2, respectively. Corresponding upconversion emission spectra and radiative lifetimes of 4I13/2 level were determined to elucidate the mid-infrared luminescent characteristics. Moreover, population behaviors of Er3+: 4I11/2 and 4I13/2 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 Er3+ ions at 2.7 μm emissions.
© 2014 Optical Society of America
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 [1–5]. 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 Er3+, Ho3+ and Dy3+et al. have been successfully utilized to develop high power radiation at ~3 μm [6–8]. For example, in 2010, a diode-pumped tunable 3 μm laser with a output power of the order of 10 W was realized in Er3+ doped ZBLAN fiber . In 2011, a maximum output power of 20.6 W at 2.825 μm in single-mode operation from erbium doped all-fiber was reported and the slope efficiency was up to 35.4% in passively cooled condition . 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-to-optical efficiency of 14.5% . On the other hand, 3 μm laser with output power of 0.77 W at a slope efficiency of 12.4% was achieved from Ho3+ doped fluoride fiber pumped by 1150 nm laser diodes (LDs) in 2011 . Dy3+ 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% . The laser was pumped by an Yb3+ doped silica fiber laser centered at 1088 nm . Although 3 μm laser can be obtained from fluoride fibers doped Ho3+ and Dy3+, 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 Ho3+ and Dy3+ doped fiber [7, 8, 10]. On the contrary, Er3+ 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 Er3+. However, higher and more stable power output from Er3+ 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 [13–17]. 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 . Previous work has reported optical characteristics of BGG glass acting as a window for high energy laser system in the near-infrared wavelength range . 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 . 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 La2O3 and Y2O3 . Besides, germanate glass containing Y2O3 has been investigated for the purpose of structure and near-infrared emissions [25, 26]. However, population dynamics for mid-infrared radiation, to our knowledge, have less been reported in Er3+ doped germanate glass. Previous studies mainly focused on qualitative analysis of mid-infrared emission spectra [27–29].
The aim of this paper is to investigate mid-infrared spectroscopic properties and energy transfer mechanism in Er3+ doped germanate glasses with the substitution of Y2O3 for La2O3. Population dynamics of upper and lower levels for Er3+: 4I11/2→4I13/2 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.
2. Experimental procedures
The investigated glasses have the following compositions in mol %: 65GeO2-15Ga2O3-5BaO-(10-x) La2O3-xY2O3-5NaF-0.5Er2O3 (x = 0, 5, 10), denoted as GLY1, GLY2 and GLY3, respectively. The raw materials were prepared from the high purity GeO2, Ga2O3, BaO, La2O3, Y2O3, NaF and Er2O3 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 (Tg). Subsequently, the annealed samples were fabricated and polished to the size of 10 × 10 × 1.5 mm3 for optical performance measurements.
The glass transition temperature (Tg), crystallization onset temperature (Tx) and crystallization peak temperature (Tp) 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.
3. Results and discussion
3.1. Absorption spectra
Figure 1 depicts absorption spectra of Er3+ 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 4I15/2 to higher levels 4I13/2, 4I11/2, 4I9/2, 4F9/2, 4S3/2, 2H11/2, 4F7/2, (4F5/2 + 4F3/2), 2H9/2 and 4G11/2 are labeled. The shape and the peak positions of each transition for Er3+ doped germanate glass are very similar to those in other Er3+-doped glasses [13, 16, 30]. It is indicated that Er3+ 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 . It is noted that no evident changes about the absorption intensity and peak positions occur with the replacement of Y2O3 for La2O3, 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 Er3+ 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.
3.2. J-O intensity parameters and radiative properties
The absorption spectra of Er3+ 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 Er3+ ions in the present glasses can be calculated based on J-O parameters by the procedure described elsewhere [31–33]. According to J-O theory, the measured and calculated oscillator strengths of Er3+ 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 Er3+ ions. Furthermore, 4I15/2→2H11/2 and 4I15/2→4G11/2 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 Er3+ ions . From Table 1, the calculated oscillators are in good agreement with the measured ones. The root mean square deviation δr.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 Er3+ in present samples and other glasses are tabulated in Table 2.The intensity parameters follow the trend of Ω2 >Ω4 >Ω6. This trend is similar to those observed for tellurite, germanate and bismuthate glass [16, 34, 36], but is different from fluoride glass . It is noticed that the J-O parameters do not show the obvious changes with the substitution of Y2O3 for La2O3. According to the previous researches, parameter Ω2 is closely related to the hypersensitive transitions . The higher the oscillator strength of the hypersensitive transition is, the larger the value of Ω2 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 Er3+ ions . The Ω2 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 Ω2 is also affected by the asymmetry of Er3+ ions sites that is reflected in the crystal field parameter . The larger Ω2 means higher asymmetry in crystal field environment around Er3+ ions. On the other hand, Ω6 depends less on the local environment nearby Er3+ ions than Ω2 but is more dependent on the overlap integrals of the 4f and 5d orbits . The Ω6 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.
Based on the J-O intensity parameters, the spontaneous radiative transition probability (Arad), branching ratios (β) and radiative lifetimes (τrad) have been determined and listed in Table 3.It can be seen that the calculated Arad for Er3+: 4I11/2→4I13/2 transition is as high as 36.45 s−1, which is evidently larger than that of fluoride glass (29.04 s−1)  and comparable to that of tellurite glass (34.4 s−1) . 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.
3.3. Mid-infrared fluorescence spectra and cross sections
Figure 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 Er3+: 4I11/2→4I13/2 transition. Moreover, the emission intensity increases gradually with the substitution of Y2O3 for La2O3, indicating that Y2O3 component is more beneficial for mid-infrared fluorescence than La2O3. As is shown in Fig. 2, the 2.7 μm emission band is asymmetric in Er3+ doped glasses. In order to evaluate the 2.7 μm broadband emission property, it is more reasonable to choose the effective emission bandwidth (Δλeff) rather than the full width at half maximum (FWHM). According to fluorescence spectra, the effective emission bandwidth Δλeff can be defined as35]. 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 (σabs(λ)) and emission cross sections (σem(λ)) have been computed derived from Füchtbauer-Ladenburg equation  and McCumber theory  as follows: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. Zl and Zu are partition functions of the lower and upper manifolds, respectively. ε is the net free energy demanded to excite one Er3+ from the 4I13/2 to 4I11/2 state at the temperature of T.
Figure 3 displays the absorption and emission cross sections at 2.7 μm in Er3+ doped germanate glass. It can be obtained that the peak absorption (σpeak abs) and emission cross sections (σpeak em) of the present sample are 1.36 × 10−20 cm2 and 1.61 × 10−20 cm2, respectively. The σpeak em of the prepared glass is substantially higher than those of tellurite (0.486 × 10−20 cm2) , bismuthate (0.661 × 10−20 cm2)  and fluoride glass (0.898 × 10−20 cm2) , while it is comparable to those of fluorotellurite (1.82 × 10−20 cm2)  and ZBYA glass (1.66 × 10−20 cm2) . For a laser medium, it is generally desirable to ensure that the emission cross section is as large as possible to provide high gain . 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 σem and Δλeff . A larger product results in better amplification behavior. Hence, Er3+ 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.
3.4. 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 Er3+ ions in the ground state are excited to the 4I11/2 level by ground state absorption (GSA: 4I15/2 + a photon→4I11/2). Then ions in 4I11/2 level, on one hand, can decay radiatively or nonradiatively to the next 4I13/2 level and the radiative process generates the 2.7 μm fluorescence (4I11/2→4I13/2 + 2.7 μm). Hereafter, the ions in 4I13/2 level relax radiatively to the ground state and 1.53 μm emission happens (4I13/2→4I15/2 + 1.53 μm). On the other hand, the excited ions in 4I11/2 level can go on excited state absorption (ESA1: 4I11/2 + a photon→4F7/2) or energy transfer upconversion process (ETU1: 4I11/2 + 4I11/2→4I15/2 + 4F7/2) making the ions in 4F7/2 level populated. Due to the small energy gap among 4F7/2, 2H11/2 4S3/2 and 4F9/2 level, the ions of 4F7/2 level can decay to the 2H11/2, 4S3/2 and 4F9/2 level by multiphonon relaxation process (MPR). Afterwards, green light and red light emissions centered at 524 nm, 547 nm and 648 nm occur corresponding to Er3+: 2H11/2, 4S3/2→4I15/2 and 4F9/2→4I15/2 radiative transitions, respectively. Furthermore, the red light emission can also be obtained by ESA2 process (4I13/2 + a photon→4F9/2).
To enhance 2.7 μm emission, it is necessary to increase the ions of 4I11/2 level and reduce the population of 4I13/2 level simultaneously. In Fig. 4, the ESA1 and ETU1 processes can decrease the population accumulation in 4I11/2 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.
3.4.1. Evolution of upconversion fluorescence
In general, upconversion emission spectra can be used to elucidate the population behavior in 4I11/2 level. It is well known that the ESA1 and ETU1 processes benefit to the upconversion emissions and, however, limit the ions accumulation in 4I11/2 level. In order to enhance the Er3+:4I11/2→4I13/2 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 Er3+ doped germanate glass. Three intense emission bands centered at 524 nm, 547 nm and 648 nm can be observed, which correspond to the 2H11/2→4I15/2, 4S3/2→4I15/2 and 4F9/2→4I15/2 transitions, respectively. Moreover, the intensities of green and red light emissions do not show the obvious divergence when La2O3 is substituted by Y2O3 in prepared samples. It is indicated that the ESA1 and ETU1 processes are not more active when Y2O3 is used to substitute La2O3. Thus, ions accumulation of Er3+:4I11/2 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 Iup increases in proportion to the kth power infrared excitation intensity IIR, that is, , where k is the number of IR photons absorbed per visible photon emitted . 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.
3.4.2. Luminescence decay from the 4I13/2 level
Figure 6 displays the decay curves of 4I13/2 level in Er3+ doped germanate glass pumped by 980 LD. It is found that the decay tendency becomes slower with the replacement of Y2O3 for La2O3. To shed light on the population behaviors of 4I13/2 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].
I-H model can be used to estimate the energy transfer processes among Er3+ ions and their interaction mechanism, which is expressed as 
Via fitting Eq. (4) to the decay curves at 1.53 μm emissions for s = 6, the lifetime (τ0) and energy transfer parameter (Q) have been obtained. Then, energy transfer rate (CDA) 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 Er3+ 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 Y2O3 for La2O3. The increased Q and CDA values indicate that population inversion between 4I11/2 and 4I13/2 level is achieved more easily when Y2O3 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 Er3+: 4I13/2 level, the concrete energy transfer upconversion process of 4I13/2 level (ETU2: 4I13/2 + 4I13/2→ 4I9/2 + 4I15/2) requires to be analyzed in detail for further understanding 2.7 μm fluorescence behaviors. Therefore, rate equation is developed to estimate the population of 4I13/2 level . It is assumed that the Er3+ ions are only distributed in 4I15/2 (n1(t)) and 4I13/2 (n2(t)) levels. Moreover, the ions in 4I13/2 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
To fit the decay curves of 4I13/2 level and determine the CETU values, we have to solve the rate equations mentioned above. It is assumed that other processes have no effects on the population of 4I13/2 level after the pump power is switched off (R0 = 0) and then Eq. (8) can be rewritten as
By solving the differential Eq. (10), the fitting function can be calculated asEq. (8) and (9) in the steady state condition (dn2(t)/dt = 0), n2(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(b), the CETU parameter can be obtained and the fitting results are also summarized in Table 4. 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 CETU value increases with La2O3 is substituted by Y2O3, 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 4I13/2 and 4I15/2 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 Er3+ to other Er3+ 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 Er3+:4I11/2 and 4I13/2 levels have been calculated via Dexter theory.
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 Er3+ 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]52]52]
To calculate the energy transfer microscopic parameters of Er3+, we firstly determined the absorption and emission cross sections of Er3+ 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 Er3+: 4I11/2→4I15/2 transition, as is the same with 1530 nm radiations. Therefore, efficient energy transfer among Er3+ ions can be realized with hardly assistance of phonons. Table 5 summarized the energy transfer microscopic parameters of Er3+: 4I11/2→4I11/2 and 4I13/2→4I13/2 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 Er3+ to adjacent Er3+ ions. Besides, the energy transfer microscopic parameter for 4I13/2 level is more than ten times larger than that of 4I11/2 level, indicating that 4I13/2 level has more opportunity to transfer its ions to the same level nearby compared to 4I11/2 level. Thus, the population inversion for 2.7 μm emission is readily realized for Er3+ doped germanate glass and efficient mid-infrared radiation can be determined.
3.5. Thermal stability analysis
Figure 8 depicts the measured DSC curves in Er3+ doped germanate glasses. It is observed that the glass transition temperature (Tg) and crystallization peak temperature (Tp) significantly increase with the replacement of Y2O3 for La2O3. It can be explained that Y2O3 acts as a network former in the structure and make the island shape network unit repolymerisation by forming Ge-O-Y bond . In order to evaluate the thermal stability of prepared samples, the glass forming ability criterion, ΔT (Tx-Tg) is obtained, which is usually used to measure the glass stability . 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 
The thermal stability parameter S reflects the resistance to devitrification after the formation of the glass. (Tp-Tx) is related to the rate of devitrification transformation of the glassy phases. Besides, the high value of (Tx-Tg) delays the nucleation process.
The obtained glass transition temperature (Tg), onset crystallization temperature (Tx), top crystallization temperature (Tp), 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 , bismuthate  and ZBLAN glass . It is suggested that the prepared glasses possess better thermal stability and the ability of anticrystallization. In addition, Tg is also an important factor for laser glass. High glass transition temperature provides good thermal stability to resist thermal damage at high pumping intensities . The prepared samples have much higher Tg compared with other glass systems as shown in Table 6. Therefore, Er3+ doped germanate glass along with excellent thermal performance might have potential applications in lasers and amplifiers.
In summary, Er3+ 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 cm2) at 2.7 μm. Moreover, upconversion emission spectra and fluorescence decay of 4I13/2 level were determined to unravel the mid-infrared emission behaviors.
Decay curves of 4I13/2 level were fitted well to I-H model with s = 6, signifying that the energy transfer among Er3+ ions was dominated by dipole-dipole interactions. Via the developed rate equation model, energy transfer upconversion process of Er3+: 4I13/2 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 Er3+: 4I11/2 →4I13/2 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.
The authors are thankful to Zhejiang Provincial Natural Science Foundation of China (LY13F050003, R14E020004 and Q13F050009), National Natural Science Foundation of China (Nos. 61308090, 61405182, 51372235, 51472225, 51172252 and 51272243), overseas students preferred funding of activities of science and technology project, and Research project of Zhejiang Province Education Department (No. Y201224887).
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