Polarized spectroscopic properties of Er3+/Yb3+ co-doped Ca9Y(VO4)3(PO4)4 crystal

Lincong Rao; Lincong Rao; Yujin Chen; Yujin Chen; Jianhua Huang; Jianhua Huang; Xinghong Gong; Xinghong Gong; Yanfu Lin; Yanfu Lin; Zundu Luo; Yidong Huang; Yidong Huang

doi:10.1364/OME.435943

1. Introduction

Er³⁺/Yb³⁺ co-doped materials have been widely investigated as gain media for the eye-safe laser around 1.55 µm, which can be used in optical communication, lidar, laser ranging, and remote sensing [1–3]. At present, Er³⁺/Yb³⁺ co-doped phosphate glass (Er:Yb:PG) has become a main commercial material for the laser around 1.55 µm. However, due to the low thermal conductivity of about 0.8 W m⁻¹ k⁻¹ [2], a high power laser operation cannot be realized in the Er:Yb:PG.

Various Er³⁺/Yb³⁺ co-doped crystals with higher thermal conductivity have been investigated as 1.55 µm laser gain media, such as YAl₃(BO₃)₄ (YAB) [3], Lu₂Si₂O₇ [4], NaGd(WO₄)₂ [5], YVO₄ [6], Y₃Al₅O₁₂ [7] and so on. Among them, Er³⁺/Yb³⁺ co-doped borate crystals have a short fluorescence lifetime of the ⁴I_11/2 multiplet because of the strong multiphonon non-radiative relaxation caused by the high phonon energy (approximately 1400 cm⁻¹) of the host, which can restrain the up-conversion and make the Er³⁺ ions populate in the ⁴I_13/2 multiplet efficiently. However, the strong multiphonon non-radiative relaxation also causes a short fluorescence lifetime of the ⁴I_13/2 multiplet. For example, the fluorescence lifetime of the ⁴I_13/2 multiplet of Er³⁺ in YAB crystal is only about 325 µs, which limits its energy storage capacity and causes a serious thermal loading [8]. Therefore, Er³⁺/Yb³⁺ co-doped crystals with proper phonon energy are favorable for realizing an efficient population of Er³⁺ ions in the ⁴I_13/2 multiplet and a long fluorescence lifetime of the ⁴I_13/2 multiplet (several ms).

Due to having similar phonon energy to the PG (about 1200 cm⁻¹), some Er³⁺/Yb³⁺ co-doped phosphate crystals have a long fluorescence lifetime of the ⁴I_13/2 multiplet and a short fluorescence lifetime of the ⁴I_11/2 multiplet. For example, for Er:Yb:LuPO₄ and Er:Yb:KGd(PO₃)₄ (KGP) crystals, the fluorescence lifetimes of the ⁴I_11/2 multiplet are 3.5 and 1.54 µs, while those of the ⁴I_13/2 multiplet are 4.47 and 6.91 ms, respectively [9–11]. Above values are comparable to those (2∼3 µs and 7.9 ms respectively) of the Er:Yb:PG [1,2]. However, all the phosphate crystals investigated up to now melt incongruently and can only be grown by the flux method with a long growth period.

At present, Ca₉Y(VO₄)_7-x(PO₄)_x (x = 0, 1, 2, 3, 4) crystals have been grown successfully by the Czochralski (CZ) method [12,13]. The crystals with x = 0, 1, 3 possess whitlockite like polar structure, space group R3c [13]. While the Ca₉Y(VO₄)₃(PO₄)₄ crystal is centrosymmetric at room temperature with space group $R\overline 3 c$, its cell parameters are: a = 10.6198 Å, c = 37.524 Å, γ = 120°, Z = 6, V = 3665.0 Å³ [13]. In the Ca₉Y(VO₄)₃(PO₄)₄ crystal, Y³⁺ and a part of Ca²⁺ ions occupy the 36f Wyckoff sites with C₁ symmetry [13]. The Ca₉Y(VO₄)_7-x(PO₄)_x crystals have good chemical and physical stability, the hardness H_v are 5.03, 4.38, 4.67, 4.67 when x = 0, 1, 2, 3, 4, respectively [13]. When x = 0, the Ca₉Y(VO₄)₇ single crystals co-doped with rare earth ions have been grown and investigated as laser gain media [14–17]. In the Ca₉Y(VO₄)_7-x(PO₄)_x system that can be grown by CZ method so far, Ca₉Y(VO₄)₃(PO₄)₄ (CYVP) crystal has the highest phosphorus content. As the value of x increases, crystal growth becomes more difficult. Up to now, rare earth ions doped Ca₉Y(VO₄)_7-x(PO₄)_x crystals have not been investigated. In this work, an Er³⁺/Yb³⁺ co-doped CYVP (Er:Yb:CYVP) crystal was successfully grown by the CZ method for the first time and the polarized spectroscopic properties of the crystal were investigated at room temperature.

2. Crystal growth

An Er:Yb:CYVP crystal was successfully grown by the CZ method. The chemical composition expression of the raw material is Ca₉Y_0.505Yb_0.45Er_0.045(VO₄)₃(PO₄)₄ and the growth process is similar to that reported in [13] except the temperature gradient in the growth solution. However, the grown Er:Yb:CYVP crystal cracked during the growth process due to the higher temperature gradient. In order to prevent the crystal cracking and improve the crystal optical quality, a more appropriate temperature gradient and a slower cooling rate must be explored in the further experiment. The crystal shown in Fig. 1 is a part of the as-grown one, so the shape of the crystal is different from that shown in Ref. [13]. As shown in Fig. 1(a), the as-grown crystal is dark brown in color, which may originate from the absorption of color center caused by oxygen vacancy inside the crystal. In order to reduce the oxygen vacancy and improve the optical quality of the crystal, the as-grown crystal had been annealed at 1100 °C for 72 h in air. The annealed crystal became more transparent, as shown in Fig. 1(b). Above phenomenon was also observed in the Tm:Ca₉La(VO₄)₇ crystal [18]. An orientated transparent crystal with dimensions of 4.5 × 3.5 × 3.1 mm³ was cut and polished for the polarized spectral experiments. In addition, a 4.5 at.% Er³⁺ doped CYVP crystal was also grown by the CZ method and then annealed in air. But it cracked severely during the growth period and was difficult for orientation. So the grown Er:CYVP crystal was only used for measuring the fluorescence decay curve.

Fig. 1. Photographs of the (a) as-grown and (b) annealed Er:Yb:CYVP crystals.

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Using a powder diffractometer (Rigaku, Miniflex-600) equipped with CuKα radiation, the phase of the crystal was determined by powder X-ray diffraction (XRD) in a range of 10–60° with a step of 0.02° and a scan speed of 5°/min. The diffraction peaks of the crystal match well with those of the CYVP crystal (ICSD card # 253848), as shown in Fig. 2(a). Because the ionic radius of P⁵⁺ (0.38 Å) is much smaller than that of V⁵⁺ (0.54 Å), the introduction of [PO₄]^3- makes the cell parameters smaller [13]. The ionic radii of Er³⁺ (0.89 Å) and Yb³⁺ (0.87 Å) are all very close to that of Y³⁺ (0.9 Å), so doping Er³⁺ and Yb³⁺ ions into the CYVP crystal hardly changes the cell parameters. The infrared spectra of the crystal was recorded by an infrared spectrometer (VERTEX 70, Bruker) and the one between 350 and 1300 cm⁻¹ is shown in Fig. 2(b). The characteristic bands in ranges of 700–900 and 950–1150 cm⁻¹ are originated from vibrations of VO₄^3- and PO₄^3- anions, respectively [15,19]. Then, it can be seen that the maximum phonon energy of the crystal is about 1110 cm⁻¹. The concentrations of P⁵⁺, V⁵⁺, Er³⁺ and Yb³⁺ in the crystal were measured to be 63.95 at.% (4.12 × 10²¹ cm⁻³), 36.05 at.% (2.36 × 10²¹ cm⁻³), 4.86 at.% (0.75 × 10²⁰ cm⁻³) and 42.96 at.% (6.68 × 10²⁰ cm⁻³), respectively, by the inductively coupled plasma atomic emission spectrometry (ICP-AES, Ultima2, Jobin-Yvon). Thus the chemical composition expression of the grown crystal can be described as Ca₉Y_0.521Yb_0.43Er_0.049(VO₄)_2.52(PO₄)_4.48 (Er:Yb:CYVP).

Fig. 2. XRD pattern (a) and FTIR spectra (b) of the Er:Yb:CYVP crystal powder.

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Specific heat (Cp) and thermal diffusion coefficients (υ) of Er:Yb:CYVP crystal were measured by a laser flash apparatus (LFA457, NETZSCH) at room temperature. The measured Cp is 0.711 Jg⁻¹K⁻¹, the υ values are 0.474 and 0.477 mm²s⁻¹for a and c direction, respectively. The thermal conductivities (k) can be calculated using below formula [20]:

(1)$$k = \upsilon \rho {C_p}$$

where ρ is the density of the Er:Yb:CYVP crystal and was measured to be 3.21 g/cm³ by Archimedes method. Therefore, the thermal conductivities were calculated to be 1.08 and 1.09 Wm⁻¹K⁻¹ for a and c direction at room temperature, respectively, which are slightly higher than that (0.8 Wm⁻¹K⁻¹ [2]) of the Er:Yb:PG.

The Er:Yb:CYVP crystal is a uniaxial crystal, but the n_o and n_e were not obtained in this work, because the grown crystal is not large enough. But the average refractive index of the crystal was measured at room temperature by a spectroscopic ellipsometry (V-VASE, J. A. Woollam) using a unoriented crystal wafer. The values in a wavelength range from 300 to 1000 nm are shown in Fig. 3. The refractive index of the Er:Yb:CYVP crystal is smaller than that of the CYV crystal whose refractive index ranges from 1.83 to 1.92 between the wavelength of 488 and 1388 nm [14]. The experimental data of the Er:Yb:CYVP crystal were fitted to the following Sellmeier equation:

(2)$${n_\lambda }^2 = \textrm{2}\textrm{.82431} + \frac{{\textrm{19179}\textrm{.38162}}}{{{\lambda ^2} - \textrm{32326}\textrm{.26065}}} + \textrm{8}\textrm{.20485} \times \textrm{1}{\textrm{0}^{ - 9}}{\lambda ^2}$$

where λ is wavelength in unit of nanometer. The average refractive index around 1550 nm was calculated to be about 1.688 based on the fitted Sellmeier equation. Then the measured and calculated average refractive index were used for the subsequent J-O theory calculation.

Fig. 3. Values of refractive index of the Er:Yb:CYVP crystal in 300–1000 nm.

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3. Spectroscopic properties

Room-temperature (RT) polarized absorption spectra in 365–1700 nm of the crystal were recorded by an UV-VIS-NIR spectrophotometer (Lambda-950, PerkinElmer), and are shown in Fig. 4. Polarized absorption spectra from 880 to 1050 nm, which are commonly used as the pumping band for 1.55 µm laser, are shown in Fig. 4(c). The peak absorption cross sections are 1.65×10⁻²⁰ and 1.03×10⁻²⁰ cm² at 978 and 974 nm for σ and π polarizations, respectively. The value for σ polarization is larger than that of the Er:Yb:PG (approximately 1×10⁻²⁰ cm² at 976 nm) [2]. The full widths at half maximum (FWHMs) of the absorption bands around 0.97 µm are 35 and 33 nm for σ and π polarizations, respectively, which are much larger than those of the Er:Yb:YAB crystal (17 nm) and the Er:Yb:PG (6 nm) [8,21]. The broad absorption band is caused by the disorder structure of the CYVP crystal, in which Y³⁺ and a part of Ca²⁺ ions occupy the same sites. Then, when the Y³⁺ sites are partially replaced by Er³⁺ and Yb³⁺ in the crystal, the inhomogeneous broadening occurs in the spectra. Therefore, the Er:Yb:CYVP crystal may be more suitable to be pumped by diode laser, after the shifting of emission wavelength of diode laser with the temperature and output power is taken into account.

Fig. 4. RT polarized absorption spectra of the Er:Yb:CYVP crystal in 365–1700nm.

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Based on the measured absorption spectra, some spectroscopic parameters, such as intensity parameters Ω_λ, transition probability A, fluorescence branching ration β, and radiative lifetime τ_rad, can be calculated by the Judd-Ofelt (J-O) theory [22,23]. The calculation procedure is similar to that reported in [24]. The experimental and calculated oscillator strengths as well as the J-O intensity parameters are listed in Table 1. And the transition probability A, fluorescence branching ratio β and radiative lifetime τ_rad are listed in Table 2. The absorption spectra of the Er:Yb:CYVP crystal are the same as those of the Er:CYVP crystal except the absorption bands between 880 and 1050 nm, which were not taken into account during the calculation of the spectroscopic parameters. So the calculated results shown in Tables 1 and 2 are reasonable.

Table 1. Experimental and calculated oscillator strengths for different transitions as well as J-O intensity parameters of Er³⁺ in the Er:Yb:CYVP crystal.

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Table 2. Transition probability, fluorescence branching ratio, and radiative lifetime of Er³⁺ in the Er:Yb:CYVP crystal.

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Excited at 976 nm, RT polarized emission spectra between 1450 and 1655 nm of the crystal were recorded by a spectrometer (FLS1000, Edinburgh). Based on the measured emission spectrum, the stimulated emission cross section in 1450–1655 nm can be calculated by the Füchtbauer–Ladenburg (F–L) formula [25]:

(3)$${\sigma _{em,q}} = \frac{{{A_q}{\lambda ^5}}}{{8\pi n_{}^2c}}\frac{{{I_q}(\lambda )}}{{\int {\lambda {I_q}(\lambda )d\lambda } }}$$

where q indicates the polarized direction, A_q is the transition probability, n is the refractive index of the crystal, c is the speed of light, and I_q(λ) is the fluorescence intensity. The calculated results are shown in Fig. 5. The peak emission cross sections are 1.04 × 10⁻²⁰ and 0.80 × 10⁻²⁰ cm² at 1533 nm for σ and π polarizations, respectively. The one for σ polarization is larger than that of the Er:Yb:PG (0.8 × 10⁻²⁰ cm²) [2]. The FWHMs are 36 and 50 nm for σ and π polarizations, respectively, which are smaller than that (55 nm) of the Er:Yb:PG [26]. The broad emission band is also caused by the disorder structure of the crystal, and may be beneficial to realizing the ultrashort pulse and tunable lasers.

Fig. 5. RT polarized emission cross section spectra in 1450–1650 nm of the Er:Yb:CYVP crystal.

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Gain cross section spectrum σ_g, which is used to analyze the wavelength and polarization of output laser, can be calculated by [27]:

(4)$${\sigma _g}(\lambda ) = \beta {\sigma _{em}}(\lambda ) - (1 - \beta ){\sigma _{abs}}(\lambda )$$

where β is the ratio of the number of Er³⁺ ions in the upper laser level ⁴I_13/2 to the total number of Er³⁺ ions, σ_abs(λ) and σ_em(λ) are the absorption and emission cross sections at wavelength λ, respectively. The results are shown in Fig. 6. It can be seen that the gain cross section for σ polarization is close to that for π polarization at the same wavelength for the same β. When β is 0.5, the peak wavelengths of the gain curves are both located at about 1560 nm for σ and π polarizations.

Fig. 6. Gain cross section spectra of the ⁴I_13/2 → ⁴I_15/2 transition of the Er:Yb:CYVP crystal for different β.

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In order to investigate the variation of fluorescence lifetimes of the related multiplets, the (4.5 at.%) Er³⁺:CYV (Er:CYV) crystalline powder was synthesized by the high temperature solid state method.

The fluorescence decay curves at 977 nm of the ⁴I_11/2 multiplet of Er³⁺ in the Er:CYV crystalline powder and the Er:CYVP crystal powder were recorded by a spectrometer (FLS1000, Edinburgh) when the exciting wavelength was 524 nm. The results are shown in Fig. 7. The fluorescence lifetimes of the Er:CYV crystalline powder and the Er:CYVP crystal powder were fitted to be 48.71 and 14.27 µs, respectively. Because the phonon energy of the CYVP (1110 cm⁻¹) is higher than that of the CYV (900 cm⁻¹), the multiphonon relaxation from ⁴I_11/2 to ⁴I_13/2 multiplet of the Er:CYVP is stronger than that of the Er:CYV, when the energy gap of about 3700 cm⁻¹ between ⁴I_11/2 and ⁴I_13/2 multiplets is taken into account. Therefore, compared with the Er:CYV, the Er:CYVP has a shorter fluorescence lifetime of the ⁴I_11/2 multiplet, which is beneficial to realizing efficient energy transfer from Yb³⁺ to Er³⁺.

Fig. 7. Fluorescence decay curves at 977 nm of the Er:CYV crystalline powder (a) and the Er:CYVP crystal powder (b).

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The fluorescence decay curves at 1534 nm of the ⁴I_13/2 multiplet of Er³⁺ in the Er:CYVP crystal powder and Er:CYV crystalline powder were also measured at the same exciting wavelength of 524 nm. In order to reduce the effect of radiation trapping, the powder samples were dispersed in the bromobenzen with a refractive index of 1.55 in the experiment. The results are shown in Fig. 8. The fitted fluorescence lifetime of the Er:CYV is close to that of the reported Er:CYV crystal (3.84 ms) and longer than the radiative lifetime (3.27 ms) [17]. The fluorescence lifetime of the Er:CYVP crystal was fitted to be 4.89 ms and is also longer than the radiative lifetime (4.30 ms), which may be caused by the calculation error based on the J-O theory and the residual radiation trapping in the powder sample [28]. And it may also indicate that the nonradiative relaxation from ⁴I_13/2 to ⁴I_15/2 multiplet is very weak. As we can see, the introduction of PO₄^3- is beneficial to lengthening the fluorescence lifetime of ⁴I_13/2 multiplet. The energy gap between ⁴I_13/2 and ⁴I_15/2 multiplets is about 6500 cm⁻¹, and about 6–7 phonons are needed for the multiphonon nonradiative relaxation in the phosphate and vanadate crystals. Therefore, the multiphonon nonradiative relaxation from ⁴I_13/2 to ⁴I_15/2 multiplet can be ignored in the above materials. In addition, the concentration-dependent fluorescence quenching of the ⁴I_13/2 multiplet of Er³⁺ is negligible for the materials with Er³⁺ concentration below 1 × 10²⁰ cm⁻³ [29]. Therefore, the fluorescence lifetime of the ⁴I_13/2 multiplet may be close to the radiative lifetime for the above materials. In theory, the radiative lifetime is related to the refractive index of the crystal and J-O intensity parameters [30]. By measuring the impact of the refractive index and J-O intensity parameters of the Er:CYV and Er:CYVP, the radiative lifetime mainly depends on the refractive index and it is negatively correlated with the refractive index. Thus, due to the smaller refractive index of the CYVP, the radiative lifetime of ⁴I_13/2 multiplet of the Er:CYVP (4.30 ms) is longer than that of the Er:CYV (3.27 ms) [17].

Fig. 8. Fluorescence decay curves at 1534 nm of the Er:CYV crystalline powder (a) and the Er:CYVP crystal powder (b).

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The efficiency of energy transfer from Yb³⁺ to Er³⁺ can be estimated by ${\eta _{ET}}\textrm{ = }1\textrm{ - }{\tau _f}/{\tau _0}$ [31], where τ₀ and τ_f are the fluorescence lifetimes of the ²F_5/2 multiplet of Yb³⁺ in the Yb³⁺ singly-doped and Er³⁺/Yb³⁺ co-doped crystals, respectively. The fluorescence decay curves at 1050 nm of the ²F_5/2 multiplet of Yb³⁺ were measured at exciting wavelength of 950 nm from the Er:Yb:CYVP crystal powder and the (45 at.%) Yb³⁺:CYVP (Yb:CYVP) crystalline powder which was prepared by the high temperature solid state method. The fluorescence lifetimes of the ²F_5/2 multiplet of Yb³⁺ in the Er:Yb:CYVP and Yb:CYVP were fitted to be 132.5 and 431 µs, respectively, as shown in Fig. 9. Then, the efficiency of energy transfer from Yb³⁺ to Er³⁺ was estimated to be 69.3% in the Er:Yb:CYVP crystal.

Fig. 9. Fluorescence decay curves at 1050 nm in the Er:Yb:CYVP (a) and Yb:CYVP powders (b).

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Table 3 shows the spectroscopic parameters related to 1.55 µm laser of some Er³⁺/Yb³⁺ co-doped phosphate glass and crystals as well as vanadate crystals. Compared with the Er:Yb:PG, the Er:Yb:CYVP crystal has larger absorption and emission cross sections, but a shorter fluorescence lifetime of the ⁴I_13/2 multiplet and a lower energy transfer efficiency, which can be improved by optimizing the concentrations of Er³⁺ and Yb³⁺. Compared with the Er³⁺/Yb³⁺ co-doped LuPO₄ and KGP crystals, the Er:Yb:CYVP crystal has a larger emission cross section, but a shorter fluorescence lifetime of the ⁴I_13/2 multiplet and a longer one of the ⁴I_11/2 multiplet. More importantly, for the above phosphate crystals, only the CYVP crystal can be grown easily by the CZ method with a short growth period. But at present, the optical quality of the as-grown Er:Yb:CYVP crystal is not high enough to realize the laser operation. So in the further experiments, optimizing the optical property of the crystal is necessary.

Table 3. Comparison of some spectroscopic parameters related to 1.55 µm laser of the Er³⁺/Yb³⁺ co-doped crystals and glass.

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4. Conclusions

An Er:Yb:CYVP crystal was grown successfully by the CZ method. The crystal has comparable spectroscopic parameters and higher thermal conductivity than those of the commercial Er:Yb:PG.Combined with the broad emission band with a FWHM of 50 nm, the Er:Yb:CYVP crystal may be a promising gain medium for the tunable and ultrashort pulse 1.55 µm lasers.

Funding

Fujian Science & Technology Innovation Laboratory for Optoelectronic Information of China (2021ZR119, 2021ZZ118); Strategic Priority Research Program of the Chinese Academy of Sciences (XDB20000000); Science and Technology Service Network Initiative of the Chinese Academy of Sciences (KFJ–STS–QYZX–069); Scientific Instrument Developing Project of the Chinese Academy of Sciences (YZLY202001).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Transition ⁴I_15/2	σ-polarization			π-polarization
Transition ⁴I_15/2	$\bar{λ}$	$f_{e x p} (\times 10^{6})$	$f_{cal} (\times 10^{6})$	$\bar{λ}$	$f_{e x p} (\times 10^{6})$	$f_{cal} (\times 10^{6})$
⁴I_13/2	1521	2.40	1.73 (ed)	1519	2.23	1.55 (ed)
			0.52 (md)			0.52 (md)
⁴I_9/2	796	0.30	0.35	796	0.32	0.29
⁴F_9/2	657	2.75	2.68	657	2.50	2.44
⁴S_3/2	546	0.55	0.84	544	0.59	0.83
²H_11/2	523	23.73	23.12	522	8.80	9.26
⁴F_7/2	490	2.57	3.12	489	2.36	3.00
⁴F_5/2 + ⁴F_3/2	449	0.85	1.64	449	0.86	1.61
²H_9/2	407	0.87	1.24	407	0.78	1.21
⁴G_11/2	381	41.05	41.73	381	17.22	16.67
RMS Δ $f$	0.57 $\times 10^{- 6}$			0.54 $\times 10^{- 6}$
RMS error	3.62%			8.22%
σ polarization		Ω₂ = 14.87 × 10⁻²⁰ cm²		Ω₄ = 1.43 × 10⁻²⁰ cm²		Ω₆ = 1.95 × 10⁻²⁰ cm²
π polarization		Ω₂ = 5.44 × 10⁻²⁰ cm²		Ω₄ = 1.17 × 10⁻²⁰ cm²		Ω₆ = 1.92 × 10⁻²⁰ cm²

J→J’	λ	σ		π		A_total (s⁻¹)	τ_rad (ms)
J→J’	λ	A (s⁻¹)	β (%)	A (s⁻¹)	β (%)	A_total (s⁻¹)	τ_rad (ms)
⁴I_13/2→⁴I_15/2	1532	192.87 (ed) 44.74 (md)	100	177.33 (ed) 44.74 (md)	100	232.34	4.30
⁴I_11/2→⁴I_13/2	2697	38.63 (ed) 11.50 (md)	12.83	33.33 (ed) 11.51 (md)	14.67	362.38	2.76
→⁴I_15/2	977	340.60	87.17	260.85	85.33	362.38	2.76

Transition ⁴I_15/2	σ-polarization			π-polarization
Transition ⁴I_15/2	$\bar{λ}$	$f_{e x p} (\times 10^{6})$	$f_{cal} (\times 10^{6})$	$\bar{λ}$	$f_{e x p} (\times 10^{6})$	$f_{cal} (\times 10^{6})$
⁴I_13/2	1521	2.40	1.73 (ed)	1519	2.23	1.55 (ed)
			0.52 (md)			0.52 (md)
⁴I_9/2	796	0.30	0.35	796	0.32	0.29
⁴F_9/2	657	2.75	2.68	657	2.50	2.44
⁴S_3/2	546	0.55	0.84	544	0.59	0.83
²H_11/2	523	23.73	23.12	522	8.80	9.26
⁴F_7/2	490	2.57	3.12	489	2.36	3.00
⁴F_5/2 + ⁴F_3/2	449	0.85	1.64	449	0.86	1.61
²H_9/2	407	0.87	1.24	407	0.78	1.21
⁴G_11/2	381	41.05	41.73	381	17.22	16.67
RMS Δ $f$	0.57 $\times 10^{- 6}$			0.54 $\times 10^{- 6}$
RMS error	3.62%			8.22%
σ polarization		Ω₂ = 14.87 × 10⁻²⁰ cm²		Ω₄ = 1.43 × 10⁻²⁰ cm²		Ω₆ = 1.95 × 10⁻²⁰ cm²
π polarization		Ω₂ = 5.44 × 10⁻²⁰ cm²		Ω₄ = 1.17 × 10⁻²⁰ cm²		Ω₆ = 1.92 × 10⁻²⁰ cm²

J→J’	λ	σ		π		A_total (s⁻¹)	τ_rad (ms)
J→J’	λ	A (s⁻¹)	β (%)	A (s⁻¹)	β (%)	A_total (s⁻¹)	τ_rad (ms)
⁴I_13/2→⁴I_15/2	1532	192.87 (ed) 44.74 (md)	100	177.33 (ed) 44.74 (md)	100	232.34	4.30
⁴I_11/2→⁴I_13/2	2697	38.63 (ed) 11.50 (md)	12.83	33.33 (ed) 11.51 (md)	14.67	362.38	2.76
→⁴I_15/2	977	340.60	87.17	260.85	85.33	362.38	2.76

Polarized spectroscopic properties of Er³⁺/Yb³⁺ co-doped Ca₉Y(VO₄)₃(PO₄)₄ crystal

Abstract

1. Introduction

2. Crystal growth

3. Spectroscopic properties

4. Conclusions

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (9)

Tables (3)

Equations (4)

Optical Materials Express

Host	CYVP	PG	LuPO₄	KGP	LaPO₄	CYV	YVO₄
Growth method	CZ	melting quenching	flux	flux	flux	CZ	CZ
N_Er (10²⁰ cm⁻³)	0.75	∼1	2.18	0.77	0.13	0.31	0.86
N_Yb (10²⁰ cm⁻³)	6.68	∼10	10.92	1.66	1.31	0.71	3.7
Peak absorption wavelength λ_p (nm)	978	976	975	976	978		980
σ_abs at λ_p (10⁻²⁰ cm²)	1.65	1.0	3.32	1.06			8
Peak emission wavelength λ_em (nm)	1533	1533	1538	1537	1527	1533	1603
σ_em at λ_p (10⁻²⁰ cm²)	1.04	0.8	0.85	0.60	0.83	1.35	0.7
τ_f of ⁴I_11/2 multiplet (µs)	14.27	2∼3	3.5	1.54	63		28
τ_f of ⁴I_13/2 multiplet (ms)	4.89	∼8	5.13	6.32	3.7	3.84	2.32
Energy transfer efficiency (%)	69.3	90		62			56
References	This work	[1,2]	[9,10]	[11]	[32]	[17]	[7,33]