Polarized spectroscopic properties of disordered Er3&#x002B;:Gd2SrAl2O7 crystal

Baicheng Deng; Baicheng Deng; Baicheng Deng; Xinhong Gong; Xinhong Gong; Yujin Chen; Yujin Chen; Jianhua Huang; Jianhua Huang; Yanfu Lin; Yanfu Lin; Zundu Luo; Zundu Luo; Yidong Huang; Yidong Huang

doi:10.1364/OME.413005

1. Introduction

The eye-safe 1.55 µm laser is located in an atmospheric transmission window and the sensitive detection areas of Ge and InGaAs detectors operating at room temperature. For now, 1.55 µm laser operation via the ⁴I_13/2→⁴I_15/2 transition in Er³⁺-doped glasses and crystals have been widely used in the fields of optical communication, lidar, and remote sensing measurement [1,2]. When Er³⁺ ions are doped as an activator for 1.55 µm laser, Yb³⁺ ions are usually highly co-doped as a sensitizer after considering the weak absorption of Er³⁺ [3,4]. In materials with phonon energy about 1100 cm⁻¹, such as phosphate glass [5] and Lu₂Si₂O₇ [6] crystal, the doped Er³⁺ ions have a strong multiphonon non-radiative transition from ⁴I_11/2 to ⁴I_13/2, therefore, an efficient 1.55 µm laser operation may be realized in above materials co-doped with Er³⁺ and Yb³⁺ ions. But hosts with higher phonon energy such as RAl₃(BO₃)₄ (R = Y, Gd, Lu) crystals [7–10], which are the most efficient gain media for the 1.55 µm laser after co-doped with Er³⁺ and Yb³⁺ ions, the shorter fluorescence lifetime of the upper laser multiplet ⁴I_13/2, which is caused by the stronger non-radiative transition, decreases their energy storage capacities and leads to a high pumping threshold and heavy thermal load for laser operation. Er³⁺ ions in hosts with lower phonon energy have higher fluorescence quantum efficiency and energy storage capacity because of the weaker non-radiative transition. However, the longer fluorescence lifetimes of the pumping multiplet ⁴I_11/2 makes reverse energy transfer and up-conversion process more serious, in turn leads to a lower efficiency of laser operation. By co-doped with Ce³⁺, the transition from ⁴I_11/2 to ⁴I_13/2 for Er³⁺ ions can be increased through the energy transfer of ⁴I_11/2(Er³⁺) + ²F₅_/2(Ce³⁺) →⁴I_13/2(Er³⁺) + ²F₇_/2(Ce³⁺) and has little effect on the fluorescence lifetime of the ⁴I_13/2 multiplet [11]. The laser operations based on Er³⁺/Yb³⁺/Ce³⁺ tri-doped Ca₂Al₂SiO₇ [12] and NaGd(WO₄)₂ [13] crystals have been achieved. Diode lasers at wavelength around 1.5 µm can also be used to pump Er³⁺ ions to the upper laser level ⁴I_13/2 directly (so called resonant pump) in Er³⁺ single-doped crystals with lower phonon energy such as Er:YAG and Er:YVO₄ [14]. The remarkable laser performance around 1.6 µm proves the research potential in this field.

Gd₂SrAl₂O₇ (GSAO) crystal with phonon energy about 800 cm⁻¹, which belongs to the tetragonal system with space group I4/mmm, has attracted research interest recently [15]. Its unit cell parameters are a = 3.705 Å, c = 19.781 Å, Z = 2 [16], It owns a layered perovskite-like structure [17], which is formed by perovskite (P) and rock salt (RS) interpenetrating in the sequence of PP/RS/PP/RS……, similar situation also occurs in Ln₂SrAl₂O₇(Ln = La-Ho) [16]. In GSAO, Gd³⁺ and Sr²⁺ generally co-occupy site A (C_4V) with the nine-coordinated in the RS layer and site B (D_4h) with the twelve-coordinated in the PP layer, but Gd³⁺ prefers to occupy the former (site A) [18], Er³⁺ ions doped into these Gd³⁺ sites would result in inhomogeneous broadening of spectral lines, and which would be benefit to the realization of ultrashort pulses and tunable lasers. This disordered crystal melts congruently at about 1780 °C and can be grown by the Czochralski method. At room temperature, thermal conductivities of the crystal are 4.98 and 5.24 Wm⁻¹K⁻¹ along the a- and c-axis, respectively [15]. It is regarded as a promising host for solid state laser. At present, laser operations based on Yb³⁺-doped, Nd³⁺-doped, and Tm³⁺-doped GSAO crystals have been achieved [15,19]. Especially, the laser operation based on the Yb³⁺-doped GSAO has the maximum output power of 7.345 W and slope efficiency of 53.7% [19]. However, no details about the spectral properties related to the 1.55 µm laser operation of the Er³⁺:GSAO crystal have been reported to our knowledge. So this work is devoted to analyze the spectral properties of the Er³⁺:GSAO crystal related to the 1.55 µm laser.

2. Experiment

A single crystal of Er³⁺:Gd₂SrAl₂O₇ was grown by the Czochralski method in a 2 kHz mid-frequency induction furnace (DJL-400). Sr₂CO₃ and Al₂O₃ with 99% purity and Er₂O₃ and Gd₂O₃ with 99.995% purity were used as starting materials. The raw materials were weighed according to the following reaction equation:

xEr₂O₃+(1-x)Gd₂O₃+SrCO₃+Al₂O₃=Er_2xGd_(1-2x)SrAl₂O₇+CO₂↑

After being mixed and ground fully, the materials had been sintered at 1200 °C for 10 h, and then 1500 °C for 10 h. The sintered polycrystal was placed in an iridium crucible and a crystal was grown at a pulling rate of 0.5–1.0 mm/h and a rotating rate of 10–15 rpm. By controlling the temperature, the crystal growth passes through four steps: necking, shoulder enlargement which has a cooling rate of about 2°C/h, equal diameter, and end, the grown crystal was detached slowly from the melt and cooled down to room temperature at a cooling rate of 10–30 °C/h. A Φ20 × 20 mm³ pale-yellow crystal was obtained finally (see Fig. 1). The yellow color of the crystal may be caused by defects in it. Similar phenomena have also been found in other Er³⁺-doped aluminate crystals [20]. The Er³⁺ concentration in the grown crystal was measured to be 0.78 at% (1.14×10²⁰ cm⁻³) by the inductively coupled plasma atomic emission spectrometry (ICP-AES) method. Segregation coefficient of Er³⁺ in the crystal was calculated to be 0.78. The pattern of X-ray powder diffraction (XRD) of the grown Er³⁺:GSAO crystal was obtained by a diffractometer (Miniflex-600). Obviously, the diffraction peak positions of the Er³⁺:GSAO crystal are basically aligned with those of the standard card (see Fig. 2), which reveals that the low concentration of Er³⁺ doping hardly affects the crystal structure.

Fig. 1. The as-grown Er³⁺:GSAO crystal and sample after cut, annealed and polished.

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Fig. 2. XRD patterns of the Er³⁺:GSAO and GSAO (JCPDS No.76-0095) crystals.

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After the optical indicatrix axes of the crystal was determined with a polarization microscope, a sample with dimensions of 5.66 × 5.57 × 2.25 mm³ was cut from the grown crystal. The 5.57 mm side of the crystal sample is parallel to the c-axis. In order to eliminate defects and thermal stress, the crystal sample was annealed at 1000 °C for 48 h in air and cooled to room temperature at a rate of 15–50 °C/h. After polished, the sample was used for spectral experiments (see Fig. 1). Room-temperature (RT) polarized absorption spectra were recorded with a Pekin-Elmer UV-VIS-NIR spectrophotometer (Lambda 950) in a range from 300 to 1700nm. RT polarized fluorescence spectra from 1400 to 1670 nm under excitation at 520 nm were recorded using a spectrometer (FLS1000, Edinburgh). The spectral resolutions were 1.0 nm in both the absorption and emission measurements. RT fluorescence decay curves at wavelengths of 980 and 1530 nm, corresponding to the transitions of ⁴I_11/2→⁴I_15/2 and ⁴I_13/2→⁴I_15/2 were recorded using the spectrometer (FLS1000, Edinburgh) when a microsecond flash xenon lamp (lF900 Edinburgh) was used as the exciting source and both the exciting wavelengths were set at 520 nm, corresponding to the transitions of ⁴I_15/2→²H_11/2.

3. Result and discussion

3.1. Absorption spectrum and Judd-Ofelt analysis

The RT polarized absorption spectra of the Er³⁺:GSAO crystal are shown in Fig. 3. They display strong anisotropy for different polarizations, and the absorptions for π polarization are generally stronger than those for σ polarization. It is worth mentioning that the absorption cross section around 1.5 µm in Er³⁺:GSAO is close to that in Er³⁺:YAG [21]. The absorption bands centered at 523 and 379 nm, which correspond to the ⁴I_15/2→²H_11/2 and ⁴I_15/2→⁴G_11/2 transitions, respectively, are usually considered as the hypersensitive transitions [22,23].

Fig. 3. RT polarized absorption spectra of the Er:GSAO crystal.

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The Judd–Ofelt theory [24,25] has been applied to calculate spectroscopic parameters of rare-earth ions in crystals and glasses [26]. Due to the lack of the values of refractive index for the GSAO crystal, the same refractive index (n≈1.94) [15] is adopted for both polarizations in calculation process. Referring to the Sellmeier equation of n_o and n_e in CaGdAlO₄ [27] with the same structure, the error caused by the possible error of the refractive index is generally less than 15% for the spontaneous transition probability. For simplicity, detailed calculating process following Ref. [26] is not described repeatedly here.

The measured oscillator strength f_exp and the calculated one f_cal are listed in Table 1. The J-O intensity parameters Ω_t (t = 2, 4, 6) of some Er³⁺-doped crystals are listed in Table 2. The effective J-O parameters of the uniaxial Er³⁺:GSAO crystal, which are defined as Ω_t,eff = (2Ω_t,σ+Ω_t,π)/3 [28,29], were calculated as: Ω_2,eff = 3.87×10⁻²⁰ cm², Ω_4,eff = 2.13×10⁻²⁰ cm², Ω_6,eff = 1.77×10⁻²⁰ cm². It is generally thought that Ω₂ is sensitive to the structure surrounding rare earth ions, and is associated with the asymmetry and the covalency of the lanthanide sites [30]; therefore, Ω₂ is closely related to the hypersensitive transition [22,23]. The distortion index D of the rare earth ion coordination polyhedron in the crystal can be calculated through the formula [31]:

(1)$$D = \frac{1}{n}\sum\nolimits_{i = 1}^n {\frac{{|{{l_i} - {l_{av}}} |}}{{{l_{av}}}}}$$

where n is the coordination number, l_i is the distance from the central atom to the ith coordinating atom, and l_av is the average bond length. The crystal structure of GSAO and its coordination polyhedral is shown in Fig. 4. The values of sites A and B in the GSAO are 0.04768 and 0.01636, respectively. The distortion index of site A is larger than those in CaGdAlO₄ (0.032) and CaYAlO₄ (0.031) crystals which belong to the tetragonal system with space group of I4/mmm as well. So the absorption spectra especially for the bands correspond to hypersensitive transitions ⁴I_15/2→²H_11/2 and ⁴I_15/2→⁴G_11/2 of the Er³⁺:GSAO show stronger anisotropy for different polarizations than those of the Er³⁺:CaGdAlO₄ [32] and Er³⁺:CaYAlO₄ [33]. Moreover, the absorption bands of Er³⁺:GSAO are flatter and broader than those of the Er³⁺:CaGdAlO₄ and Er³⁺:CaYAlO₄ because of its multi-position and disordered structure. However, the average distance between Er³⁺ and its coordination ions of site A and B in Er³⁺:GSAO are 2.521 Å and 2.686 Å, respectively, both of them are longer than those in the CaGdAlO₄ (2.518 Å) and CaYAlO₄ (2.509 Å). The longer distance leads to a weaker crystal field, and thus a smaller Ω_2,eff [34]. Under the combined effect of distortion index and crystal field, the value of Ω_2,eff for the Er³⁺:GSAO is close to those for the Er³⁺:CaYAlO₄ and Er³⁺:CaGdAlO₄

Fig. 4. Crystal structure of GSAO and coordination polyhedral Gd(Sr)O₉ and Sr(Gd)O₁₂.

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Table 1. Mean wavelengths and polarized experimental and calculated oscillator strengths of Er³⁺ ions in the GSAO crystal at room-temperature.

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Table 2. Comparison of the J-O parameters of Er³⁺ ions in the GSAO and some other crystals (in unit of 10⁻²⁰cm²).

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Based on the J-O intensity parameters, the spontaneous transition probability A_q, fluorescence branching ratio β, and radiative lifetime τ_r for different fluorescence multiplets of Er³⁺ in the GSAO can be calculated, the results of some transitions are listed in Table 3.

Table 3. Spectral parameters of the Er³⁺:GSAO crystal calculated by the J–O theory.

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3.2. Analysis of infrared emission properties

The Fuchtbauer–Ladenburg (F–L) formula can be used to calculate stimulated emission cross-section [38].

(2)$${\mathrm{\sigma }_{em,q}}(\mathrm{\lambda } )= \frac{{{\mathrm{\lambda }^5}{A_q}({J \to J^{\prime}} ){I_q}(\mathrm{\lambda } )}}{{8\pi cn_q^2\int \mathrm{\lambda } {I_q}(\mathrm{\lambda } )d\mathrm{\lambda }}}$$

where q indicates the polarization of the fluorescence spectrum, ${I_q}(\lambda )$ is the fluorescence intensity at wavelength λ, $\; $c is the velocity of light, and n_q is the refractive index of the crystal. It can be found from Fig. 4 that the emission cross-sections for π polarization are larger than those for σ polarization, and the peak emission cross-sections for the ⁴I_13/2→⁴I_15/2 transition are 0.79 ×10⁻²⁰ cm² at 1549 nm and 1.25×10⁻²⁰ cm² at 1546 nm for σ and π polarizations, respectively. Comparing with those of other Er³⁺-doped materials, for example, 1.13×10⁻²⁰ cm² (σ) for YAl₃(BO₃)₄ [39], 1.12×10⁻²⁰ cm² (E//x) for Lu₂Si₂O₇ [6], 1.09×10⁻²⁰cm² (π) for CaGdAlO₄ [32], and 0.6×10⁻²⁰cm² for YAG [40], it can be found that the peak emission cross-sections of the Er³⁺:GSAO around 1550 nm are close to those of the typical Er³⁺-doped crystals.

Generally, the emission cross-section for the ⁴I_13/2→⁴I_15/2 transition calculated from the measured fluorescence spectrum by the F–L formula may be influenced by the radiation trapping [41]. Alternately, a reciprocity method (RM) can also be used to calculate the emission cross-section [42].

(3)$$ \sigma_{e m, q}(\lambda)=\sigma_{a b s, q}(\lambda) \frac{z_{l}}{z_{u}} \exp \left(\frac{E_{z p l}-h c \lambda^{-1}}{k_{B} T}\right) $$

where ${\sigma _{abs,q}}(\lambda )$ is the polarized absorption cross-section, z_l and z_u are the partition functions of the lower and upper multiplets, due to lack of values for crystal field level positions of the Er³⁺:GSAO, those of aluminate crystals with the same structure [43–45] were adopted and the value of z_l/z_u was estimated as 0.8, E_zpl is the energy separation between the lowest crystal field level of the upper and lower multiplets, which was estimated as 6591 cm⁻¹ by the same way, k_B is the Boltzmann constant, h is the Planck constant, and T is the temperature.

The wavelength dependences of polarized stimulated emission cross-sections of the ⁴I_13/2→⁴I_15/2 transition calculated by the above two methods are shown in Fig. 5. It can be found that the emission cross-section calculated by the two methods are similar at short wavelength, but at long wavelength, the emission cross-sections calculated by the F–L formula are larger than those calculated by the reciprocity method, which is caused by the radiation trapping.

Fig. 5. Polarized stimulated emission cross-sections for the ⁴I_13/2→⁴I_15/2 transition of the Er³⁺:GSAO crystal calculated by the F–L formula and the reciprocity method.

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The gain curve can be used to predict the possible laser wavelength. The 1.55 µm laser via the ⁴I_13/2→⁴I_15/2 transition operates in a three-level scheme, the gain curve can be calculated by

(4)$$ \sigma_{g a i n}(\lambda)=P \sigma_{e m}(\lambda)-(1-P) \sigma_{a b s}(\lambda) $$

where P is the ratio of the population of Er³⁺ ions in the upper laser multiplet ⁴I_13/2 to the total number of Er³⁺ ions. The gain curves are shown in Fig. 5.

It can be found from Fig. 6 that the gain cross section for π-polarization is larger than that for σ-polarization in a certain P, it indicates that π-polarization has a lower threshold of laser oscillation [46]. Therefore, polarized 1.55 µm laser output may be realized in a c-cut Er³⁺:GSAO crystal. For π-polarization with P ≥ 0.5, a positive gain can be achieved in a range from 1516 to 1635 nm at least. The curves are quite flat with full widths at half the maximum of 66 and 62 nm for σ and π polarizations, respectively, when P = 0.5. They are larger than those of Er:Yb:Lu₂Si₂O₇ (about 30 nm for E//Y) [6], Er:Yb:KGd(PO₃)₄ (48 nm for E//Y) [47], and Er:CaGdAlO₄ (56 nm for π polarization) [32] with the same value of P, and which is due to the multi-position disordered structure of the crystal. The broad and flat gain curves reveal that tunable and ultra-short lasers may be realized in the Er³⁺:GSAO crystal.

Fig. 6. Gain curves of the ⁴I_13/2→⁴I_15/2 transition for the Er³⁺:GSAO crystal with different P (P = 0.1, 0.2, …, 0.6, 0.7).

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The radiation trapping enhanced by the total reflection in crystal will cause the measured fluorescence lifetime longer than the intrinsic one [48]. The fluorescence decay curves of the ⁴I_13/2→⁴I_15/2 transition were recorded from both the bulk and powder samples (see Fig. 7) to display this phenomenon. It is worth mentioning that, when the measurement was carried out, the powder sample was dispersed in bromobenzene, which is low-toxic and has a refractive index (n = 1.55) close to that of the GSAO (n = 1.9). The linear relationship in Fig. 6 shows a single exponential behavior of the fluorescence decays and the fluorescence lifetimes of the ⁴I_13/2 multiplet were fitted to be 4.93 and 3.48 ms for the bulk and powder samples, respectively. As for the ⁴I_11/2 multiplet, the fluorescence lifetimes were fitted to be 612 and 585 µs for the bulk and powder samples, respectively. The shorter fluorescence lifetimes for the powder sample confirms the existence of radiation trapping, but the fluorescence lifetimes of the ⁴I_13/2 multiplet for powder is still longer than the radiative lifetime of the ⁴I_13/2 multiplet calculated by J-O theory (see Table 3). This may be caused by the uncertainty of the J–O theory [49] and still existence of the radiation trapping in the powder sample. Meanwhile, it also shows that the multiplet has a high fluorescence quantum efficiency. The same phenomenon also occurs in other Er³⁺-doped crystals with lower phonon energy, such as: Er³⁺:CaGdAlO₄ [32], Er³⁺:LiNbO₃ [50], and Er³⁺:Ca₉Y(VO₄)₇ [51].

Fig. 7. RT fluorescence decay curves of the Er:GSAO bulk and powders samples at 1535 nm. Exciting wavelength is 520 nm.

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In general, the product of the emission cross-section σ_em and the fluorescence lifetime τ_f is used to compare the laser oscillating thresholds of different gain media [52]. For the convenience of comparison, the fluorescence lifetimes τ_f used in the calculation were all measured from crystals. The value of the product for Er³⁺:GSAO is 6.2×10⁻²³ cm²s and larger than the 4.67×10⁻²⁴ cm²s for Er³⁺:YAl₃(BO₃)₄, and slightly larger than the 5.4×10⁻²³ cm²s for Er³⁺:YAG. Therefore, when other factors are similar, it can be expected that the Er:GSAO has a lower oscillating threshold for 1.55 µm laser.

4. Conclusions

An Er³⁺:Gd₂SrAl₂O₇ single crystal was grown by the Czochralski method. RT polarized spectral properties of the crystal as a gain medium for 1.55 µm laser were investigated in detail. The absorption spectra exhibit strong anisotropy. The emission cross-sections were determined from the polarized emission spectra by the F–L formula and also from the polarized absorption spectra by the reciprocity method. The peak emission cross sections around 1.55 µm are 0.79 ×10⁻²⁰ cm² for σ-polarization and 1.25×10⁻²⁰ cm² for π-polarization. For π-polarization with P ≥ 0.5, a positive gain can be achieved in a range from 1516 to 1635 nm at least. Because of the multi-position disordered structure of the crystal, the gain curves with P = 0.5 are flat with full widths at half the maximum of 66 and 62 nm for σ and π polarizations, respectively. The large emission cross section, wide and flat gain curves, and long fluorescence lifetime for upper laser level reveal that tunable and ultra-short 1.55 µm lasers may be realize in the crystal with a low oscillating threshold.

Funding

Ministry of Science and Technology of the People's Republic of China (2016YFB0701002); Chinese Academy of Sciences Key Project (KFJ–STS–QYZX–069, XDB20000000); Natural Science Foundation of Fujian Province (2019J01127).

Disclosures

The authors declare no conflicts of interest.

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Transition (from ⁴I_15/2)	π-Polarization			σ-Polarization
Transition (from ⁴I_15/2)	$\bar{λ}$ (nm)	$f_{e x p}^{e d}$ (10⁻⁶)	$f_{c a l}^{e d}$ (10⁻⁶)	$\bar{λ}$ (nm)	$f_{e x p}^{e d}$ (10⁻⁶)	$f_{c a l}^{e d}$ (10⁻⁶)
⁴I_13/2	1516	3.08	2.41(ed) 0.59(md)	1519	2.26	1.55(ed) 0.58(md)
⁴I_11/2	982	1.31	1.48	978.35	0.61	0.86
⁴I_9/2	798	0.20	0.12	800	0.35	0.88
⁴F_9/2	656	2.37	2.43	655	4.70	4.55
⁴S_3/2	545	1.16	1.23	547	0.25	0.77
²H_11/2	524	13.6	13.2	524	7.66	7.43
⁴F_7/2	491	3.90	3.97	488	3.65	3.63
⁴F_5/2+⁴F_3/2	451	1.98	2.35	450	0.84	1.48
²H_9/2	407	1.53	1.69	408	0.72	1.23
⁴G_11/2	380	22.9	23.4	380	12.9	13.1
RMSΔf	2.83 × 10⁻⁷			4.54 × 10⁻⁷
RMS error (%)	3.27			8.78

Crystal		Ω₂	Ω₄	Ω₆	Reference
CaGdAlO₄		4.38	2.45	1.54	[32]
CaYAlO₄		3.78	2.52	1.91	[33]
SrGdGa₃O₇		2.46	1.24	0.51	[35]
Y₃Al₅O₁₂		0.79	1.19	1.08	[36]
YAlO₃		2.83	1.39	1.29	[37]
GSAO	Ω_σ	2.28	3.04	1.48	this work
	Ω_π	7.04	0.29	2.34
	Ω_eff	3.87	2.13	1.77

J-J'	$\bar{λ}$ (nm)	A_σ(s⁻¹)	A_π(s⁻¹)	A_total(s⁻¹)	β(%)	τ_r(ms)
⁴I_13/2→
⁴I_15/2	1549	250.04(ed)	352.20(ed)	353.98	100.00	2.83
		69.76(md)	70.16(md)
⁴I_11/2→
⁴I_13/2	2744	46.87	58.04	50.60	12.77	2.46
⁴I_15/2	990	296.41	472.89	355.24	87.23
⁴I_9/2→
⁴I_11/2	4172	2.04	2.90	2.32	0.30	1.22
⁴I_13/2	1655	241.13	374.79	285.68	36.87
⁴I_15/2	800	656.40	279.73	530.84	62.83
⁴F_9/2→						0.25
⁴I_9/2	3719	4.22	5.56	4.67	0.13
⁴I_11/2	1967	154.60	222.86	177.35	5.20
⁴I_13/2	1145	217.61	81.61	172.28	4.17
⁴I_15/2	658	4370.13	2178.21	3639.49	90.57
⁴S_3/2→						0.21
⁴F_9/2	3312	1.42	2.28	1.71	0.036
⁴I_9/2	1752	156.13	148.35	153.54	3.40
⁴I_11/2	1234	88.18	121.21	99.19	2.13
⁴I_13/2	851	1116.35	1732.32	1321.67	28.10
⁴I_15/2	549	2623.20	4127.14	3124.51	66.33
²H_11/2→						0.098
⁴S_3/2	12269	0.15	0.01	0.10	0.001
⁴F_9/2	2623	23.72	34.61	27.35	0.27
⁴I_9/2	1520	143.02	186.90	157.65	1.57
⁴I_11/2	1113	181.59	79.88	147.69	1.47
⁴I_13/2	792	285.64	199.01	256.76	2.53
⁴I_15/2	524	9696.69	9366.58	9586.65	94.23

Transition (from ⁴I_15/2)	π-Polarization			σ-Polarization
Transition (from ⁴I_15/2)	$\bar{λ}$ (nm)	$f_{e x p}^{e d}$ (10⁻⁶)	$f_{c a l}^{e d}$ (10⁻⁶)	$\bar{λ}$ (nm)	$f_{e x p}^{e d}$ (10⁻⁶)	$f_{c a l}^{e d}$ (10⁻⁶)
⁴I_13/2	1516	3.08	2.41(ed) 0.59(md)	1519	2.26	1.55(ed) 0.58(md)
⁴I_11/2	982	1.31	1.48	978.35	0.61	0.86
⁴I_9/2	798	0.20	0.12	800	0.35	0.88
⁴F_9/2	656	2.37	2.43	655	4.70	4.55
⁴S_3/2	545	1.16	1.23	547	0.25	0.77
²H_11/2	524	13.6	13.2	524	7.66	7.43
⁴F_7/2	491	3.90	3.97	488	3.65	3.63
⁴F_5/2+⁴F_3/2	451	1.98	2.35	450	0.84	1.48
²H_9/2	407	1.53	1.69	408	0.72	1.23
⁴G_11/2	380	22.9	23.4	380	12.9	13.1
RMSΔf	2.83 × 10⁻⁷			4.54 × 10⁻⁷
RMS error (%)	3.27			8.78

Crystal		Ω₂	Ω₄	Ω₆	Reference
CaGdAlO₄		4.38	2.45	1.54	[32]
CaYAlO₄		3.78	2.52	1.91	[33]
SrGdGa₃O₇		2.46	1.24	0.51	[35]
Y₃Al₅O₁₂		0.79	1.19	1.08	[36]
YAlO₃		2.83	1.39	1.29	[37]
GSAO	Ω_σ	2.28	3.04	1.48	this work
	Ω_π	7.04	0.29	2.34
	Ω_eff	3.87	2.13	1.77

Polarized spectroscopic properties of disordered Er³⁺:Gd₂SrAl₂O₇ crystal

Abstract

1. Introduction

2. Experiment

3. Result and discussion

3.1. Absorption spectrum and Judd-Ofelt analysis

3.2. Analysis of infrared emission properties

4. Conclusions

Funding

Disclosures

References

Cited By

Figures (7)

Tables (3)

Equations (4)

Optical Materials Express