Spectroscopic properties and energy transfer in Er–Tm co-doped bismuth silicate glass

Optical Materials 35 (2013) 2290–2295

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Spectroscopic properties and energy transfer in Er–Tm co-doped bismuth silicate glass Xin Wang a,b,⇑, Zhilan Li a,b, Kefeng Li a, Lei Zhang a, Jimeng Cheng a, Lili Hu a a b

Key Laboratory of Materials for High Power Laser, Shanghai Institute of Optics and Mechanics, Chinese Academy of Sciences, Shanghai 201800, China University of Chinese Academy of Sciences, Beijing 100039, China

a r t i c l e

i n f o

Article history: Received 18 January 2013 Received in revised form 30 April 2013 Accepted 9 June 2013 Available online 9 July 2013 Keywords: Energy transfer Laser glass 2 lm

a b s t r a c t In this paper, we investigate the spectroscopic properties of and energy transfer processes in Er–Tm codoped bismuth silicate glass. The Judd–Ofelt parameters of Er3+ and Tm3+ are calculated, and the similar values indicate that the local environments of these two kinds of rare earth ions are almost the same. When the samples are pumped at 980 nm, the emission intensity ratio of Tm:3F4 ? 3H6 to Er:4I13/2 ? 4I15/2 increases with increased Er3+ and Tm3+ contents, indicating energy transfer from Er:4I13/2 to Tm:3F4. When the samples are pumped at 800 nm, the emission intensity ratio of Er:4I13/2 ? 4I15/2 to Tm:3H4 ? 3F4 increases with increased Tm2O3 concentration, indicating energy transfer from Tm:3H4 to Er:4I13/2. The rate equations are given to explain the variations. The microscopic and macroscopic energy transfer parameters are calculated, and the values of energy transfer from Er:4I13/2 to Tm:3F4 are found to be higher than those of the other processes. For the Tm singly-doped glass pumped at 800 nm and Er–Tm co-doped glass pumped at 980 nm, the pumping rate needed to realize population reversion is calculated. The result shows that when the Er2O3 doping level is high, pumping the co-doped glass by a 980 nm laser is an effective way of obtaining a low-threshold 2 lm gain. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction In recent years, Tm3+-doped glasses for 2 lm lasers have received considerable attention because of their valuable applications, such as in the high-resolution spectroscopy of low-pressure gases, laser medicine surgery, eye-safe laser radar, and so on [1–3]. Tm3+-doped glass is highly attractive because of the crossrelaxation process (3H4 + 3H6 ? 3F4 + 3F4) that offers the possibility of 200% pumping quantum efficiency. However, to realize this process, the doping level must be high, which may induce concentration quenching caused by the self-generated quenching center [4]. Meanwhile, Er3+-doped glasses have absorption bands at the commercial diode wavelengths 800 nm and 980 nm, and the energy transfer from Er3+:4I13/2 to Tm3+:3F4 has a very high efficiency [5]. Therefore, co-doping Er3+ and Tm3+ may be a new way of obtaining 2 lm emission. To date, most Er–Tm co-doped glasses are applied in broadband amplifiers and up-conversion emissions [6–8]. A high slope efficiency of 72% has been obtained using Tm doped fiber pumped by Er–Yb co-doped fiber [9]. However, research on Er–Tm co-doped glass focusing on 2 lm emission is limited. ⇑ Corresponding author at: Key Laboratory of Materials for High Power Laser, Shanghai Institute of Optics and Mechanics, Chinese Academy of Sciences, Shanghai 201800, China. Tel.: +86 18721784025. E-mail address: [email protected] (X. Wang). 0925-3467/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optmat.2013.06.020

In this work, a kind of bismuth silicate glass doped with Er2O3 and/or Tm2O3 is used to investigate the energy transfer processes. The Judd–Ofelt parameters as well as microscopic and macroscopic energy transfer coefficients are obtained. The rate equation method is used to explain the spectroscopic property variation with the rare earth ion doping level.

2. Experiment Glasses with composition in mol% 50SiO2–33Bi2O3–17PbO– xTm2O3–yEr2O3 were prepared by a conventional quenching method. The first set of samples had fixed Tm2O3 (x = 0.5) and varied Er2O3 (y = 0, 0.25, 0.5, 0.75, 1, 1.5, 2) contents, and are hereafter denoted as E0, E0.25, E0.5, E0.75, E1, E1.5, and E2, respectively. The second set had fixed Er2O3 (y = 0.5) and varied Tm2O3 (x = 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5) contents, and are denoted as T0, T0.25, T0.5 (E0.5), T0.75, T1 and T1.5, respectively. All raw materials are analytically pure powders. The glass samples are melted at 1050 °C and annealed at 465 °C. For optical and spectroscopic property measurements, the samples were cut and polished to 20  20  1 mm3. The refractive index and density of the samples were measured by the prism minimum deviation method and the Archimedes method using distilled water as an immersion liquid. The absorption spectra were recorded by a PerkinElmer Lambda 900 UV/

X. Wang et al. / Optical Materials 35 (2013) 2290–2295

VIS/NIR spectrophotometer. The emission spectra were measured with an Edinburg FLS920 spectrometer. The Raman spectra were detected with a Renishaw invia Raman microscope using the 488 nm excitation line. All measurements were conducted at room temperature. 3. Results and discussion 3.1. Absorption spectra and Judd–Ofelt analysis The absorption spectra of the samples are recorded at room temperature from 400 nm to 2100 nm. For clarity, only the absorption spectra of E0, T0, and T0.5 are shown in Fig. 1. The absorption peaks are labeled with the corresponding energy levels. The absorption at 980 nm is found to entirely originating from Er3+, whereas the absorption at 800 nm is mostly from Tm3+. The spectroscopic intensity parameters (X2, X4, and X6) of Er3+ and Tm3+ are calculated based on the Judd–Ofelt theory [10–12], and the results are shown in Table 1. For the two types of rare earth ions, the intensity parameters follow the trend as X2 > X4 > X6. All intensity parameters of Tm3+ and Er3+ in this kind of glass are similar, indicating that the local environments of Tm3+ and Er3+ are nearly the same. X2 is related to environment of rare earth ion. If the rare ions exist at the more asymmetric site, X2 will be larger. It is reported that X6 in glasses can be increased by decreasing the covalency between rare earth and oxide ions [13]. As shown in Table 1, the X2 and X6 in present glass is smaller than that in yttria–alumina–silica glass indicating that the rare earth site in present glass is less asymmetric and more covalent. The calculated spontaneous transition probabilities and lifetimes are listed in Table 2. During the calculation, it is should be note that only when the selection rule (DS = DL = 0, DJ = 0, ±1) is fulfilled the magneticdipole contributions are considered. The magnetic transitions are almost independent of the neighboring atoms. 3.2. Emission properties when pumped at 800 nm The emission spectra of the samples with varied Er2O3 content pumped by an 800 nm laser are shown in Fig. 2. Three peaks are localized at 1470, 1810, and 1540 nm, and the corresponding transitions are 3H4 ? 3F4 (Tm3+), 3F4 ? 3H6 (Tm3+), and 4I13/2 ? 4I15/2 (Er3+). The 1810 nm emission intensity is enhanced by co-doping with Er2O3, whereas the 1470 nm emission is compressed. This change is due to the energy transfer process. The overlap of emission bands of the Tm3+:3H4 ? 3F4 and Er3+:4I13/2 ? 4I15/2 transitions induces the transfer from Tm:3H4 to Er:4I13/2 and compresses the

T0

0.5

Optical density (a.u.)

T0.5 E0

0.4

0.3

0.2

0.1

0.0 500

1000

1500

Wavelength (nm) Fig. 1. Absorption spectra of three samples.

2000

2291

1470 nm band emission. The energy transfer from Er:4I13/2 to Tm3+:3F4 enhances the emission at 1810 nm. To investigate the influence of the Er2O3 content variation on the emission property, the ratios of emission intensities are displayed as functions of the Er2O3 concentration in Fig. 3. Given the emission overlap of the 1470 and 1540 nm bands, 1420 nm fluorescence is selected to indicate the Tm3+:3H4 ? 3F4 emission. With increased Er2O3 content, the intensity ratio of the 1540 nm band to the 1420 nm band increases, indicating effective energy transfer from Tm3+:3H4 to Er3+:4I13/2. The intensity ratios I1540/I1810 and I1810/I1420 also increase with increased Er2O3 concentration. The emission spectra of the samples with varied Tm2O3 content pumped by an 800 nm laser are shown in Fig. 4. The emission band based on the Er3+:4I13/2 ? 4I15/2 transition can be effectively quenched by Tm2O3, even at the low Tm2O3 doping level of 0.25 mol%. With increased Tm2O3 content, the band with a peak at 1540 nm decreases and the 1810 nm band is enhanced. This finding is due to the more effective energy transfer from Er:4I13/2 to Tm:3F4 at a higher acceptor (Tm3+) doping level. 3.3. Emission properties when pumped at 980 nm The emission spectra of the samples with varied Er3+ content pumped by a 980 nm laser are shown in Fig. 5. To avoid secondorder dispersion of the pumping laser, only the fluorescence below 1910 nm is detected. The peak intensity at 1810 nm is weaker than that at 1540 nm when the doping level is low. With increased Er2O3 doping level, the emission intensity of the 3F4 ? 3H6 transition is enhanced. The emission spectra of the samples with varied Tm3+ content pumped by a 980 nm laser are not shown because of their similar shape. However, the peak emission intensity ratios of the Tm3+:3F4 ? 3H6 transition to the Er3+:4I13/2 ? 4I15/2 transition with different Er2O3 and Tm2O3 contents are shown in Fig. 6. With increased Er2O3 and Tm2O3 concentrations, the energy transfer process from Er:4I13/2 to Tm:3F4 is enhanced because of the enhanced emission intensity ratio of the Tm3+:3F4 ? 3H6 transition to the Er3+:4I13/2 ? 4I15/2 transition. 3.4. Lifetimes The lifetimes of the Er:4I13/2 and Tm:3F4 energy levels are obtained by fitting the decay curve using a single exponential form, and the values are shown in Table 3. The measured lifetimes of the Er2O3 singly-doped sample pumped at 800 nm and 980 nm are 5.74 and 8.9 ms, respectively. They are higher than those calculated by the Judd–Ofelt theory and that may come from the radiation trapping process because of the large overlap between the absorption and emission as shown in Fig. 8. The large refractive index (2.0) of present glass induces big Fresnel reflection and enhances the radiation trapping. Such big difference of calculated and measured lifetimes of Er3+ has been reported in Chalcogenide glass [17]. With increased Tm2O3 content, the lifetime of Er:4I13/2 decreases because of the effective energy transfer from Er:4I13/2 to Tm:3F4. When the sample is pumped by an 800 nm laser, the energy transfer process from Tm:3H4 to Er:4I13/2 is more efficient because more Tm3+ ions occupy the 3H4 level. This finding suggests that the value of the Er:4I13/2 lifetime pumped by a 980 nm laser decreases faster than that pumped at 800 nm with increased Tm2O3. The lifetime of Tm:3F4 decreases with increased Tm2O3 content because of concentration quenching. However, the lifetime of the 3F4 level when pumped by a 980 nm laser is longer than that pumped by an 800 nm laser. When the samples are excited by 800 nm laser, the incident light is mainly absorbed by Tm3+ ions, while by 980 nm laser, all the incident light is absorbed by Er3+. Only part of 3F4 ions are excited by the transfer process from

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Table 1 Judd–Ofelt parameters of Er3+ and Tm3+ in glasses. Tm3+

Glasses

Er3+ 20

X2 (10 T0 E0 T0.5 Silica YAS

2

cm )

X4 (10

3.26 2.92 6.23 6.98

20

2

cm )

X6 (10

1.66 1.26 1.21 0.17

20

2

cm )

0.92 0.92 1.16 1.65

Reference

X2 (10

20

Aed (s1)

Amd (s1)

Lifetime (ms)

250.48 226.41 49.58 219.47 104.91 2369.00 122.80 144.99 4.67 1765.18 286.64 22.46 37.08

171.56 226.41 27.43 219.47 68.37 2369.00 122.80 144.99 4.67 1765.18 286.64 22.47 37.08

78.92 0 22.15 0 36.55 0 0 0 0 0 0 0 0

3.99 3.62

6.97 542.34 201.78 3345.40 63.49 152.11 1942.32 8.18 526.64 415.53

6.97 542.34 84.12 3345.40 44.39 152.11 1942.32 8.18 396.18 415.53

0 0 117.67 0 19.10 0 0 0 130.46 0

0.24

I13/2 ? I15/2 I11/2 ? 4I15/2 ?4I13/2 4 I9/2 ? 4I15/2 ?4I13/2 4 F9/2 ? 4I15/2 ?4I13/2 ?4I11/2 ?4I9/2 4 S3/2 ? 4I15/2 ?4I13/2 ?4I11/2 ?4I9/2 4

Tm3+

3

F3 ? 3H4 ?3H5 ?3F4 ?3H6 3 H4 ? 3H5 ?3F4 ?3H6 3 H5 ? 3F4 ?3H6 3 F4 ? 3H6

Emission intensity (a.u.)

280.0k 240.0k 200.0k

3.08 0.38

cm )

X6 (10

2

cm )

0.86

This work

3.92 3.80 6.04

1.10 0.60 1.85

0.78 0.30 1.34

[14,15] [16]

0.35 1540/1810 1810/1420 1540/1420

0.30

250 200

0.25 0.20

150

0.15

100

0.10

50

0.05 0

0.47

0.00

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

Er2O3 concentration (mol%) Fig. 3. Emission intensity ratios as functions of the Er2O3 concentration when the samples are pumped at 800 nm in glasses.

0.46

10 1.87

9

2.41

8

Emission intensity (a.u.)

4

X4 (10

20

1.30

Intensity ratio

A (s1)

4

cm )

2

Intensity ratio

Er

Transition

20

3.49

Table 2 Spontaneous transfer probabilities and lifetimes of Er3+ and Tm3+ in 50SiO2–33Bi2O3– 17PbO glass.

3+

2

E0.25 E0.5 E1 E2

T0 T0.25 T0.5

7

T0.75

6

T1.5

5 4 3 2 1

160.0k

0 1200

1400

120.0k 80.0k

1800

2000

2200

Fig. 4. Emission spectra of 0.5 mol% Er2O3-doped 50SiO2–33Bi2O3–17PbO samples pumped at 800 nm with varied Tm2O3 content.

40.0k 0.0 1200

1600

Wavelength (nm)

1400

1600

1800

2000

2200

Wavelength (nm) Fig. 2. Emission spectra of 0.5 mol% Tm2O3-doped 50SiO2–33Bi2O3–17PbO samples with varied Er2O3 contents pumped at 800 nm.

Er:4I13/2 to Tm:3F4, when the incident light absorbed by Tm3+, but when the samples pumped at 980 nm, all the Tm3+ at 3F4 energy level is excited by the transfer process. Because the lifetime of Er:4I13/2 is longer than that of Tm:3F4, the latter is prolonged as the sample is codoped with Er and Tm and will be longer when pumped at 980 nm than 800 nm.

3.5. Rate equations All the change trends can be explained by solving the rate equations. The energy level diagram is drawn based on the absorption spectra and shown in Fig. 7. The numbers used to mark the corresponding levels and energy transfer processes considered in the rate equations are also shown in Fig. 7. Thus, when the samples pumped by 800 nm laser, the rate equations are established as follows:

dn4 =dt ¼ Rn1 r1 þ k81 n1 n8  ðA42 þ W 42 þ A41 Þn4

ð1Þ

dn2 =dt ¼ ðA42 þ W 42 Þn4 þ k80 10 n1 n8  k25 n2 n5  ðA21 þ W 21 Þn2

ð2Þ

X. Wang et al. / Optical Materials 35 (2013) 2290–2295

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9 E0.25

8

Emission intensity (a.u.)

E0.5 7

E0.75

6

E1.5 E2

5 4 3 2 1 0 1300

1400

1500

1600

1700

1800

1900

Wavelength (nm)

Fig. 7. Energy diagram of Er3+ and Tm3+.

Fig. 5. Emission spectra of some 0.5 mol% Tm2O3-doped 50SiO2–33Bi2O3–17PbO samples pumped at 980 nm with varied Er2O3 content.

n8 ¼ 5.0 4.5

n4 k81 n1 Rr1 n1 ¼ þ n8 A42 þ A41 þ W 42 A42 þ A41 þ W 42   k81 n1 þ k80 10 n1 þ A86 þ W 86 þ A85 k58  þ Rr2 n5 Rr 2

Er

4.0

Tm

3.5

1810/1540

Rr2 n5 k81 n1 þ k80 10 n1 þ A86 þ W 86 þ A85 þ k58 n5

ð5Þ

ð6Þ

3.0 2.5 2.0 1.5 1.0

n2 W 42 þ A42 n4 k80 10 n1 ¼  þ n8 k25 n5 þ A21 þ W 21 n8 k25 n5 þ A21 þ W 21

ð7Þ

n6 A86 þ W 86 þ 2k58 n5 k25 n5 n2 ¼ þ  n8 A65 þ W 65 A65 þ W 65 n8

ð8Þ

0.5 0.0 -0.2 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

n6 A86 þ W 86 þ 2k58 n5 k25 n5 þ A21 þ W 21 ¼  n2 A65 þ W 65 k80 10 n1 þ ðW 42 þ A42 Þn4 =n8

2.2

Er2O3 or Tm2O3 concentration (mol%)

þ Fig. 6. Emission intensity ratios (I1810/I1540) as functions of the Er2O3 and Tm2O3 concentrations in bismuth silicate glasses when the samples are pumped at 980 nm.

Table 3 Measured lifetimes of the samples pumped at 800 nm and 980 nm. Sample

Pumped at 800 nm

Pumped at 980 nm

4

3

4

3

5.74 1.26 0.94 0.76 0.68 0.54

1.71 1.38 1.32 1.13 0.90

8.90 1.36 0.90 0.71 0.55 Too weak

2.14 1.64 1.59 1.31 0.99

I13/2 lifetime (ms)

T0 T0.25 T0.5 T0.75 T1 T1.5

F4 lifetime (ms)

I13/2 lifetime (ms)

F4 lifetime (ms)

dn8 =dt ¼ Rn5 r2  k81 n1 n8  k80 10 n1 n8  ðA86 þ W 86 þ A85 Þn8  k58 n5 n8

ð3Þ

ð4Þ

Aij is the spontaneous transition probability, Wij is the multiphonon relaxation probability, and kij is the energy transfer rate from level i to final level j. For the steady-state process, all four expressions above are equal to zero. By solving the equation, the following expressions are obtained:

ð9Þ

Given the low pump power, n1 and n5 are approximately equal to the Er3+ and Tm3+ concentrations, respectively. n4/n8 is positively proportional to n1, so n2/n8 and n6/n2 increase with increased Er3+ doping level. So the emission intensity ratios I1540/I1420 and I1810/I1540 increase with increased Er2O3 content. The rate equations can also be applied to explain the emission intensity ratio variation when the samples pumped at 980 nm. If the multi-phonon relaxation from Er:4I11/2 to Er:4I13/2 is sufficiently fast, the following rate equations can be obtained:

dn2 ¼ Rn1  k25 n2 n5  ðA21 þ W 21 Þn2 dt

ð10Þ

dn6 ¼ k25 n2 n5  ðA65 þ W 65 Þn6 dt

ð11Þ

For a steady-state process, the following expression can be obtained:

n6 k25 n5 ¼ n2 A65 þ W 65

dn6 =dt ¼ ðA86 þ W 86 Þn8 þ k25 n2 n5  ðA65 þ W 65 Þn6 þ 2k58 n5 n8

k25 n5 A65 þ W 65

ð12Þ

For a dipole–dipole interaction, the energy transfer rate k25 is directly proportional to the donor (Er3+ in this case) concentration. Thus, the emission intensity ratio of 1810 nm to 1530 nm increases with increased Er2O3 and Tm2O3 doping level. The deviation from the linear form in Fig. 6 may be due to the simplification of the rate equations.

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X. Wang et al. / Optical Materials 35 (2013) 2290–2295

Fig. 8. Absorption and emission cross-sections used to calculate the energy transfer parameters.

Table 4 The calculated macroscopic and microscopic energy transfer parameters. Energy transfer process

Tm:3H4 ? Er:4I13/2 4

3

Er: I13/2 ? Tm: F4 Tm:3H4 ? Tm:3F4

Energy migration m% phonons

CDD (10

0, 1 100, 0 0, 1 100, 0 0, 1 100, 0

16.80

6

cm /s)

31.97 16.80

The extended overlap integral method is widely used to analyze the donor–acceptor energy transfer processes [1,18,19]. The microscopic energy transfer probability between donor and acceptor ions concerning a dipole–dipole interaction can be expressed by[20]

W D—A ðRÞ ¼ C D—A =R6 ;

ð13Þ

where R is the distance between the donor and acceptor, and CD–A is the transfer coefficient. CD–A is defined as

C D—A ¼ R6C =sD ;

ð14Þ

where RC is the critical radius of the interaction and sD is the intrinsic lifetime of the donor-excited level. If phonons participate in the considered process, the transfer coefficient can be obtained by the following equation [21,22]:

6cg Dlow ð2p

Z 1 X sm  þ 1Þm 0 eð2nþ1ÞS0 ðn m!

Þ4 n2 g Dup m¼0

40

6

m% phonons

CDA (10

0,1 100, 0 0, 1 21, 79 0, 1 5, 95

12.53

cm /s) 335.62

34.67

770.10

6.54

242.45

macroscopic parameter kij of the energy transfer from energy level i to j can be calculated by

3.6. Energy transfer parameters

C D—A ¼

kDA (1020 cm3/s)

Energy transfer 40

rDems ðkþm ÞrAab ðkÞdk; ð15Þ g Dlow =g Dup

where c is the light speed; n is the refractive index; is the degeneracy of the lower and upper levels of the donor, respectively; hx0 is the maximum phonon energy (925 cm1 as measured by Ra  ¼ 1=ðehx0 =kT  1Þ is the average occupancy of man spectroscopy); n the phonon mode at temperature T; m is the number of phonons that participate in the energy transfer; S0 is Huang–Rhys factor; and kþ hx0 Þ is the wavelength with m phonon cream ¼ 1=ð1=k  m tion. The absorption and emission cross-sections used during the calculation are shown in Fig. 8. Using the hopping model [23], the

kDA ¼ 13ðC D—A Þ1=2 ðC D—D Þ1=2 nd :

ð16Þ

The calculated microscopic energy transfer coefficients are listed in Table 4. The calculated macroscopic energy transfer kDA parameters of the sample doped with 0.5 mol% Tm2O3 as well as the sample co-doped with 0.5 mol% Tm2O3 and 0.5 mol% Er2O3 are also listed. The microscopic energy transfer parameter of Er:4I13/2 ? Tm:3F4 is larger than that of Tm:3H4 ? Tm:3F4, indicating that the energy transfer process from Er3+ to Tm3+ is more efficient than the cross-relaxation process. The higher microscopic energy transfer parameter is caused by the larger overlap between the emission and absorption cross-sections of the corresponding transitions. The microscopic parameter of the energy transfer from Er:4I13/2 to Tm:3F4 in present glass is larger than that in tellurite [9] and bismuthate [24] glasses but smaller than in fluoride glass [1]. This energy transition with zero phonon has a large proportion in present glass inducing the large value. With the same reason, the microscopic parameter for cross relaxation (Tm:3H4 ? Tm:3F4) in present glass is larger than that in 15Bi2O3–50SiO2–10ZnO– 15Al2O3–10La2O3 glass [25]. These big microscopic parameters are beneficial for the 2 lm emission. 3.7. Evaluation of pump rate and pump power need to realize population inversion By combining Eqs. (10) with (11), the 980 nm pumping rate of the Er–Tm co-doped samples can be deduced for a steady-state process and expressed by

X. Wang et al. / Optical Materials 35 (2013) 2290–2295

R¼

ðk25 n5 þ A21 þ W 21 ÞðA65 þ W 65 Þ : k25 NEr  A65  W 65

ð17Þ

For the Tm-doped samples, the 800 nm pumping rate can be given by [26]

R¼

ðW 65 þ A65 ÞðA85 þ A86 þ W 87 þ k85 n5 Þ : W 65 þ A65 þ k85 n5

ð18Þ

The minimum 980 nm pumping rate of the sample doped with 0.5 mol% Er2O3 and 0.5 mol% Tm2O3 to realize population inversion is calculated and found to be 917.15 s1. The minimum pumping rate of the sample doped with 0.5 mol% Tm2O3 to realize population inversion is 240.94 s1. For the calculation, the following assumptions are made: (1) the occupancy of Er:4I11/2 is zero because of the fast multi-phonon relaxation to Er:4I13/2, and (2) upconversion does not occur. The sum of the radiation probability and multi-phonon relaxation rate is replaced by the reciprocal of the corresponding measured lifetime in Er or Tm singly-doped samples. The pumping rate and power to realize population reversion of the co-doped glass are 3.8 and 3.1 times higher than those of the Tm2O3 singly-doped glass. However, based on Eq. (17), with increased Er2O3 concentration, the pumping rate needed to realize population reversion decreases. When the Er3+ concentration is 3.43  1020 cm3 (0.96 mol% Er2O3), the 980 nm pumping rate needed for the co-doped glass is equal to the 800 nm pumping rate needed for the Tm2O3 singly-doped samples. When the pumping powers needed to realize population reversion are equal, the Er3+ concentration is 2.98  1020 cm3 (0.83 mol% Er2O3). Thus, the pumping Er–Tm co-doped glass by a 980 nm laser is an effective way of obtaining2 lm gain, especially at a high Er2O3 doping level. 4. Conclusion A new kind of Er–Tm co-doped bismuth silicate (50SiO2– 33Bi2O3–17PbO) glass is prepared and the Judd–Ofelt parameters of both Er3+ and Tm3+ ions are calculated. The similar J–O parameter values of Er3+ and Tm3+ ions show that the local environments of these two ions are almost the same. The variation in the emission spectra with the Er2O3 and Tm2O3 contents indicates the occurrence of energy transfer processes. The energy transfer efficiency of Er:4I13/2 ? Tm:3F4 may reach P90% at a high Tm2O3 doping level. The calculated macroscopic and microscopic energy transfer parameters show that the Er:4I13/2 ? Tm:3F4 transfer is

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more effective than the cross-relaxation between Tm3+ ions (3H4 + 3H6 ? 3F4 + 3F4) process. The pumping rate and energy needed to realize population reversion are calculated based on the rate equations. The result shows that glass with a high Er2O3 content pumped by a 980 nm laser can realize population reversion more easily than the Tm2O3 only-doped glass pumped at 800 nm. Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 60937003) and the GF Foundation (No. GXJJ11-M23). References [1] Y. Tian, R. Xu, L. Hu, J. Zhang, J. Quant. Spectrosc. Radiat. Transfer 113 (2012) 87–95. [2] R. Zhou, Y. Ju, Y. Zhang, Y. Wang, Chin. Opt. Lett. 9 (2011). 071401-1–071401-3. [3] B.M. Walsh, Laser Phys. 19 (2009) 855–866. [4] F. Auzel, J. Lumin. 100 (2002) 125–130. [5] J.P. Rainho, M. Pillinger, L.D. Carlos, S.J.L. Ribeiro, R.M. Almeida, J. Rocha, J. Mater. Chem. 12 (2002) 1162–1168. [6] L.H. Huang, A. Jha, S.X. Shen, X.B. Liu, Opt. Express 12 (2004) 2429–2434. [7] H. Jeong, K. Oh, S.R. Han, T.F. Morse, Opt. Lett. 28 (2003) 161–163. [8] R. Xu, Y. Tian, L. Hu, J. Zhang, J. Appl. Phys. 111 (2012) 033524–033527. [9] X. Xu, Y. Zhou, S. Zheng, D. Yin, X. Wang, J. Alloys Compd. 556 (2013) 221–227. [10] B.R. Judd, Phys. Rev. 127 (1962) 750–761. [11] G.S. Ofelt, J. Chem. Phys. 37 (1962) 511–520. [12] B. Walsh, Judd-Ofelt theory: principles and practices, in: B. Bartolo, O. Forte (Eds.), Advances in Spectroscopy for Lasers and Sensing, Springer, Netherlands, 2006, pp. 403–433. [13] S. Tanabe, T. Ohyagi, N. Soga, T. Hanada, Phys. Rev. B 46 (1992) 3305–3310. [14] B.M. Walsh, N.P. Barnes, Appl. Phys. B-Lasers Opt. 78 (2004) 325–333. [15] L. Le Neindre, S. Jiang, B.-C. Hwang, T. Luo, J. Watson, N. Peyghambarian, J. Non-Cryst. Solids 255 (1999) 97–102. [16] P. Jander, W.S. Brocklesby, Quantum Electron., IEEE J. 40 (2004) 509–512. [17] K. Koughia, M. Munzar, D. Tonchev, C. Haugen, R. Decorby, J. McMullin, S. Kasap, J. Lumin. 112 (2005) 92–96. [18] Y. Tian, R. Xu, L. Zhang, L. Hu, J. Zhang, J. Appl. Phys. 109 (2011) 083535. [19] R. Xu, Y. Tian, L. Hu, J. Zhang, J. Phys. Chem. A (2011) 6488–6492. [20] Q. Zhang, J. Ding, Y. Shen, G. Zhang, G. Lin, J. Qiu, D. Chen, J. Opt. Soc. Am. B 27 (2010) 975–980. [21] Q. Zhang, G.R. Chen, G. Zhang, J.R. Qiu, D.P. Chen, J. Appl. Phys. 107 (2010) 023102. [22] L.V.G. Tarelho, L. Gomes, I.M. Ranieri, Phys. Rev. B 56 (1997) 14344–14351. [23] D. de Sousa, L. Nunes, Phys. Rev. B 66 (2002). 024207-1–024207-7. [24] G. Zhao, P.-W. Kuan, H. Fan, L. Hu, Opt. Mater. 35 (2013) 910–914. [25] X. Wang, L. Hu, K. Li, Y. Tian, S. Fan, Chin. Opt. Lett. 10 (2012). 101601-1– 101601-5. [26] X. Wang, S. Fan, K. Li, L. Zhang, S. Wang, L. Hu, J. Appl. Phys. 112 (2012) 103521–103527.