Spectroscopic analysis of Nd3+: Gd3AlxGa5−xO12 garnet crystal

Andrea Arcangeli; Stefano Bigotta; Mauro Tonelli; Zhitai Jia; Jian Zhang; Xutang Tao

doi:10.1364/JOSAB.28.001475

Journal of the Optical Society of America B
Vol. 28,
Issue 6,
pp. 1475-1480
(2011)
•https://doi.org/10.1364/JOSAB.28.001475

Spectroscopic analysis of ${Nd}^{3 +}$ : ${Gd}_{3} {Al}_{x} {Ga}_{5 - x} O_{12}$ garnet crystal

Andrea Arcangeli, Stefano Bigotta, Mauro Tonelli, Zhitai Jia, Jian Zhang, and Xutang Tao

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Andrea Arcangeli, Stefano Bigotta, Mauro Tonelli, Zhitai Jia, Jian Zhang, and Xutang Tao, "Spectroscopic analysis of Nd³⁺: Gd₃Al_xGa_5−xO₁₂ garnet crystal," J. Opt. Soc. Am. B 28, 1475-1480 (2011)

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Abstract

We report a complete spectroscopic analysis of ${Nd}^{3 +}$ -doped ${Gd}_{3} {Al}_{x} {Ga}_{5 - x} O_{12}$ garnet crystal (Nd:GAGG), including absorption and emission spectra at low and room temperatures, excitation spectra showing the multisite structure of the host crystal, and temperature dependence of the lifetime of the ${}^{4}{F_{\frac{3}{2}}}$ manifold. We also report the emission cross sections for the transitions from the ${}^{4}{F_{\frac{3}{2}}}$ manifold and a Judd–Ofelt analysis with the calculation of the spontaneous emission probabilities and the radiative branching ratios.

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${}^{2 S + 1}{L_{J}}$	Energy ( ${cm}^{- 1}$ )	Number of Observed Levels
${}^{4}{I_{\frac{15}{2}}}$	5767.4, 5769.2, 5772.7, 5822.2, 5825.5, 5829.5, 5918.6, 5930.9, 5943.5, 6509.5, 6526.2, 6559.7, 6566.1, 6579.7, 6666.9, 6682.2	16
${}^{4}{F_{\frac{3}{2}}}$	11,434.7, 11,441.8, 11,483.9, 11,491.1, 11,499.0, 11,506.2, 11,512.9	7
${}^{4}{F_{\frac{5}{2}}}$	12,286.9, 12,330.1, 12,375.5, 12,383.9, 12,425.8, 12,432.0, 12,439.4, 12,518.4, 12,525.1	9
${}^{2}{H_{\frac{9}{2}}}$	12,568.7, 12,573.5, 12,594.5, 12,605.2, 12,611.5, 12,814.4, 12,824.6, 12,834.9	8
${}^{4}{F_{\frac{7}{2}}} + {}^{4}{S_{\frac{3}{2}}}$	13,278.9, 13,320.5, 13,375.2, 13,415.6, 13,422.4, 13,429.1, 13,460.8, 13,553.8, 13,559.3, 13,568.5, 13,582.3, 13,604.1, 13,612.9, 13,665.9, 13,736.7	15
${}^{4}{F_{\frac{9}{2}}}$	14,628.9, 14,637.5, 14,657.9, 14,675.1, 14,782.5, 14,795.1, 14,821.4, 14,882.6, 14,895.4	9
${}^{2}{H_{\frac{11}{2}}}$	15,664.2, 15,708.5, 15,764.2, 15,803.4, 15,839.1, 15,849.1, 15,873.0, 15,883.1, 15,956.6, 15,987.9, 16,086.9, 16,091.4	12
${}^{4}{G_{\frac{5}{2}}}$	16,772.2, 16,870.5, 16,880.5, 16,955.6, 16,982.3, 17,001.7, 17,019.8, 17,051.8, 17,058.3, 17,088.2	10
${}^{2}{G_{\frac{7}{2}}}$	17,162.9, 17,219.1, 17,251.8, 17,260.7, 17,273.4, 17,319.8, 17,331.8, 17,455.1, 17,552.3, 17,560.8, 17,666.3	11
${}^{4}{G_{\frac{7}{2}}}$	18,654.9, 18,752.9, 18,763.5, 18,836.8, 18,851.9, 18,863.5, 18,985.2, 19,091.3	8
${}^{2}{K_{\frac{13}{2}}} + {}^{4}{G_{\frac{9}{2}}}$	19,180.9, 19,233.5, 19,310.6, 19,330.2, 19,442.9, 19,519.8, 19,558.9, 19,573.3, 19,602.1, 19,634.8, 19,823.6, 19,983.0	12
${}^{2}{G_{\frac{9}{2}}}$	20,659.0, 20,700.7, 20,725.4, 20,763.0, 20,768.4, 20,797.6, 20,804.1, 20,821.4, 20,828.9	9
${}^{4}{G_{\frac{11}{2}}}$	21,008.4, 21,057.1, 21,065.9, 21,108.2, 21,123.8, 21,174.1, 21,186.4	7
${}^{2}{D_{\frac{3}{2}}} + {}^{2}{K_{\frac{15}{2}}}$	21,592.4, 21,608.8, 21,653.2, 21,682.6, 21,689.6, 21,761.6, 21,869.9, 21,897.4, 21,970.8, 22,016.7	10
${}^{2}{P_{\frac{1}{2}}}$	23,165.3, 23,166.9, 23,173.6	3
${}^{2}{D_{\frac{5}{2}}}$	23,706.5, 23,717.8, 23,755.8, 23,762.9, 23,788.3	5

Excited State	Barycenter ( ${cm}^{- 1}$ )	$P_{exp}$ ( $10^{6}$ )	$P_{calc}$ ( $10^{6}$ )
${}^{4}{F_{\frac{3}{2}}}$	11,388	9.85	12.5
${}^{4}{F_{\frac{5}{2}}} + {}^{2}{H_{\frac{9}{2}}}$	12,421	43.5	40.1
${}^{4}{F_{\frac{7}{2}}} + {}^{4}{S_{\frac{3}{2}}}$	13,405	37.6	40.6
${}^{4}{F_{\frac{9}{2}}}$	14,682	3.16	2.83
${}^{2}{H_{\frac{11}{2}}} + {}^{4}{G_{\frac{5}{2}}} + {}^{2}{G_{\frac{7}{2}}}$	17,074	33.3	33.6
${}^{4}{G_{\frac{7}{2}}} + {}^{2}{K_{\frac{13}{2}}} + {}^{4}{G_{\frac{9}{2}}}$	19,113	20.1	16.6
${}^{2}{G_{\frac{9}{2}}} + {}^{2}{D_{\frac{3}{2}}} + {}^{4}{G_{\frac{11}{2}}} + {}^{2}{K_{\frac{15}{2}}}$	21,191	6.35	3.93
${}^{2}{P_{\frac{1}{2}}} + {}^{2}{D_{\frac{5}{2}}}$	23,127	1.31	1.61
${}^{4}{D_{\frac{3}{2}}} + {}^{4}{D_{\frac{5}{2}}} + {}^{2}{I_{\frac{11}{2}}} + {}^{4}{D_{\frac{1}{2}}}$	28,050	22.5	24.0
$Ω_{2} = 5.04 \times 10^{- 21} {cm}^{2}$	$Ω_{4} = 4.03 \times 10^{- 20} {cm}^{2}$
$Ω_{6} = 5.89 \times 10^{- 20} {cm}^{2}$	$RMS = 2.80 \times 10^{- 21} {cm}^{2}$		$% RMS = 14.4$

Final State	A ( $s^{- 1}$ )	$β_{calc}$	$β_{exp}$	$τ_{R}$ ( $μs$ )
${}^{4}{I_{\frac{9}{2}}}$	$2.39 \times 10^{3}$	0.377	0.305
${}^{4}{I_{\frac{11}{2}}}$	$3.23 \times 10^{3}$	0.510	0.557	158
${}^{4}{I_{\frac{13}{2}}}$	$6.81 \times 10^{2}$	0.108	0.138
${}^{4}{I_{\frac{15}{2}}}$	$3.53 \times 10^{1}$	0.006	0

${}^{2 S + 1}{L_{J}}$	Energy ( ${cm}^{- 1}$ )	Number of Observed Levels
${}^{4}{I_{\frac{15}{2}}}$	5767.4, 5769.2, 5772.7, 5822.2, 5825.5, 5829.5, 5918.6, 5930.9, 5943.5, 6509.5, 6526.2, 6559.7, 6566.1, 6579.7, 6666.9, 6682.2	16
${}^{4}{F_{\frac{3}{2}}}$	11,434.7, 11,441.8, 11,483.9, 11,491.1, 11,499.0, 11,506.2, 11,512.9	7
${}^{4}{F_{\frac{5}{2}}}$	12,286.9, 12,330.1, 12,375.5, 12,383.9, 12,425.8, 12,432.0, 12,439.4, 12,518.4, 12,525.1	9
${}^{2}{H_{\frac{9}{2}}}$	12,568.7, 12,573.5, 12,594.5, 12,605.2, 12,611.5, 12,814.4, 12,824.6, 12,834.9	8
${}^{4}{F_{\frac{7}{2}}} + {}^{4}{S_{\frac{3}{2}}}$	13,278.9, 13,320.5, 13,375.2, 13,415.6, 13,422.4, 13,429.1, 13,460.8, 13,553.8, 13,559.3, 13,568.5, 13,582.3, 13,604.1, 13,612.9, 13,665.9, 13,736.7	15
${}^{4}{F_{\frac{9}{2}}}$	14,628.9, 14,637.5, 14,657.9, 14,675.1, 14,782.5, 14,795.1, 14,821.4, 14,882.6, 14,895.4	9
${}^{2}{H_{\frac{11}{2}}}$	15,664.2, 15,708.5, 15,764.2, 15,803.4, 15,839.1, 15,849.1, 15,873.0, 15,883.1, 15,956.6, 15,987.9, 16,086.9, 16,091.4	12
${}^{4}{G_{\frac{5}{2}}}$	16,772.2, 16,870.5, 16,880.5, 16,955.6, 16,982.3, 17,001.7, 17,019.8, 17,051.8, 17,058.3, 17,088.2	10
${}^{2}{G_{\frac{7}{2}}}$	17,162.9, 17,219.1, 17,251.8, 17,260.7, 17,273.4, 17,319.8, 17,331.8, 17,455.1, 17,552.3, 17,560.8, 17,666.3	11
${}^{4}{G_{\frac{7}{2}}}$	18,654.9, 18,752.9, 18,763.5, 18,836.8, 18,851.9, 18,863.5, 18,985.2, 19,091.3	8
${}^{2}{K_{\frac{13}{2}}} + {}^{4}{G_{\frac{9}{2}}}$	19,180.9, 19,233.5, 19,310.6, 19,330.2, 19,442.9, 19,519.8, 19,558.9, 19,573.3, 19,602.1, 19,634.8, 19,823.6, 19,983.0	12
${}^{2}{G_{\frac{9}{2}}}$	20,659.0, 20,700.7, 20,725.4, 20,763.0, 20,768.4, 20,797.6, 20,804.1, 20,821.4, 20,828.9	9
${}^{4}{G_{\frac{11}{2}}}$	21,008.4, 21,057.1, 21,065.9, 21,108.2, 21,123.8, 21,174.1, 21,186.4	7
${}^{2}{D_{\frac{3}{2}}} + {}^{2}{K_{\frac{15}{2}}}$	21,592.4, 21,608.8, 21,653.2, 21,682.6, 21,689.6, 21,761.6, 21,869.9, 21,897.4, 21,970.8, 22,016.7	10
${}^{2}{P_{\frac{1}{2}}}$	23,165.3, 23,166.9, 23,173.6	3
${}^{2}{D_{\frac{5}{2}}}$	23,706.5, 23,717.8, 23,755.8, 23,762.9, 23,788.3	5

Excited State	Barycenter ( ${cm}^{- 1}$ )	$P_{exp}$ ( $10^{6}$ )	$P_{calc}$ ( $10^{6}$ )
${}^{4}{F_{\frac{3}{2}}}$	11,388	9.85	12.5
${}^{4}{F_{\frac{5}{2}}} + {}^{2}{H_{\frac{9}{2}}}$	12,421	43.5	40.1
${}^{4}{F_{\frac{7}{2}}} + {}^{4}{S_{\frac{3}{2}}}$	13,405	37.6	40.6
${}^{4}{F_{\frac{9}{2}}}$	14,682	3.16	2.83
${}^{2}{H_{\frac{11}{2}}} + {}^{4}{G_{\frac{5}{2}}} + {}^{2}{G_{\frac{7}{2}}}$	17,074	33.3	33.6
${}^{4}{G_{\frac{7}{2}}} + {}^{2}{K_{\frac{13}{2}}} + {}^{4}{G_{\frac{9}{2}}}$	19,113	20.1	16.6
${}^{2}{G_{\frac{9}{2}}} + {}^{2}{D_{\frac{3}{2}}} + {}^{4}{G_{\frac{11}{2}}} + {}^{2}{K_{\frac{15}{2}}}$	21,191	6.35	3.93
${}^{2}{P_{\frac{1}{2}}} + {}^{2}{D_{\frac{5}{2}}}$	23,127	1.31	1.61
${}^{4}{D_{\frac{3}{2}}} + {}^{4}{D_{\frac{5}{2}}} + {}^{2}{I_{\frac{11}{2}}} + {}^{4}{D_{\frac{1}{2}}}$	28,050	22.5	24.0
$Ω_{2} = 5.04 \times 10^{- 21} {cm}^{2}$	$Ω_{4} = 4.03 \times 10^{- 20} {cm}^{2}$
$Ω_{6} = 5.89 \times 10^{- 20} {cm}^{2}$	$RMS = 2.80 \times 10^{- 21} {cm}^{2}$		$% RMS = 14.4$

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Journal of the Optical Society of America B