# Optical Transition Probabilities of Er3+ Ions in ErBa3B9O18 Crystal

Authors: Ming He; Tiezheng Liu; Junling Xiu; Yuanguang Tang; Zhihua Zhang
Journal: Journal of Spectroscopy
 (2015)

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## Abstract

The optical absorption and emission intensity of luminescent and birefringent crystal ErBa3B9O18 were examined from optical absorption data based on Judd-Ofelt theory. The three intensity parameters Ω
t (t
=
2,4
,
6) are 3.10 × 10−20, 0.87 × 10−20, and 1.80 × 10−20 cm2, respectively. From the obtained intensity parameters, the radiative probabilities A
r, radiative lifetime τ
f, fluorescence branching ratios β
c, and integrated emission cross sections ∑ have been calculated. In comparison with other Er-doped luminescent crystals, ErBa3B9O18 may find application in thin disk laser.


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## Body

## 1. Introduction

Er3+ activator has attracted much attention for its two laser emissions at 2.94 μm (4I11/2 → 4I13/2) and 1.54 μm (4I13/2 → 4I15/2). The emissions have potential applications in optocommunication, sensors, or lidar system [1–3]. To now, the Er3+ ion has exhibited laser operations in various Er3+-doped crystals or glasses [4–9]. For a laser crystal, the host material should be stable and efficient. Sometimes, the emission efficiency can be limited by the relatively low concentration of luminescent centers, because the quenching effect will occur if the Er3+ ions concentration is too high. Host material determines the luminescent efficiency of the laser crystal or phosphor in many cases. Thus, it is necessary to search for new materials with higher doping tolerance to enhance the performance of the laser.Borates are well known for their applications in optical communications, nonlinear optics, luminescence material and lasers, and so forth [10–16]. A series of isostructural compounds RBa3B9O18 (R = Y, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb) [17, 18] were found to exhibit good luminescence properties under UV or X-ray excitations. These rare earth alkaline-earth isostructural compounds were first identified and structurally characterized by Li et al. [19]. They crystallize in centric space group P63/m with lattice parameters of about a
=
7.17 Å and c
=
16.97 Å. Three O atoms are bonded to one B atom and three BO3 groups form a planar hexagonal [B3O6]3− ring [20]. The parallel arranged [B3O6]3− groups can separate the R3+ ions, which makes the energy migration between two rare earth ions difficult. Taking YBa3B9O18 and ErBa3B9O18 (EBBO) as examples, the shortest distance of two Y3+ or Er3+ ions is 7.16-7.17 Å, which is long enough to limit the energy transfer between luminescent centers [20–22]. So, the quenching effect in EBBO is proved to be small and Er3+ may be an efficient luminescent center. The transition properties of the optical crystals can determine their luminescent performance. So, we performed the research on spectroscopic properties of EBBO.


## 2. Experimental

The crystals were grown by a pulling method [21]. An absorption spectrum was measured for EBBO using a crystal plate with faces (001) and about 0.4 mm thickness [23]. The absorption spectrum was measured from ultraviolet to infrared wavelength by the use of Lambda-900 UV–VIS–NIR spectrophotometer at room temperature.


## 3. Results and Discussions

The spectrum presented in Figure1 is measured in the wavelength ranges from 200 to 1700 nm. The strong absorption peaks related to Er3+ ions transitions can be assigned. The absorption bands located at 255, 376, 407, 485, 519, 650, 971, and 1539 nm corresponding to the transitions from 4I15/2 to 4D7/2, 4G11/2, 2H11/2, 4F7/2, 4H11/2, 4F9/2, 4I11/2, and 4I13/2, respectively. These strong absorption peaks show mainly the eigenmultiplets typically observed in free Er3+ ions at similar spectral position due to the weak crystal field for rare earth ions. The absorption at 1539 nm is very strong, which indicated that the transition probability of 4I15/2 → 4I13/2 is big, and the integrated emission cross section is expected to be great.Figure 1
The absorption spectra of EBBO crystal. This figure is from [23] with permission.The Judd-Ofelt theory was applied to evaluate the optical transition probabilities of Er3+ ions in EBBO. Based on Judd-Ofelt theory of the parity-forbidden electric-dipole transitions of rare earth ions [24, 25], the electric and magnetic dipole line strengths of a transition from initial J
i level to the terminal J
t level are described by
(1)
S
ed
J
i
,
J
t
=
∑
t
=
2,4
,
6
Ω
t
Φ
J
i
U
t
Φ
J
t
2
,
S
md
(
J
i
,
J
t
)
=
h
4
π
m
c
2
∑
t
=
2,4
,
6
Ω
t
Φ
J
i
L
+
2
S
Φ
J
t
2
,
where h is Planck’s constant, c is the speed of light, m is the mass of electron, and Φ
J
i
U
(
t
)
Φ
J
t is the reduced matrix elements depending on the Er3+ ions. In this work, the values of the squares of the reduced matrix elements are cited from Carnall’s calculations [26]. Ω
t (t
=
2,4
,
6) are the three intensity parameters related to crystal field. Magnetic dipole line strengths are very small compared to electric ones and can be neglected in the calculation of the parameters except for 4I15/2 → 4I13/2. The value of S
md is cited from [27] to be 0.683 × 10−20 cm2 because S
md does not vary with the host crystal.Then the measured line strengthsS
ed
meas
⁡
(
J
i
,
J
t
) from the absorption spectrum can be given by
(2)
S
ed
meas
⁡
J
i
,
J
t
=
9
n
n
2
+
2
2
∫
J
i
→
J
t
O
D
(
λ
)
d
λ
-
n
S
m
d
3
c
h
8
π
3
e
2
2
J
+
1
N
c
2.303
λ
d
9
n
n
2
+
2
2
×
∫
J
i
→
J
t
OD
λ
d
λ
-
n
S
md
,
where λ is the mean wavelength of the absorption band, OD
(
λ
) presents the measured optical density, and d is the thickness of the crystal. The concentration of Er3+ ions N
c in ErBa3B9O18 is calculated based on the crystal structure parameter. The crystal structure of ErBa3B9O18 adopts a centric space group P63/m and the lattice parameters are a = 7.1817 Å and c = 16.996 Å [21]. There are two Er3+ in one unit cell, so N
c is calculated to be 2.63 × 1027/m3. n is the refractive index, which can be obtained by Sellmeier’s equation [21], and e is the electron charge. Table 1 presents the line strengths S
ed of nine absorption peaks of Er3+ in crystal. Three intensity parameters Ω
t (t
=
2,4
,
6) were fitted by least-square method to be 3.10 × 10−20, 0.87 × 10−20, and 1.80 × 10−20 cm2.Table 1
Calculated strength parameters for Er3+ in EBBO.
Peak
Configuration
Wavelength (nm)
∫
OD
λ
d
λ (nm)
S
meas
⁡ (10−20 cm2)
S
cal (10−20 cm2)
Δ
s
.
2
1
4
I
13
/
2
1539
25.73
3.27
2.76
0.26
2
4
I
11
/
2
971
0.83
0.20
0.80
0.36
3
4
F
9
/
2
650
2.09
0.75
1.32
0.32
4
4
H
11
/
2
519
5.35
2.37
2.72
0.12
5
4
F
7
/
2
485
1.97
0.94
1.27
0.11
6
2
H
9
/
2
407
0.53
0.29
0.43
0.02
7
4
G
11
/
2
376
6.29
3.77
3.50
0.08
8
4
D
7
/
2
255
1.35
1.18
0.85
0.11
Rms-Δs. = 0.40 × 10−20 cm2, Ω
2,4
,
6 = (3.10, 0.87, 1.80) × 10−20 cm2From Judd-Ofelt theory, the electric-dipole and magnetic-dipole contributions,A
ed and A
md, of the total spontaneous emission probability are given by
(3)
A
J
J
′
=
A
ed
+
A
md
=
64
π
4
e
2
3
h
2
J
+
1
λ
3
n
n
2
+
2
2
9
S
ed
+
n
3
S
md
=
165.3
+
43.8
=
209.1
s
-
1
.The luminescence parameters can be calculated from the following equations:(4)
A
J
J
′
=
64
π
4
e
2
3
h
2
J
+
1
λ
¯
3
n
n
2
+
2
2
9
S
ed
+
n
3
S
md
1
τ
r
=
∑
J
′
A
J
J
′
β
c
=
A
J
J
′
∑
J
′
A
J
J
′
∑
J
J
′
=
A
J
J
′
λ
2
8
π
c
n
2
,
where β
c is the fluorescence branch ratio, τ
r is the radiative lifetime of a given upper level, A
J
J
′ is the transition probability of spontaneous emission, and ∑
J
J
′ is the integrated emission cross section. The calculated results are listed in Table 2.Table 2
The spectral parameters for Er3+ ions in EBBO crystal.
Transitions
Wavelength (nm)
A
ed (s−1)
A
md (s−1)
τ
r (μs)
β
c
∑
J
J
′ (10−18 cm)
4I13/2 → 4I15/2
1539
165.28
43.76
4783
1
2.243
4I11/2 → 4I15/2
971
233.32
3733
0.87
1.00
4I11/2 → 4I13/2
2778
25.85
8.68
0.13
1.212
4F9/2 → 4I15/2
650
1583.41
568
0.90
3.03
4F9/2 → 4I13/2
1156
68.49
0.04
0.42
4F9/2 → 4I11/2
1980
104.75
0.06
1.86
4F9/2 → 4I9/2
3448
2.59
0.00
0.14
4S3/2 → 4I13/2
844
852.40
983
0.83
2.75
4S3/2 → 4I11/2
1212
66.72
0.07
0.44
4S3/2 → 4I9/2
1639
97.38
0.10
1.19
2H9/2 → 4I15/2
407
1616.62
238
0.38
1.21
2H9/2 → 4I13/2
555
2044.55
0.49
2.86
2H9/2 → 4I11/2
703
477.28
0.11
1.07
2H9/2 → 4I9/2
841
18.100
0.01
0.06
2H9/2 → 4F9/2
1089
41.36
0.01
0.22
4G11/2 → 4I15/2
376
19505.40
4D7/2 → 4I15/2
255
22544.50
4I9/2 → 4I13/2
1739
72.16
4H11/2 → 4I15/2
519
5420.35
4F7/2 → 4I15/2
485
4658.79The results show that radiative probabilities (209 s−1) of 4I15/2 → 4I13/2 are comparable to those of Er:YAG (211 s−1) [28], Er
x
Y
1
-
x
Al
3
BO
3
4 (233 s−1) [29], and Er:La2CaB10O19 (262 s−1) [30]. The integrated emission cross section of 1539 nm is 2.24 × 10−18 cm, which indicates that large amplification gains near 1.54 μm are expected to be obtained. So the crystal has the potential to be a laser material with good chemical and physical properties. What is more, due to the high concentrations of Er3+ activators, EBBO may find applications in thin disk laser.


## 4. Conclusion

The spectroscopic properties of ErBa3B9O18 crystal have been investigated at room temperature. The Judd-Ofelt theory has been applied to evaluate the optical transition probabilities of Er3+ ions in ErBa3B9O18. Based on the Judd-Ofelt theory, the intensity parameters obtained by the least-square fitting method Ω
t (t
=
2,4
,
6) are 3.10 × 10−20, 0.87 × 10−20, and 1.80 × 10−20 cm2, respectively. The radiative probabilities, lifetime, and fluorescence branching ratios have been calculated. Compared with other Er-doped laser crystals, ErBa3B9O18 crystal has large integrated emission cross sections and radiative probabilities. With good chemical and physical properties, ErBa3B9O18 may find application in thin disk laser.



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*Source: 871320-2015-02-22.xml*