Journal of Spectroscopy
Volume 2015 (2015), Article ID 871320, 4 pages
http://dx.doi.org/10.1155/2015/871320

Research Article

Optical Transition Probabilities of Er³⁺ Ions in ErBa₃B₉O₁₈ Crystal

Ming He,¹ Tiezheng Liu,² Junling Xiu,¹ Yuanguang Tang,¹ and Zhihua Zhang²

¹Department of Physics, College of Science, Dalian Jiaotong University, Dalian 116028, China
²Liaoning Key Materials Laboratory for Railway, College of Materials Science and Engineering, Dalian Jiaotong University, Dalian 116028, China

Received 13 October 2014; Revised 24 December 2014; Accepted 24 December 2014

Academic Editor: Veer P. S. Awana

Copyright © 2015 Ming He et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 () are 3.10 × 10⁻²⁰, 0.87 × 10⁻²⁰, and 1.80 × 10⁻²⁰ cm², respectively. From the obtained intensity parameters, the radiative probabilities , radiative lifetime , fluorescence branching ratios , and integrated emission cross sections have been calculated. In comparison with other Er-doped luminescent crystals, ErBa₃B₉O₁₈ may find application in thin disk laser.

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  Å and  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 Figure 1 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 level to the terminal level are described by

where is Planck’s constant, is the speed of light, is the mass of electron, and 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]. () 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 is cited from [27] to be 0.683 × 10⁻²⁰ cm² because does not vary with the host crystal.

Then the measured line strengths from the absorption spectrum can be given by

where is the mean wavelength of the absorption band, presents the measured optical density, and is the thickness of the crystal. The concentration of Er³⁺ ions 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 = 7.1817 Å and = 16.996 Å [21]. There are two Er³⁺ in one unit cell, so is calculated to be 2.63 × 10²⁷/m³. is the refractive index, which can be obtained by Sellmeier’s equation [21], and is the electron charge. Table 1 presents the line strengths of nine absorption peaks of Er³⁺ in crystal. Three intensity parameters () 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)
(nm)
(10⁻²⁰ cm²)
(10⁻²⁰ cm²)

1

1539
25.73
3.27
2.76
0.26

2

971
0.83
0.20
0.80
0.36

3

650
2.09
0.75
1.32
0.32

4

519
5.35
2.37
2.72
0.12

5

485
1.97
0.94
1.27
0.11

6

407
0.53
0.29
0.43
0.02

7

376
6.29
3.77
3.50
0.08

8

255
1.35
1.18
0.85
0.11

Rms-Δ. = 0.40 10⁻²⁰ cm², = (3.10, 0.87, 1.80) 10⁻²⁰ cm²

From Judd-Ofelt theory, the electric-dipole and magnetic-dipole contributions, and , of the total spontaneous emission probability are given by

The luminescence parameters can be calculated from the following equations:

where is the fluorescence branch ratio, is the radiative lifetime of a given upper level, is the transition probability of spontaneous emission, and 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)
(s⁻¹)
(s⁻¹)
(s)

(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
4658.79

The results show that radiative probabilities (209 s⁻¹) of ⁴I15/2 → ⁴I13/2 are comparable to those of Er:YAG (211 s⁻¹) [28], (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 () 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.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgment

The authors gratefully acknowledge the support from the National Natural Science Foundation of China (Grant nos. 51372026 and 51372027).

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