Judd-Ofelt Analysis of High Erbium Content Yttrium-Aluminum and Yttrium-Scandium-Aluminum Garnet Ceramics

Abstract

The Er_1.5Y_1.5Al₅O₁₂ (Er:YAG) and (Er_1.43Y_1.43Sc_0.14)(Sc_0.24Al_1.76)Al₃O₁₂ (Er:YSAG) ceramics have been characterized using the Judd-Ofelt (JO) theory. The line strengths and oscillator strengths of several transitions from the ground state ⁴I_15/2 to excited state manifolds have been evaluated from transmittance spectra measured at room temperature (300 K). The JO parameters have been calculated, and the values of the radiative decays rate and the radiative lifetimes for the ⁴I_13/2 excited state, and the luminescence cross-section of ⁴I_15/2 → ⁴I_13/2 in Er-doped ceramic samples have been established. We have traced the influence of Sc³⁺ inclusion on spectroscopic properties and crystal quality and estimate prospects of application in laser systems.

1. Introduction

Rare-earth-doped yttrium-aluminum garnet Y₃Al₅O₁₂ materials (YAG) are well-known as active media for solid-state lasers [1,2,3,4]. In recent years, rare-earth-doped materials have been broadly used in solid-state lasers, colour displays [5,6,7], optical amplifiers [8], free-space optical communications [9,10], sensors [11,12,13], 3D waveguides [14,15], and X-ray screens [16]. Recently, Er³⁺:YAG has attracted considerable interest for its high-power, high-energy eye-safe lasers operating near 1.5 μm for range finding, flash lidar, and other remote-sensing applications [17]. Emitting at mid-infrared 2.9 μm Er:YAG has found wide application in medicine—in gynecology [18,19], dentistry [20], and microsurgery [21].

Transparent ceramics were initially developed to replace single crystals in cases of disk geometry and multilayer and concentration gradient architectures. Among solid-state lasers, disk lasers offer significant advantages for both ultrafast and continuous wave operation [22]. In a disk laser, the gain medium is shaped like a disk with a large diameter in comparison to its thickness. This geometry allows the gain medium to be very efficiently cooled. The large mode areas on the gain medium and the short propagation distance of the pulses through the gain medium make it inherently advantageous for small nonlinearities at very high pulse energies. Mode-locked thin-disk oscillators have consistently achieved orders of magnitude higher than the average power and pulse energy of other narrow pulse and ultranarrow pulse oscillator technology, reaching comparable levels to advanced high-power amplifiers operating at an MHz repetition rate [23].

The doping concentration of rare-earth ions in YAG ceramics can reach 100% [24,25]. A promising feature of YSAG ceramics is the introduction of scandium into the dodecahedral and octahedral positions of the garnet that leads to disordering of the crystal lattice. This is expressed in the broadening of the absorption bands that may results in achievement of laser pulses with high power and short duration. These lasing parameters are useful because they decrease medical laser interventions and are therefore less traumatic.

In this paper, we report optical characterization of Er_1.5Y_1.5Al₅O₁₂ and (Er_1.43Y_1.43Sc_0.14)(Sc_0.24Al_1.76)Al₃O₁₂ ceramics carried out through a comparative Judd-Ofelt (JO) analysis [26,27]. The Judd-Ofelt parameters were calculated from the experimental absorption spectra of the ceramics to trace the influence of Sc³⁺ inclusion on spectroscopic properties and crystal quality and estimate the prospects for application in laser systems.

2. Results and Discussion

The normalized transmittance spectrum and absorption coefficient for Er³⁺:YSAG ceramic samples (S₄) are given in Figure 1. The spectra consist of eight complex Er³⁺ (⁴f₁₁) lines, which are observed at 372.9, 407.8, 448.7, 513.7, 653.2, 798.5, 968.1, and 1494.1 nm and correspond to ⁴I_15/2 → ⁴G_11/2 + ⁴G_9/2 + ²K_15/2 + ²G_7/2, ²H_9/2, ⁴F_5/2 + ⁴F_3/2, ⁴S_3/2 + ²H_11/2 + ⁴F_7/2, ⁴F_9/2, ⁴I_9/2, ⁴I_11/2, and ⁴I_13/2 electron transitions, respectively.

The room-temperature absorption spectra of Er³⁺-doped YAG/YSAG ceramics in the spectral range of 770–860 nm corresponding to ⁴I_15/2 → ⁴I_9/2 electron transitions in Er³⁺ ion are presented in Figure 2. The broadening of spectral lines is recognized as result of the partially disordering crystal structure of the ceramics due to Sc³⁺ doping.

JO analysis has been applied to estimate the spectroscopic parameter changes in Er:YSAG ceramics in comparison with Er:YAG ones. Eight complex lines of the room-temperature transmittance spectra were chosen to determine the JO parameters for the corresponding Er³⁺ (⁴f₁₁) transitions in samples.

The mean wavelengths and integrated absorption coefficients of Er:YAG and Er:YSAG ceramics (

Table 1. The mean wavelengths ($\overline{\lambda }$) and integrated absorption coefficient (Г) corresponding to electron transitions of Er³⁺:YAG (Er³⁺:YSAG) ceramic samples at 300 K.

Transition 4I15/2→	S1		S2		S3		S4
	$\overline{\mathit{\lambda }}$ (nm)	Г (nm × cm−1)	$\overline{\mathit{\lambda }}$ (nm)	Г (nm × cm−1)	$\overline{\mathit{\lambda }}$ (nm)	Г (nm × cm−1)	$\overline{\mathit{\lambda }}$ (nm)	Г (nm × cm−1)
4I13/2	1495.0	-	1494.9	-	1494.1	-	1494.1	-
4I11/2	968.8	268.250	967.2	275.135	968.4	295.429	968.1	297.084
4I9/2	797.5	100.318	796.1	90.996	795.9	97.574	798.5	110.707
4F9/2	653.5	339.720	653.3	331.758	653.2	379.385	653.2	376.760
4S3/2+2H11/2+4F7/2	514.1	491.496	514.7	456.811	514.1	489.456	513.7	496.346
4F5/2+4F3/2	449.9	78.839	448.6	71.185	448.5	76.869	448.7	78.585
2H9/2	408.5	44.988	407.7	41.845	407.8	45.055	407.8	43.392
4G11/2+4G9/2+2K15/2+2G7/2	372.8	389.977	372.6	385.820	372.8	383.785	372.9	374.759

) were used for the determining of line strengths s_meas and oscillator strengths f_meas (

Table 2. Values of the measured and calculated absorption line strengths of Er³⁺ in the YAG (YSAG) ceramic samples at 300 K; ed is electric dipole transition, md is magnetic dipole one.

Transition 4I15/2→	S1		S2		S3		S4
	sexp × 10−20 (cm2)	scalc × 10−20 (cm2)	sexp × 10−20 (cm2)	scalc × 10−20 (cm2)	sexp × 10−20 (cm2)	scalc × 10−20 (cm2)	sexp × 10−20 (cm2)	scalc × 10−20 (cm2)
4I13/2	-	1.97(16) ed +0.72 md	-	1.94(17) ed +0.72 md	-	2.19(20) ed +0.72 md	-	2.34(11) ed +0.72 md
4I11/2	0.38	0.26(2)	0.42	0.27(3)	0.42	0.25(2)	0.40	0.28(1)
4I9/2	0.19	0.14(5)	0.17	0.16(1)	0.17	0.15(1)	0.18	0.15(1)
4F9/2	0.71	0.72(9)	0.79	0.79(7)	0.73	0.73(7)	0.75	0.76(4)
4S3/2+2H11/2 + 4F7/2	1.19	1.26(1)	1.29	1.36(1)	1.27	1.36(1)	1.14	1.43(7)
4F5/2 + 4F3/2	0.25	0.22(3)	0.23	0.23(2)	0.22	0.21(2)	0.25	0.23(1)
2H9/2	0.13	0.16(1)	0.15	0.17(2)	0.14	0.15(1)	0.15	0.16(1)
4G11/2+4G9/2 + 2K15/2 + 2G7/2	1.24	1.19(4)	1.35	1.292(1)	1.43	1.35(1)	1.44	1.39(8)
$RMS ∆s$	$5.97\times {10}^{-2}$		$7.13\times {10}^{-2}$		$7.32\times {10}^{-2}$		$8.25\times {10}^{-2}$
$RMS \mathrm{error}$(%)	8.17		9.02		9.19		5.05

). The determined line strengths are used to calculate Ω₂, Ω₄, and Ω₆ parameters by the Judd-Ofelt theory. The values of the measured (s_meas) and calculated (s_calc) absorption line strengths are tabulated in Table 2. The values of the measured (f_meas) and calculated (f_calc) absorption oscillator strengths are summarized in

Table 3. Values of the measured and calculated absorption oscillator strengths of Er³⁺ in the YAG (YSAG) ceramic samples at 300 K; ed is electric dipole transition, md is magnetic dipole one.

Transition 4I15/2→	S1		S2		S3		S4
	fexp × 10−6	fcalc × 10−6	fexp × 10−6	fcalc × 10−6	fexp × 10−6	fcalc × 10−6	fexp × 10−6	fcalc × 10−6
4I13/2	-	1.54(20) ed +0.59 md	-	1.51(5) ed +0.59 md	-	1.71(7) ed +0.59 md	-	1.84(11) ed +0.59 md
4I11/2	0.46	0.31(4)	0.52	0.34(1)	0.50	0.30(1)	0.49	0.33(7)
4I9/2	0.26	0.17(2)	0.25	0.24(1)	0.25	0.22(1)	0.27	0.22(5)
4F9/2	1.28	1.32(2)	1.46	1.45(5)	1.33	1.33(6)	1.36	1.37(4)
4S3/2 + 2H11/2 + 4F7/2	3.00	2.97(4)	3.03	3.20(2)	2.95	3.18(2)	3.18	3.35(2)
4F5/2 + 4F3/2	0.63	0.61(8)	0.63	0.65(1)	0.61	0.57(3)	0.67	0.63(2)
2H9/2	0.44	0.48(7)	0.44	0.51(2)	0.43	0.46(2)	0.46	0.50(2)
4G11/2 + 4G9/2 + 2K15/2 + 2G7/2	4.53	3.96(7)	4.52	4.34(2)	4.76	4.51(2)	4.80	4.63(2)
$RMS ∆f$	$2.920\times {10}^{-1}$		$0.785\times {10}^{-1}$		$1.004\times {10}^{-1}$		$0.769\times {10}^{-1}$
$\mathrm{RMS} \mathrm{error}$(%)	13.6		3.64		4.54		3.39

. The values of root mean square (RMS) and relative error for the oscillator strength and absorption oscillator strengths are listed in Table 2 and Table 3, respectively. The values of JO parameters are given in

Table 4. Judd–Ofelt parameters of the Er³⁺-doped YAG (YSAG) ceramics at 300 K.

Ceramic Samples	Judd-Ofelt Parameters
	Ω2 × 10−20, cm2	Ω4 × 10−20, cm2	Ω6 × 10−20, cm2
S1	0.2955	0.8037	0.6410
S2	0.3064	0.8984	0.6818
S3	0.4446	0.8521	0.6080
S4	0.4681	0.8378	0.6741

. The spectral intensity parameters are reflected in many crystal effects such as chemical bonds between the ions in the host, the charge distribution on the ions in the cell, and the lattice distortion. The Ω₂ value is the most affected to changes in the environment of the lanthanide ion. The Ω₂ value is higher in Er:YSAG compared with Er:YAG due to substitution of Y³⁺ by Sc³⁺ ions and local distortion in the dodecahedral position. Meanwhile, the other two JO parameters of Er:YSAG ceramics are similar to corresponding parameters of the Er:YAG ones and vary insignificantly. This behavior can be explained by the fact that Ω₆ and Ω₄ are usually more sensitive to change in f-electron number (changing a type of a rare-earth ion) and are less affected (or unaffected) by the environment [28].

Room-temperature luminescence spectra of all ceramic samples in comparison with the Er³⁺:YAG single crystal are shown in Figure 3. The line widths of the YAG samples S₁ and S₂ are comparable with the single crystal one. Line widths of the ceramics containing Sc³⁺ (S₃, S₄) look broader due to the higher degree of disorder in the crystal structure. We observe a shift of the line maxima in Er:YSAG ceramic samples relative to Er:YAG ceramics and the single crystal.

The radiative decay rate (A_rad) and the radiative decay time (τ_rad) for the ⁴I_13/2 → ⁴I_15/2 electron transition has been evaluated using the JO parameters (

Table 5. Radiative decay rates (A_J→J’), radiative decay time ${\tau }_{rad}^{calc}$, fluorescence lifetime (${\tau }_{lum}^{exp}$), the intrinsic quantum yield (η), non-radiative multiphonon decay rates (W_NR) of the ⁴I_13/2 multiplet, and the values of emission cross section ($\sigma$) of the ⁴I_13/2 → ⁴I_15/2 electron transition in Er³⁺-doped YAG (YSAG) ceramics at 300 K.

Parameters	S1	S2	S3	S4
AJ→J’ (s−1)	137.74	143.98	133.08	140.26
${\tau }_{rad}^{calc}$ (ms)	3.2	3.1	3.2	3.1
${\tau }_{lum}^{exp}$ (ms)	0.146 (3)	0.180 (2)	0.264 (4)	0.266 (3)
η (%)	4.56	5.81	8.25	8.58
WNR (s−1)	6536	5233	3475	3437
$\sigma$·10−19 (cm2)	0.105	0.110	0.097	0.082

). To obtain more reliable information about the perspective of application of our materials, we have calculated the values of an emission cross-section of the ⁴I_13/2 → ⁴I_15/2 electron transition.

Another important parameter is the intrinsic quantum yield (η) being evaluated from the ratio of the fluorescence to radiative decay time (Formula (S13), Supporting Information). Figure 4 shows decay curves being measured for the ⁴I_13/2 → ⁴I_15/2 electron transition in Er:YAG and Er:YSAG ceramics. The fluorescence lifetimes and the intrinsic quantum yield being obtained for the ⁴I_13/2 → ⁴I_15/2 electron transition are given in Table 5.

The non-radiative multiphonon decay rates may be given by Expression (S14) (Supporting Information). The main contribution to non-radiative decay for the ceramic samples with high dopant comes from multiphonon relaxation from the host and energy transfer interaction between nearby ions. Moreover, numerous grain boundaries can act as quenchers.

3. Materials and Methods

The ceramic samples have been synthesized by co-precipitation from an aqueous solution following annealing at a high temperature according to earlier published protocol [29,30,31]. We investigated four ceramic samples of the following chemical composition: Er_1.5Y_1.5Al₅O₁₂ (S₁ and S₂ samples) and Er_1.43Y_1.43Sc_0.38Al_4.76O₁₂ (S₃ and S₄ samples). Values of uniaxial pressing vary in the range of 50–100 MPa, and temperature of vacuum sintering—in the range of 1760–1780 °C [32]. The Er:YAG and Er:YSAG ceramics looked like disks with a diameter of 10 mm and thickness of about 1 mm.

The room-temperature transmittance spectra of the Er³⁺:YAG ceramics were recorded using the Shimadzu UW-3101PC spectrophotometer controlled by a desktop computer in the range of 250–1700 nm with resolution of 1 nm. The high-resolved (0.1 nm) transmittance spectra have been measured in the range of 770 to 860 nm (⁴I_15/2 → ⁴F_9/2 electron transitions in Er³⁺ ion).

Transmittance spectra of the ceramics have been analyzed using JO theory. The analysis is described in detail in Supporting Information. The absorption coefficients of the samples are calculated by Equation (1) using experimental transition spectra:

$$\alpha \left(\lambda \right)=\left(I/I_0\right)$$

(1)

where α(λ) is the absorption coefficient; I and I₀ are spectral intensities of the light transmitted through the sample and directed into the sample, respectively; l is the thickness of the sample.

The room-temperature fluorescence spectra have been recorded in the range of 1400 to 1700 nm corresponding to ⁴I_13/2 → ⁴I_15/2 electron transitions in Er³⁺:YAG/YSAG ceramics. The Er³⁺:YAG single crystal has been grown at the Research Institute of Materials Science and Technology (Zelenograd, Russia) and used as a standard. The spectra have been measured using the ARC SpectraPro-300i monochromator at diode laser excitation at a wavelength of 965 nm and irradiation of up to 3 mW. The signals were detected with a thermoelectrically cooled InGaAs detector.

4. Conclusions

A spectroscopic analysis of Er³⁺ in YAG (S₁, S₂) and YSAG (S₃, S₄) ceramics has been performed by the Judd-Ofelt theory. The Judd-Ofelt parameters such as Ω₂, Ω₄, and Ω₆ are determined for Er:YAG (S₁, S₂) and Er:YSAG (S₃, S₄) ceramics. The Ω₂ value is increased in S₁ to S₄ samples due to asymmetry of the crystal field around Er³⁺ and increases with a disorder degree in the crystal structure. The predicted radiative decay time of the ⁴I_13/2 electron level varies insignificantly. Disordering in YSAG ceramics results in the broadening the emission lines and smoothing of the luminescence/gain spectrum in the 1.5-µm range in comparison with the YAG crystal or ceramic host. This factor makes it a promising active media for the amplifiers in this spectral range. The shorter experimental lifetimes and relatively low intrinsic quantum yield in the heavily doped Er³⁺:YSAG ceramics can be attributed to the concentration effect, where the energy up-conversion and cross-relaxation mechanisms become increasingly important. However, the heavily doped Er³⁺:YSAG ceramics can therefore be considered as an excellent active media for a 3-µm laser system.