Scholarly article on topic 'Mid-infrared fluorescence, energy transfer process and rate equation analysis in Er3+ doped germanate glass'

Mid-infrared fluorescence, energy transfer process and rate equation analysis in Er3+ doped germanate glass Academic research paper on "Nano-technology"

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Academic research paper on topic "Mid-infrared fluorescence, energy transfer process and rate equation analysis in Er3+ doped germanate glass"

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SUBJECT AREAS:

MATERIALS FOR OPTICS

OPTICAL MATERIALS AND STRUCTURES

ENERGY TRANSFER

Received 30 May 2014

Accepted 23 July 2014

Published 14 August 2014

Correspondence and requests for materials should be addressed to Y.T. (tianyingcjlu@ 163.com) or S.X. (sxucjlu@hotmail.com)

Mid-infrared fluorescence, energy transfer process and rate equation analysis in Er3+ doped germanate glass

Tao Wei1, Ying Tian1, Fangze Chen1, Muzhi Cai1, Junjie Zhang1, Xufeng Jing2, Fengchao Wang1, Qinyuan Zhang3 & Shiqing Xu1

1College of Materials Scienceand Engineering, China Jiliang University, Hangzhou 310018, PRChina, 2Institute of Optoelectronic Technology, China Jiliang University, Hangzhou 310018, PR China, 3State Key Lab of Luminescent Materials and Devices, and Institute of Optical Communication Materials, South China University of Technology, Guangzhou 510641, P.R. China.

Er31 doped Y2O3 and Nb2O5 modified germanate glasses with different Er31 concentrations were prepared. J-O intensity parameters were computed to estimate the structural changes due to the additions of Y2O3 and Nb2O5. The main mid-infrared spectroscopic features were investigated. To shed light on the observed mid-infrared radiative behavior, 975 nm and 1.53 mm emission spectra along with their decay lifetimes were also discussed. Moreover, the energy transfer processes of 4In/2 and %3/2 level were quantitatively analyzed. In view of the experimental lifetimes, the simplified rate equation was utilized to calculate the energy transfer upconversion processes of upper and lower laser level of 2.7 mm emission. The theoretical calculations are in good agreement with the observed 2.7 mm fluorescence phenomena. Finally, the stimulated emission and gain cross sections were calculated and the results indicate that Er31 doped germanate glasses have great potential for mid-infrared application.

Recently, rare earth ions doped solid state lasers operating at mid-infrared (~3 mm) wavelength have attracted considerable interests. This is mainly due to the strong absorption band by water around this wavelength, which makes mid-infrared fiber lasers suitable for various applications including medical surgery, remote sensing, and atmosphere pollution monitoring1-4. The merits of good beam quality, high conversion efficiency, power scalability and excellent heat dissipation promote fiber lasers greatly developed compared with bulk solid state lasers5. So far, mid-infrared fluoride glass fibers have been researched widely when doped with various rare earth ions such as Er31, Ho31 and Dy31, etc6-10.

Because of the lack of commercially high-power pump diodes that can emit 1100 nm or 1300 nm wavelength energy, Ho31 and Dy31 doped fiber lasers have great difficulty in the realization of achievable output power. On the contrary, Er31 doped fiber lasers are currently the most practical and convenient high power 3 mm laser, since the 980 nm or 808 nm absorption bands of Er31 are readily excited by available high power AlGaAs and InGaAs laser diodes (LDs)11. In terms of this idea, in 2007, X. Zhu, et al. demonstrated the 2.78 mm laser emission with 9 W of output power as well as the slope efficiency of 21.3% when pumped at 975 nm from Er31 doped ZBLAN fiber laser12. In 2009, S. Tokita, et al. reported 24 W of output power at 2.8 mm with slope efficiency of 14.5% using an Er31 doped ZBLAN fiber13. However, the output power of 24 W was achieved in liquid-cooled condition owing to inferior thermal stability of the host13. Afterwards, higher output power has hardly been reported in Er31 doped fluoride fiber lasers. Although fluoride glass fiber is the most efficient gain media for ~3 mm laser due to very low maximum phonon energy (—500 cm1), its poor glass forming ability and troublesome fabrication process make it difficult for practical applications.

In order to solve the questions mentioned above and enhance output power of—3 mm laser, search for a more appropriate glass host is urgent. Up to now, various glass hosts have been investigated for mid-infrared applications, including germanate, tellurite, bismuthate and fluorophoshate glasses14-17. Germanate glass, especially barium gallogermanate glass, has been of great interest due to the excellent combination of the infrared transparency, thermal stability, chemical durability and availability in large-size and complex shaping18. In addition, compared with silicate, borate or phosphate glasses, barium gallogermanate glass has a relatively low maximum phonon energy (800 — 900 cm21). For Er31 ions, the energy gap between 4I11/2 and 4I13/2 level is about 3700 cm21. Thus, low phonon energy is beneficial for high radiative decay rate of Er31: 4I11/2r 4I13/2 transition and corresponding mid- infrared emission. However, some disadvantages hamper its further applications in the mid-

400 500 600 700 Temperature (°C) Figure 1 | DSC curves of prepared (a) YxEr and (b) NxEr samples (x= 1,2,3).

infrared fields, such as high melting temperature, high viscosity and a large amount of hydroxyl groups19. To address the questions, fluorides involving BaF2 and LiF have been added into germanate glass so as to reduce the concentration of hydroxyl groups as well as lowering glass melting temperature for energy conservation19. At the same time, it has been demonstrated that the Y2O3 and Nb2O5 additions can be used to modify the properties of barium gallogermanate glass20,21. The addition of Y2O3 component is expected to improve thermal stability and reduce OH2 content in glass due to its collection of non-bridging oxygen of glass, while Nb2O5 is expected to enhance radiative transition probability and emission cross section for mid-infrared emission due to its high refractive index21.

Hence, Y2O3 and Nb2O5 modified germanate glasses were prepared and mid- infrared spectroscopic properties were investigated in present work. In general, the long lifetime of the lower laser level 4I13/2 level compared with the upper level of 4I11/2 level leads a population bottleneck. Thus, it limits the CW laser transition and output power. Fortunately, the population bottleneck problem in Er31 doped laser systems have been overcome effectively to improve corresponding mid-infrared emission and it can be explained by energy transfer upconversion (ETU) process between two Er31 ions5. Moreover, the ETU: 4I13/21 4I13/2R 4I15/2+ 4I9/2 process can lead to a fast depletion of the lower laser level and the realization of CW operation as well as recycling of the energy. However, only qualitative analysis on enhanced mid-infrared emission has been

carried out, up to now. Hence, energy transfer processes of Er31: 4I11/2 and 4I13/2 level have been analyzed quantitatively in this work. According to the measured lifetimes, the energy transfer upconversion processes of upper and lower level of 2.7 mm emission were calculated based on the simplified rate equation model so as to elucidate the observed mid-infrared radiative behavior.

Experimental

The investigated samples have the following molar compositions in mol%: 62GeO2-9Ga2O3-13BaF2-7Y2O3(Nb2O5)-9LiF-xEr2O3, denoted as YxEr and NxEr, respectively (x=1, 2, 3). Batches of 20 g samples were well-mixed and melted in aluminum crucibles at 1400°C for 45 min. Then melts were cast on a preheated steel plate and annealed for several hours around the glass transition temperature. All the annealed samples were fabricated and polished to the size of 10 mm X 10 mm X 1.5 mm for the optical property measurements.

The characteristic temperatures (temperatures of glass transition Tg, onset crystallization peak Tx and top crystallization peak Tp) of prepared samples were characterized using a Netzsch STA 449/C differential scanning calorimetry (DSC) at a heating rate of 10 K min"1. The densities and refractive indexes of samples were tested by the Archimedes method and the prism minimum deviation method, respectively. Furthermore, absorption spectra were recorded with a Perkin-Elmer Lambda 900 UV/VIS/NIR spectro-

Table 1 | The temperatures of glass transition (Tg), onset crystallization (Tx) and peak crystallization (Tp) as well as thermal stability parameters AT and S in various glass systems (mol%)

Samples

Tg(°C)

Tp (°C)

AT (°C)

References

Tx (°C)

Table 2 | Oscillator strength and wave number of Er3+ for selected transitions in « all prepared samples

Transition Wave number (cm 1) Oscillator strength fexp (x10~6)

N2Er Y2Er Silicate31 Tellurite32 Fluoride30

4Il5/2—4Il3/2 6532 1.947 1.562 1.681 2.64 1.67

4|15/2r4|11/2 10225 0.793 0.66 0.509 0.89 0.55

4Il5/2—4l9/2 12516 1.004 0.413 0.265 0.35 0.32

4|15/2r4F9/2 15361 2.534 2.234 1.804 3.21 2.14

4|15/2r4S3/2 18450 0.308 0.296 0.310 0.65 0.51

4Il5/2—2Hii/2 19231 10.175 8.656 5.696 13.73 3.44

4Il5/2—4F7/2 20492 1.897 1.748 1.548 2.32 0.87

photometer in the range of 360-1700 nm. The emission spectra (950-1025 nm, 1400-1700 nm and 2550-2800 nm) were measured via a Triax 320 type spectrometer upon excitation of 808 nm. Besides, the decay curves of 975 nm and 1530 nm were determined by light pulses of the 808 nm LD and HP546800B 100-MHz oscilloscope. All the measurements were carried out at room temperature.

Results and discussion

Thermal stability. Fig. 1 shows the measured DSC curves of present samples. In order to analyze the effect of Er2O3 content on the thermal property, Table 1 lists the characteristic temperatures such as temperatures of glass transition (Tg), onset crystallization (Tx) and peak crystallization (Tp) as well as the calculated thermal stability parameters AT and S in present work. For comparison, other values reported are also tabulated in Table 1. For YxEr sample, the characteristic temperatures have no evident changes with the increase of Er2O3 content whereas the increment of Er2O3 concentration leads to the enhanced characteristic temperatures for NxEr sample. In addition, the Tg, Tx and Tp of Y1Er sample are higher than those of N1Er sample along with the same tendency of

other concentrations. On the other hand, the AT, which is defined as Tx-Tg, of all present samples is similar, about 135°C. It is much higher than those of fluorophosphate and MgO/Al2O3/SiO2/TiO2 system, as shown in Table 1. It is noted that the Tg of Y2O3 modified sample is much higher than those of fluorophosphate and NxEr glasses while lower than that of MgO/Al2O3/SiO2/TiO2 system22. The reason that YxEr sample has higher glass transition temperature compared with NxEr sample may be ascribe to the fact that Y2O3 in YxEr sample can collect glass network and strengthen the structure of the network21.

The parameter S is more accurate to estimate the glass stability, which reflects the resistance to devitrification after the formation of the glass and can be defined by22

AT x(Tp -Tx)

where (Tp-Tx) is related to the rate of devitrification transformation of the glassy phases. On the other hand, the high value of AT delays the nucleation process. It can be observed from Table 1 that the S values in present samples are both larger than those of fluoropho-sphate glass and MgO/Al2O3/SiO2/TiO2 system22,23. It is indicated

Table 2 | Oscillator strength and wave number of Er3+ for selected transitions in all prepared samples

Oscillator strength fexp (x 10"6)

Transition

Wave number (cm ])

Silicate31

Tellurite32

Fluoride30

4Il5/2R4Il3/2

4|15/2r4|11/2

4Il5/2R4l9/2

4II5/2R4FÇ/2

4'I5/2R4S3/2

4Il5/2R2Hii/2

115/2-

6532 10225 12516 15361 18450 19231 20492

1.947 0.793 1.004 2.534 0.308 10.175 1.897

1.562 0.66 0.413 2.234 0.296 8.656 1.748

l.68l 0.509 0.265 1.804 0.310 5.696 1.548

2.64 0.89 0.35 3.21 0.65 13.73 2.32

1.67 0.55 0.32 2.14 0.51 3.44 0.87

Table 3 | The J-O parameters V (x10220cm2) of Er31 in various glass systems

Samples V2 V4 V6 Sr.m.s (x 10 6) Ref.

Y2Er 5.22 ± 0.04 1.65 ± 0.04 1.10 ± 0.10 0.15 Present work

N2Er 6.10 ± 0.03 1.92 ± 0.18 1.08 ± 0.07 0.14

5Al(PO3)3-95fluorides 2.68 1.65 1.27 0.17 17

50ZrF4-33BaF2 -17(LaF3+AlF3+YF3) 3.08 1.46 1.69 0.32 24

55Bi03/2-30Ge02-15Na01/2 4.89 1.62 0.77 0.12 34

60Ge02-20Na01/2-20Nb05/2 5.97 0.83 0.48 2.1 35

that excellent thermal stability can be achieved from the prepared glasses, which is greatly beneficial to optical fiber drawing. It is worth mentioned that the S of NxEr sample is larger than that of YxEr sample, indicating that anti-crystallization ability for Nb2O5 modified germanate glass is superior than that of Y2O3 modified one. This phenomenon might be explained by the fact that field strength of Nb51 ion is higher than that of Y31 ion, and higher field strength can restrain the crystallization behavior of glass21.

Absorption spectra and J-O analysis. Fig. 2 displays the absorption spectra in Er31 doped germanate glasses. Ten absorption bands corresponding to the ground state 4I15/2 to other higher levels are labeled in this figure. For YxEr series, absorption intensity is proportional to the Er31 concentration as is the same with NxEr samples. In order to compare the difference of YxEr and NxEr, the inset (a) of Fig. 2 shows the absorption spectra of Y3Er and N3Er sample. It is observed that similar shape and peak positions occur in various glasses. It is also similar to other reported glasses16,24. Minor divergence can be found from absorption spectra for different glasses and can be devoted to the various strengths ofligand fields. It is noted that two very sharp peaks corresponding to the transitions of 4I15/2r 4G11/2 and 4I15/2r 2H11/2 are evident, which is designated as hypersensitive transitions (HSTs)25. They are sensitive to the local environment around rare earth ions. The intensity divergence between YxEr and NxEr results from the different composition of the germanate glasses and the changes in Er31 surrounding local environment.

The solubility of rare earth ions can be estimated roughly by the variation of the absorption intensities with Er31 concentration. Variation of integral absorption intensities of the 4I15/2r 4I13/2 transition as a function of Er31 content is presented in the inset (b) of Fig. 2. It shows good linearity for YxEr and NxEr, which means excellent solubility of rare earth ions for the current melting scheme in both series. Additionally, it is observed from Fig. 2 that an absorption band around 800 nm is obvious, suggesting that Er31 doped germanate glasses can be pumped by commercially available and low-cost 808 nm LD.

According to Judd-Ofelt (J-O) theory26,27, the magnitude of the measured and calculated oscillator strengths can be determined as well as some important spectroscopic parameters of trivalent rare earths doped glasses. Details of the theory and method have been well described earlier28,29. Hence only results are presented here. The

experimental oscillator strengths of Er3+ in germanate glasses are listed in Table 2 and compared with other results reported. It can be seen from Table 2 that the measured oscillator strengths in present work are higher than those of Er31 doped silicate and fluoride glasses30,31 but lower than those of Er31 doped tellurite glass32. This behavior is in good agreement with the instinct rule of environment in glasses surrounding the rare-earth ions. It is worth noting that the oscillator strength corresponding to Er31: 4I15/2r 2H11/2 (HST) is much higher than those of other transitions for all glass systems. Moreover, it is interesting to note that the oscillator strength of the HST shows great changes in different glasses, which results from the different ligand environment in the vicinity of Er31 ions. In addition, the N2Er possesses larger oscillator strengths in comparison with Y2Er, suggesting the additions of Nb2O5 and Y2O3 have substantial influence on the local ligand around Er31 ions.

To further investigate the effects of Nb2O5 and Y2O3 on the local environment of glasses, the J-O parameters V (1=2,4,6) of Er31 in present work have been determined and shown in Table 3. At the same time, the values of other glass systems doped with Er31 are also listed in Table 3 for comparison. The root mean square deviation (Sr.m.s) between the calculated (fexp) and experimental (fcal) oscillator strengths can be as low as 0.14 X 1026 and 0.15 X 1026, respectively, for N2Er and Y2Er as revealed in Table 3, indicating that the calculation process is reliable. According to jQrgensen and Reisfeld33, V2 is strongly affected by covalency and V6 is closely related to the rigidity of glass host. As is shown in Table 3, the obtained V2 values in this work are both higher than those of fluorophosphate, bismuthate and fluoride glasses17,24,34, and comparable to that of other germanate glass35. This behavior is derived from the more covalent nature of germanate glass. It is reported by Tanabe et al that V6 increases with the drop of local basicity in the ligands36-38. The present glasses possess higher V6 compared with bismuthate and germanate glasses and it is slightly lower than those of fluorophosphate and fluoride glasses, indicating the lower local basicity of present germanate glasses. Furthermore, the V2 of N2Er is larger than that of Y2Er, while the V6 between them is similar. It is suggested that higher covalency in N2Er can be determined in comparison with Y2Er. It might be ascribed to the fact that the covalency of Nb-O bond is stronger than that of Y-O bond and the effect of Nb-O bond on the local ligand field around Er31 is larger than that of Y-O bond21.

Some important radiative parameters can be calculated by using the intensity parameters V to estimate the potential mid-infrared

Table 4 | The spontaneous radiative transition probability (Arad), branching ratios (b) and radiative lifetimes (trad) of Er31 for selected level

transition in prepared samples

Y2Er N2Er

Transition A(s ') b (%%) Trad (ms) A(s ') b (%%) Trad (ms)

4|13/2r4|15/2 55.42 100 6.43 179.55 100 5.57

4l11/2 *4115/2 48.35 83.07 5.60 175.48 83.32 4.75

44 111/2 * 113/2 30.24 16.93 - 35.12 16.68 -

4l9/2R4l15/2 41.69 74.45 5.25 187.98 77.53 4.12

44 |9/2r I13/2 45.70 24.01 - 51.27 21.14 -

4l9/2R4l11/2 2.93 1.54 - 3.21 1.32 -

—•-'—■-'—■—1—■—1—■—i—^—1-■-1-■-1-■--"T—■—i—■—i—■—i—■—i ■ ■ -I

2550 2600 2650 2700 2750 2800 960 980 1000 1020 1450 1500 1550 1600 1650 1700

Wavelength (nm) Wavelength (nm) Wavelength (nm)

2550 2600 2650 2700 2750 2800 960 980 1000 1020 1450 1500 1550 1600 1650 1700

Wavelength (nm) Wavelength (nm) Wavelength (nm)

Figure 3 | 2.7 mm, 975 nm and 1.53 mm fluorescence spectra in Er31 doped germanate glasses.

emission performance. The detailed procedure has been well described earlier29. Table 4 displays the spontaneous radiative transition probability (Arad), branching ratios (b) and radiative lifetimes (trad) of Er31 for selected level transition in germanate glasses. The results show that the Arad for Er31: 4I11/2r 4I13/2 transition in Y2Er and N2Er samples can be as high as 30.24 and 35.12 s21, respectively, both are higher than those of ZBLAY (26.10 s"1)25 and ZBLA (19 s21)39. High radiative transition probability provides a better

opportunity to achieve 2.7 mm fluorescence from Er3

4I13/2 transition.

Fluorescence spectra. To investigate the effect of additions of Y2O3 and Nb2O5 on the mid-infrared emission properties in Er31 doped germanate glasses, the 2.7 mm fluorescence spectra of Y2Er and N2Er, as an example, were measured upon the excitation of 808 nm LD and revealed in Fig. 3(a). It can be seen that one emission peak centered at 2.7 mm occurs, which corresponds to the Er31: 4I11/2r 4I13/2 transition. Besides, the emission intensity of Y2Er is evidently stronger than that of N2Er. It is indicated that Y2O3 modified germanate glass is more suitable for mid-infrared material. Subsequently, the mid-infrared emission spectra of Y2O3 modified germanate glass with different Er31 concentrations were determined, as shown in Fig. 3(b). It is found that the intensity of 2.7 mm fluorescence increases with increasing Er2O3 concentration and no luminescence quenching happens.

To clearly elucidate the 2.7 mm emission phenomenon, the 975 nm and 1.53 mm fluorescence spectra were tested by 808 nm LD pumping, as shown in Fig. 3(c), (d), (e) and (f). Furthermore, the simplified energy level diagram and energy transfer mechanism of Er31 is given in Fig. 4 so as to readily comprehend the relation of 2.7 mm, 975 nm and 1.53 mm emissions. As is shown in Fig. 4, when

the sample is radiated by 808 nm LD, the ions in ground state 4I15/2 are excited to the 4I9/2 level. Due to the small energy gap between 4I9/2 and 4I11/2 level, ions of 4I9/2 level relax non-radiatively to the next 4I11/2 level and then the 975 nm and 2.7 mm radiations take place according to the 4In/2R %5/2

and 4I

11/2R I13/2 transitions, respectively. Finally, the ions in 4I13/2 level decay radiatively to the ground state and the 1.53 mm emission occurs. According to Fig. 3(c), the 975 nm emission of Y2Er is weaker than that of N2Er. It might be attributed to the divergence of local environment surrounding Er31 ions and leading to different fluorescent behaviors between Y2Er and N2Er. Decay curves will be determined to further elucidate the divergence of fluorescent behavior in next section. It means that more ions

Figure 4 | The simplified energy level diagram and energy transfer mechanism of Er31.

Figure 5 | Decay curves of (a) 975 nm;(b)1.53 mm emissions in Y2Er and N2Er samples and Decay curves of (c) 975 nm;(d)1.53 mm emissions in YxEr samples with various Er31 concentration excited by 808 nm LD.

in 4I11/2 level have undergone the 4I11/2r 4Ii3/2 transition for Y2Er compared with N2Er. Hence, the 2.7 |im emission intensity of Y2Er is higher than that of N2Er. In addition, it can be obtained from Fig. 3(d) that the intensity of 1.53 mm emission for Y2Er is slightly higher than that of N2Er, which is in good agreement with the behavior of 2.7 mm fluorescence.

Furthermore, the 975 nm and 1.53 mm fluorescence spectra of YxEr samples doped with different Er31 concentrations were determined and given in Fig. 3(e) and (f). It is found that the 975 nm and 1.53 mm fluorescence intensities increase with the increment of Er31 content. They are in good accordance with the behavior of 2.7 mm fluorescence. However, they can not be used to comprehend the origin of 2.7 mm emission behavior. Hence, more comprehensive discussions will be carried out to understand the mid-infrared fluorescence behavior in the next section.

Decay curves, energy transfer evaluation and rate equation analysis. Fluorescence lifetime is an important parameter to estimate the ions behavior of the excited state. Higher lifetime is indicative of slower ions decay and is beneficial for population accumulation. Fig. 5 (a) and (b) signifies the decay curves of 975 nm and 1.53 mm emissions in Y2Er and N2Er by 808 nm LD pumping. According to the measured decay curves, the fluorescence lifetime can be determined by the time of the intensity of 1/e. From Fig. 5(a), it can be found that the 4I11/2 level lifetime of Y2Er is longer than that of N2Er while the 4I13/2 level lifetimes between Y2Er and N2Er are similar as shown in Fig. 5(b). It is suggested that the upper

level of 2.7 mm emission for Y2Er is more favorable for ions accumulation and Y2Er is more helpful for population inversion between 4I11/2 and 4I13/2 level compared with N2Er. Hence, the more intense 2.7 mm radiation can be observed from Y2O3 modified germanate glass as demonstrated in Fig. 3(a).

Fig. 5(c) and (d) shows the decay curves of 975 nm and 1.53 mm emissions in YxEr samples with various Er31 concentration excited by 808 nm LD. It is expected to elucidate the origin of enhanced 2.7 mm emission with Er31 concentration. From Fig. 5 (c) and (d), it is observed that the 975 nm lifetime increases basically from 192 to 239 ms, whereas the 1.53 mm lifetime reduces from 7.16 to 3.31 ms. Thus, ions in 4I11/2 level can be accumulated effectively and ions in 4I13/2 level can be greatly reduced. Hence, population inversion corresponding to 2.7 mm emission is easier to achieve with increasing Er31. Therefore, 2.7 mm emission intensity increases with the increment of Er31 in present work.

Energy transfer coefficient is another important parameter to affect 2.7 mm fluorescence characteristics. As is shown in Fig. 6, in order to obtain excellent mid-infrared emission, it is necessary to weaken the ET1 and strengthen ET2 process. To verify the Y2Er is more superior for mid-infrared material compared with N2Er, energy transfer coefficients of both glasses were calculated and analyzed. The energy transfer processes ET1 and ET2 can be evaluated by the calculation of the absorption and emission cross sections. The extended overlap integral method is extensively utilized to investigate energy transfer processes between donor and acceptor. For a dipole-dipole interaction, the microscopic energy transfer probabil-

Figure 6 | The absorption and emission cross sections at 975 nm and 1.53 mm.

ity between donor (D) and acceptor (A) ions can be denoted as4

Wd-A (R) =

where R is the distance between donor and acceptor, the CD-A is the energy transfer constant that can be expressed as follows41

^ _R6c

CD-A = -

where RC is the critical radius of the interaction and tD is the intrinsic lifetime of the donor excited level. When phonons participate in the considered process, the energy transfer coefficient (CD-A) can be determined by the following equation40,41

In this work, the donor and acceptor both are Er3+ ions. For the purpose of obtaining the CD-A values of ET1 and ET2 processes, firstly the absorption and emission cross sections at 975 nm and 1.53 mm need to be calculated.

The absorption cross section (sabs) is defined as

2.303 xOD(A) Sabs (A) =-Nil--(5)

where OD(l), N, l represent the optical density which is obtained from absorption spectra, Er31 doping concentration in this paper and sample thickness, respectively. The stimulated emission cross-section (sem) is calculated according to the McCumber theory42 as follows

CD-A =

6csL (2p)4 n2 gD

0 m (n+i)

JSL( iZ) <stths (i)di (4)

a em (l) = Sabs (1)(Zi / Zu ) exp[(s - Hv)/kT]

where c is the light speed, n is the refractive index, and g^ is the degeneracy of the lower and upper levels of the donor, respectively. hv0is the maximum phonon energy, n=1/(ehv0=kT — 1) is the average occupancy of the phonon mode at the temperature of T. m is the number of the phonons that participate in the energy transfer. S0 is the Huang-Rhys factor and = 1/ (1/1 — mhv0) is the wavelength with m phonon creation.

where Zi and Zu are partition functions of the lower and upper manifolds, respectively. e is the net free energy demanded to excite one Er3+ from the 4Ii5/2 to the excited state at the temperature of T.

According to equation (5) and (6), the absorption and emission cross sections were determined and displayed in Fig. 6 (a) and (b). Further, the energy transfer coefficients of ET1 and ET2 processes were computed by equation (4) and they are listed in Table 5. The results indicate that the energy transfer ET1 and ET2 processes in Y2Er and N2Er glasses scarcely need phonon assistance. From Fig. 6,

Table 5 | Calculated microscopic parameters for energy transfer process, the number of phonons the percentage of each phonon participated in the process in Y2Er and N2Er samples Sample Energy transfer N (number of phonons) (% phonon assisted) necessary to assist the energy transfer and Cd-a (x 10 40 cm6 s)

Y2Er ETl (4Iii/2-4Iii/2) 0 1 2.68

99.99 0.01

ET2 (4Ii3/2-4Ii3/2) 0 1 10.4

N2Er ETl (4Iii/2-4Iii/2) 0 1 4.17

99.986 0.014

ET2 (4Ii3/2-4Ii3/2) 0 1 13.0

Figure 7 | A plot of (N0/Nt)exp(-t/x) vs. (1 - exp(-t/x)) for 975 nm and 1.53 mm decay data. The inset is the slope values by linear fitting of the data.

we observe overlap to a large extent between absorption and emission cross sections at 975 nm and 1.53 mm. Thereby, ET1 and ET2 processes mainly undergo resonant energy transfer and scarcely phonon assistance is needed. For ET1 process, the energy transfer coefficient (CD-A) of Y2Er is dramatically lower than that of N2Er while the CD-A of Y2Er is slightly smaller than that of N2Er for ET2 process. Smaller energy transfer coefficient of 4I11/2 level and larger CD-A of 4I13/2 state indicate that Y2Er is more beneficial for population inversion and more efficient 2.7 mm emission can be achieved compared with N2Er.

For YxEr glass system, the mid-infrared intensity increases with increased Er31 concentration. To explain the behavior, the rate equation model is proposed and the simplified rate equation is given as

follows43

dNt Nt 2

-7- =---2CETuNt2

where CETU is energy transfer upconversion coefficient. Assuming that when the pumping source is turned off, feeding from higher level

to lower level 1 and 2 becomes negligible as shown in Fig. 6. The decaying behavior is mainly governed by the steady-state populations. By solving this simplified rate equation, the formula can be obtained as

(No/ Nt) exp (-1/ t) -1 ~2CetuNot [1 - exp (-1/ t)] (8)

where N0 is the steady-state population of level 1 and 2 immediately before switch-off. A plot of (N0/Nt)exp(-t/t) vs. (1 - exp(-t/t)) will give a slope k, which is denoted as

k~2CETuN01 (9)

Fig. 7 (a) and (b) indicate the plots of (N0/Nt)exp(-t/t) vs. (1 - exp(-t/ t)) for 975 nm and 1.53 mm decay data, respectively. By linear fitting of the data of Fig. 7, the slope values can be determined and tabulated in the inset of Fig. 7 (a) and (b), respectively. Finally, the energy transfer upconversion coefficient can be obtained using equation (9). Fig. 8 gives the dependence of energy transfer upconversion (ETU) coefficient on the Er31 concentration for 4I11/2 and 4I13/2 level.

From Fig. 8, it can be clearly seen that the CETU value substantially reduces with increasing Er31 concentration for 4I11/2 level. Lower CETU means that more ions can be accumulated in 4I11/2 level, which can enhance the 2.7 mm emission. In parallel, the CETU of 4I13/2 level increases on the whole with Er31 concentration, which is helpful to decrease the ions of 4I13/2 level by transferring energy to adjacent level. Thus, population inversion between the 4I11/2 and 4I13/2 level is greatly improved and the 2.7 mm fluorescence is enhanced with increasing Er31 concentration.

Absorption, emission and gain cross sections at 2.7 mm. On the

basis of discussions above, it can be concluded that Y3Er sample possesses optimal fluorescence characteristics. Therefore, by selecting the Y3Er, the absorption, emission and gain cross sections were calculated to further estimate its possibility as mid-infrared laser material. The stimulated emission cross section (sem) of 2.7 mm fluorescence can be determined by Fuchtbauer-Ladenburg equation44

l*Arad 1I(1)

8pcn2 J" II (l)d l

Figure 8 | The dependence of energy transfer upconversion (ETU) coefficient on the Er31 concentration for 4I11/2 and 4I13/2 level.

where Arad is the spontaneous transition probability, I(l) is the fluorescence spectra intensity. Combining equation (10) and (6),

Figure 9 | (a) Absorption and emission; (b) gain cross sections of Y3Er sample.

the absorption (sabs) and emission cross sections (sem) at 2.7 mm in Y3Er have been calculated and displayed in Fig. 9(a). It can been seen that the peak absorption and emission cross sections can reach to 10.6 X 10"21 cm2 and 12.4 X 10"21 cm2, respectively. It is reported that high emission cross section is extremely useful to determine the possibility to achieve laser effect25. The sem of present work is much higher than those of bismuth germanate glass (6.61 X 10"21 cm2)45, fluoride glass (9.16 X 10"21 cm2)24 and other germante glass (7.02 X 10"21 cm2)46. Moreover, The value of sem is also larger than that of ZBLAN (9.5 X 10"21 cm2)4, from which the 2.7 mm laser output has been achieved so far12,13. It is expected that 2.7 mm laser emission can also be obtained from the prepared germanate glass. Hence, the investigated germanate glass has potential advantages for mid-infrared applications.

Besides, the gain cross section (G) was calculated derived from sabs and sem to evaluate the mid-infrared gain properties. The room temperature gain cross section can be simply evaluated by47

G(lP) ~ Psem(l) - (1 - P)Sabs(l) (11)

where P is the population inversion given by the ratio between the population of Er31: 4I11/2 level and the total Er31 concentration. Fig. 9(b) shows the gain cross sections of Y3Er sample. It is found that the gain becomes positive when P is more than 0.4, which is similar to the case of ZBLAN3. It is indicated that a low pumping threshold can be achieved for the 2.7 mm in prepared glass.

Conclusions

Er31 doped germanate glass with additions of Y2O3 and Nb2O5 and different Er31 concentrations were prepared. Their main mid-infrared spectroscopic properties were evaluated. To elucidate clearly the mid-infrared emission behavior, the 975 nm and 1.53 mm emission spectra, their decay curves were tested and analyzed. Moreover, the energy transfer processes of 4I11/2 and 4I13/2 level have been quantitatively calculated and discussed. Based on the lifetime measurement, the simplified rate equation was used to determine the energy transfer upconversion coefficients of the upper and lower levels of 2.7 mm emission. The theoretical calculations coincide well with the observed phenomena. Furthermore, the prepared germanate glasses

possess high stimulated emission cross section (12.4 X 10"21 cm2) and a low pumping threshold, which might have potential application in mid-infrared laser.

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Acknowledgments

The authors are thankful to Zhejiang Provincial Natural Science Foundation of China (Nos.LY13F050003, R14E020004), National Natural Science Foundation of China (Nos. 61308090, 51372235, 51172252 and 51272243), overseas students preferred funding of activities of science and technology project, and International S&T Cooperation Program of China 2013DFE63070.

Author contributions

T.W. wrote the main manuscript text. X.F.J., F.Z.C. andF.C.W. checked up. Y.T. and S.Q.X. were responsible for the experiment. J.J.Z. Q.Y.Z. and M.Z.C. proposed valuable suggestions for our manuscript revised. All authors reviewed the manuscript.

Additional information

Competing financial interests: The authors declare no competing financial interests. How to cite this article: Wei, T. et al. Mid-infrared fluorescence, energy transfer process and rate equation analysis in Er31 doped germanate glass. Sci. Rep. 4, 6060; DOI:10.1038/ srep06060 (2014).

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