Optical Transition Probabilities of Er 3 + Ions in ErBa 3 B 9 O 18 Crystal

The optical absorption and emission intensity of luminescent and birefringent crystal ErBa 3 B 9 O 18 were examined from optical absorption data based on Judd-Ofelt theory. The three intensity parametersΩ t (t = 2, 4, 6) are 3.10 × 10, 0.87 × 10, and 1.80 × 10 cm, respectively. From the obtained intensity parameters, the radiative probabilities A r , radiative lifetime τ f , fluorescence branching ratiosβ c , and integrated emission cross sections∑ have been calculated. In comparisonwith other Er-doped luminescent crystals, ErBa 3 B 9 O 18 may find application in thin disk laser.


Introduction
Er 3+ activator has attracted much attention for its two laser emissions at 2.94 m ( 4 I 11/2 → 4 I 13/2 ) and 1.54 m ( 4 I 13/2 → 4 I 15/2 ).The emissions have potential applications in optocommunication, sensors, or lidar system [1][2][3].To now, the Er 3+ ion has exhibited laser operations in various Er 3+ -doped crystals or glasses [4][5][6][7][8][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 Er 3+ 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.
They crystallize in centric space group P6 3 /m with lattice parameters of about  = 7.17 Å and  = 16.97Å.Three O atoms are bonded to one B atom and three BO 3 groups form a planar hexagonal [B 3 O 6 ] 3− ring [20].The parallel arranged [B 3 O 6 ] 3− groups can separate the R 3+ ions, which makes the energy migration between two rare earth ions difficult.Taking YBa 3 B 9 O 18 and ErBa 3 B 9 O 18 (EBBO) as examples, the shortest distance of two Y 3+ or Er 3+ ions is 7.16-7.17Å, which is long enough to limit the energy transfer between luminescent centers [20][21][22].So, the quenching effect in EBBO is proved to be small and Er 3+ 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.

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.

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 Er 3+ ions transitions can be assigned., respectively.These strong absorption peaks show mainly the eigenmultiplets typically observed in free Er 3+ 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 4 I 15/2 → 4 I 13/2 is big, and the integrated emission cross section is expected to be great.The Judd-Ofelt theory was applied to evaluate the optical transition probabilities of Er 3+ 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 ℎ is Planck's constant,  is the speed of light,  is the mass of electron, and ⟨Φ   ‖ () ‖Φ   ⟩ is the reduced matrix elements depending on the Er 3+ ions.In this work, the values of the squares of the reduced matrix elements are cited from Carnall's calculations [26].Ω  ( = 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 4 I 15/2 → 4 I 13/2 .The value of  md is cited from [27] to be 0.683 × 10 −20 cm 2 because  md does not vary with the host crystal.Then the measured line strengths  meas ed (  ,   ) from the absorption spectrum can be given by where  is the mean wavelength of the absorption band, OD() presents the measured optical density, and  is the thickness of the crystal.The concentration of Er 3+ ions   in ErBa 3 B 9 O 18 is calculated based on the crystal structure parameter.The crystal structure of ErBa 3 B 9 O 18 adopts a centric space group P6 3 /m and the lattice parameters are  = 7.1817 Å and  = 16.996Å [21].There are two Er 3+ in one unit cell, so   is calculated to be 2.63 × 10 27 /m 3 . is the refractive index, which can be obtained by Sellmeier's equation [21], and  is the electron charge.Table 1 presents the line strengths  ed of nine absorption peaks of Er 3+ in crystal.Three intensity parameters Ω  ( = 2, 4, 6) were fitted by least-square method to be 3.10 × 10 −20 , 0.87 × 10 −20 , and 1.80 × 10 −20 cm 2 .From Judd-Ofelt theory, the electric-dipole and magneticdipole contributions,  ed and  md , 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. The results show that radiative probabilities (209 s −1 ) of 4 I 15/2 → 4 I 13/2 are comparable to those of Er:YAG (211 s −1 )

Conclusion
The spectroscopic properties of ErBa

Figure 1 :
Figure 1: The absorption spectra of EBBO crystal.This figure is from [23] with permission.

Table 2 :
[30]spectral parameters for Er 3+ ions in EBBO crystal.Er  Y 1− Al 3 (BO 3 ) 4 (233 s −1 )[29], and Er:La 2 CaB 10 O 19 (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 m 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 Er 3+ activators, EBBO may find applications in thin disk laser.
3 B 9 O 18 crystal have been investigated at room temperature.The Judd-Ofelt theory has been applied to evaluate the optical transition probabilities of Er 3+ ions in ErBa 3 B 9 O 18 .Based on the Judd-Ofelt theory, the intensity parameters obtained by the least-square fitting method Ω  ( = 2, 4, 6) are 3.10 × 10 −20 , 0.87 × 10 −20 , and 1.80 × 10 −20 cm 2 , respectively.The radiative probabilities, lifetime, and fluorescence branching ratios have been calculated.Compared with other Er-doped laser crystals, ErBa 3 B 9 O 18 crystal has large integrated emission cross sections and radiative probabilities.With good chemical and physical properties, ErBa 3 B 9 O 18 may find application in thin disk laser.