Spectroscopic study and Judd&#x2013;Ofelt analysis of Pr<sup>3+</sup>-doped Zr&#x2013;Ba&#x2013;La&#x2013;Al glasses in visible spectral range

Melinda Olivier; Jean-Louis Doualan; Virginie Nazabal; Patrice Camy; Jean-Luc Adam

doi:10.1364/JOSAB.30.002032

Journal of the Optical Society of America B
Vol. 30,
Issue 8,
pp. 2032-2042
(2013)
•https://doi.org/10.1364/JOSAB.30.002032

Spectroscopic study and Judd–Ofelt analysis of Pr³⁺-doped Zr–Ba–La–Al glasses in visible spectral range

Melinda Olivier, Jean-Louis Doualan, Virginie Nazabal, Patrice Camy, and Jean-Luc Adam

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Melinda Olivier, Jean-Louis Doualan, Virginie Nazabal, Patrice Camy, and Jean-Luc Adam, "Spectroscopic study and Judd–Ofelt analysis of Pr³⁺-doped Zr–Ba–La–Al glasses in visible spectral range," J. Opt. Soc. Am. B 30, 2032-2042 (2013)

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Abstract

Visible transitions in the blue, green, and red of $\Pr^{3 +}$ ions are of interest for laser applications. A description of spectroscopic properties of this rare earth ion in Zr–Ba–La–Al (ZBLA) fluorozirconate glass matrix is presented, using an original approach. Magnetic-dipole and electric-dipole contributions are calculated, in the context of the Judd–Ofelt theory, to determine the $Ω_{t}$ ( $t = 2$ , 4, 6) parameters, lifetime, and branching ratios of ${{}^{3}P}_{0}$ emitting level. Influence of overlapping transitions and sensitized transitions are discussed, as well as the use of the standard or normalized method. Branching ratios are measured using an experimental method and compared to theoretical ones. The influence of higher energy and thermally populated ${{}^{3}P}_{1}$ and ${{}^{1}I}_{6}$ levels on the ${{}^{3}P}_{0}$ lifetime is also studied. Considering this influence, a good agreement is found between theoretical and experimental ${{}^{3}P}_{0}$ lifetimes. Finally, emission cross sections are calculated for the visible transitions, using either the reciprocity method or the Füchtbauer–Ladenburg formula, for different calculated Judd–Ofelt parameters, highlighting the ability of $\Pr^{3 +}$ -doped ZBLA to be used as a laser material.

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Transition	${‖ L + 2 S ‖}^{2}$	$S_{MD} (10^{- 20} {cm}^{2})$
${}^{3}{H_{4}} \to {}^{3}{H_{5}}$	10.538	0.3929
${}^{3}{H_{4}} \to {}^{3}{F_{3}}$	0.005	0.0002
${}^{3}{H_{4}} \to {}^{3}{F_{4}}$	0.126	0.0047
${}^{3}{H_{4}} \to {}^{1}{G_{4}}$	0.068	0.0025

Transition	$λ$ (nm)	$\int σ_{a} (λ) d λ$ ( $10^{- 20} cm \cdot nm$ )	$f_{exp}$ ( $10^{- 8}$ )
${}^{3}{H_{4}} \to {}^{3}{H_{5}}$	4668.4	14.6	26.9
${}^{3}{H_{4}} \to {}^{3}{H_{6}}$	2231.4	28.7	65.1
${}^{3}{H_{4}} \to {}^{3}{F_{2}}$	1968.7	85.1	248.1
${}^{3}{H_{4}} \to {}^{3}{H_{6}}$ , ${{}^{3}F}_{2}$	2035.6	113.8	310.2
${}^{3}{H_{4}} \to {}^{3}{F_{3}}$	1556.9	115.7	539.2
${}^{3}{H_{4}} \to {}^{3}{F_{4}}$	1446	45.2	244.9
${}^{3}{H_{4}} \to {}^{3}{F_{3, 4}}$	1525.7	160.9	781.4
${}^{3}{H_{4}} \to {}^{1}{G_{4}}$	1007.1	2.5	28.1
${}^{3}{H_{4}} \to {}^{1}{D_{2}}$	588.4	5.5	179.4
${}^{3}{H_{4}} \to {}^{3}{P_{0}}$	481.4	3.9	190.3
${}^{3}{H_{4}} \to {}^{3}{P_{1}}$	468.6	5.7	293.2
${}^{3}{H_{4}} \to {}^{1}{I_{6}}$	460.1	2.5	133.4
${}^{3}{H_{4}} \to {}^{3}{P_{1}}$ , ${{}^{1}I}_{6}$	466.0	8.2	426.5
${}^{3}{H_{4}} \to {}^{3}{P_{2}}$	443.3	14.5	835.1

Transition	Levels Included
Transition	1	2	3	4	5	6	7	8	Average
${}^{3}{H_{4}} \to {}^{3}{H_{5}}$
${}^{3}{H_{4}} \to {}^{3}{H_{6}}$		×			×	×		×
${}^{3}{H_{4}} \to {}^{3}{F_{2}}$		×			×	×		×
${}^{3}{H_{4}} \to {}^{3}{H_{6}}$ , ${}^{3}{F_{2}}$	×		×	×			×
${}^{3}{H_{4}} \to {}^{3}{F_{3}}$			×		×		×	×
${}^{3}{H_{4}} \to {}^{3}{F_{4}}$			×		×		×	×
${}^{3}{H_{4}} \to {}^{3}{F_{3, 4}}$	×	×		×		×
${}^{3}{H_{4}} \to {}^{1}{G_{4}}$	×	×	×	×	×	×	×	×
${}^{3}{H_{4}} \to {}^{1}{D_{2}}$	×	×	×	×	×	×	×	×
${}^{3}{H_{4}} \to {}^{3}{P_{0}}$	×	×	×	×	×	×	×	×
${}^{3}{H_{4}} \to {}^{3}{P_{1}}$				×		×	×	×
${}^{3}{H_{4}} \to {}^{1}{I_{6}}$				×		×	×	×
${}^{3}{H_{4}} \to {}^{3}{P_{1}}$ , ${{}^{1}I}_{6}$	×	×	×		×
${}^{3}{H_{4}} \to {}^{3}{P_{2}}$
$Ω_{2 standard}$	1.55	1.36	0.50	5.21	1.17	1.55	20.79	0.92	$1.2 \pm 0.4$
$Ω_{4 standard}$	4.37	4.36	5.56	4.11	5.67	4.12	4.12	5.00	$4.8 \pm 0.7$
$Ω_{6 standard}$	4.59	4.62	4.34	4.43	4.18	4.68	3.38	4.52	$4.5 \pm 0.2$
$δ_{standard}$	0.49	0.43	0.52	0.47	0.49	0.38	1.03	0.39	$0.42 \pm 0.07$
$Ω_{2 normalized}$	1.09	1.66	0.30	0.99	1.68	1.56	1.97	1.76	$1.7 \pm 0.2$
$Ω_{4 normalized}$	3.65	3.67	3.97	3.84	3.66	3.87	3.99	3.99	$3.8 \pm 0.2$
$Ω_{6 normalized}$	7.05	6.42	5.52	7.07	5.25	6.44	5.39	5.44	$5.9 \pm 0.7$
$δ_{normalized}$	0.40	0.37	0.42	0.36	0.39	0.33	0.38	0.34	$0.36 \pm 0.03$

		Branching Ratio $β$ (%)
		2		5		6		8		Average
Em. Level	Final Level	Std	N	Std	N	Std	N	Std	N	Std	N
$P_{0}$	${}^{1}{D_{2}}$	0	0	0	0	0	0	0	0	$0.0 \pm 0.0$	$0.0 \pm 0.0$
	${}^{1}{G_{4}}$	2.1	1.8	2.3	1.9	2	2	2	2	$2.1 \pm 0.2$	$1.9 \pm 0.2$
	${}^{3}{F_{4}}$	12.4	10.9	13.6	11.2	12	11	13	11	$12.8 \pm 0.8$	$11.0 \pm 0.2$
	${}^{3}{F_{3}}$	0	0	0	0	0	0	0	0	$0.0 \pm 0.0$	$0.0 \pm 0.0$
	${}^{3}{F_{2}}$	13.7	17.2	9.8	18.1	16	16	9	18	$12.1 \pm 3.9$	$17.3 \pm 1.3$
	${}^{3}{H_{6}}$	12.8	18.5	9.7	15.6	13	18	12	15	$11.9 \pm 2.2$	$16.8 \pm 1.8$
	${}^{3}{H_{5}}$	0	0	0	0	0	0	0	0	$0.0 \pm 0.0$	$0.0 \pm 0.0$
	${}^{3}{H_{4}}$	59.0	51.6	64.6	53.2	57	53	63	54	$60.9 \pm 3.7$	$53.0 \pm 1.4$
	$τ_{rad}$ ( $μs$ )	38.8	40.3	32.6	41.7	40.3	39.4	36.6	38.9	$37 \pm 5$	$40 \pm 2$
${}^{3}{P_{1}}$	${}^{3}{P_{0}}$	0	0	0	0	0	0	0	0	$0.0 \pm 0.0$	$0.0 \pm 0.0$
	${}^{1}{D_{2}}$	0.3	0.3	0.2	0.3	0	0.3	0	0	$0.1 \pm 0.2$	$0.2 \pm 0.1$
	${}^{1}{G_{4}}$	1.2	1	1.3	1	1	1	1	1	$1.1 \pm 0.2$	$1.0 \pm 0.0$
	${}^{3}{F_{4}}$	11.2	9.6	12.4	9.9	11	10	12	10	$11.6 \pm 0.8$	$9.9 \pm 0.4$
	${}^{3}{F_{3}}$	16.2	16.8	15.1	17.7	17	16	14	18	$15.6 \pm 1.6$	$17.1 \pm 1.1$
	${}^{3}{F_{2}}$	6.0	7.2	4.6	7.6	7	7	4	7	$5.4 \pm 1.6$	$7.2 \pm 0.4$
	${}^{3}{H_{6}}$	8.2	11.6	6.3	9.9	9	11.4	8	10	$7.9 \pm 1.6$	$10.7 \pm 0.9$
	${}^{3}{H_{5}}$	35.1	34.9	35.9	34.0	34	35.3	37	34	$35.5 \pm 1.5$	$34.6 \pm 0.7$
	${}^{3}{H_{4}}$	21.8	18.6	24.2	19.4	21	19	24	20	$22.8 \pm 1.4$	$19.3 \pm 0.7$
	$τ_{rad} (μs)$	39.5	40.1	33.6	42	40.3	39.3	37.5	39.5	$38 \pm 4$	$40 \pm 1$
${}^{1}{I_{6}}$	${}^{3}{P_{1}}$	0	0	0	0	0	0	0	0	$0.0 \pm 0.0$	$0.0 \pm 0.0$
	${}^{3}{P_{0}}$	0	0	0	0	0	0	0	0	$0.0 \pm 0.0$	$0.0 \pm 0.0$
	${}^{1}{D_{2}}$	2.6	3.3	2.2	3	3	3	2	3	$2.5 \pm 0.5$	$3.1 \pm 0.2$
	${}^{1}{G_{4}}$	50.1	48.8	51.0	49.4	50	49	50.5	50	$50.4 \pm 0.6$	$49.3 \pm 0.7$
	${}^{3}{F_{4}}$	34.6	35.1	34.3	34.9	35	35	35	35	$34.7 \pm 0.4$	$35.0 \pm 0.1$
	${}^{3}{F_{3}}$	0.2	0.2	0.1	0.1	0	0	0	0	$0.1 \pm 0.1$	$0.1 \pm 0.1$
	${}^{3}{F_{2}}$	2.1	2.6	1.8	2.4	2	3	2	2	$2.0 \pm 0.2$	$2.5 \pm 0.5$
	${}^{3}{H_{6}}$	1.3	1.2	1.3	1.2	1	1	1.2	1	$1.2 \pm 0.2$	$1.1 \pm 0.1$
	${}^{3}{H_{5}}$	0.3	0.3	0.3	0.3	0	0	0.3	0	$0.2 \pm 0.1$	$0.2 \pm 0.1$
	${}^{3}{H_{4}}$	8.8	8.5	9	8.6	9	9	9	9	$9.0 \pm 0.2$	$8.8 \pm 0.3$
	$τ_{rad}$ ( $μs$ )	163.5	153.5	144	169.4	167.5	150	153	159	$157 \pm 13$	$158 \pm 12$
		Std	N	Std	N	Std	N	Std	N	Std	N

Transition	$Λ (nm)$		Integrated Intensity (au.nm)		Ratios	Branching Ratios (%)
${}^{3}{P_{0}} \to {}^{1}{G_{4}}$	890.8	$I_{6 \to 5}^{int}$	1.7	$R_{50}$	0.16	10
${}^{3}{P_{0}} \to {}^{3}{F_{4}}$	719.3	$I_{6 \to 4}^{int}$	1.9	$R_{40}$	0.18	9
${}^{3}{P_{0}} \to {}^{3}{F_{2}}$	635.7	$I_{6 \to 3}^{int}$	4.7	$R_{30}$	0.45	19
${}^{3}{P_{0}} \to {}^{3}{H_{6}}$	604.6	$I_{6 \to 2}^{int}$	6.8	$R_{20}$	0.63	26
${}^{3}{P_{0}} \to {}^{3}{H_{5}}$	538.1	$I_{6 \to 1}^{int}$	1.3	$R_{10}$	0.13	4
${}^{3}{P_{0}} \to {}^{3}{H_{4}}$	483.3	$I_{6 \to 0}^{int}$	10.4	$R_{00}$	1	32

		Calculated Emission Cross Section ( $10^{- 20} {cm}^{2}$ )
		Füchtbauer–Ladenburg (average)
Transition	Wavelength (nm)	Std	Norm	McCumber	Exp. $β$ and $τ$
${}^{3}{P_{0}} \to {}^{3}{H_{4}}$	479.1	$4.6 \pm 0.9$	$3.7 \pm 0.2$	2.2	2.4
${}^{3}{P_{1}} \to {}^{3}{H_{5}}$	535.3	$0.4 \pm 0.1$	$0.4 \pm 0.1$
${}^{3}{P_{0}} \to {}^{3}{H_{5}}$	519.9	0	0		3.8
${}^{3}{P_{0}} \to {}^{3}{H_{6}}$	602.1	$2.4 \pm 0.3$	$3.2 \pm 0.4$		5.3
${}^{3}{P_{0}} \to {}^{3}{F_{2}}$	634.6	$4.6 \pm 1.1$	$6.1 \pm 0.4$		7.2

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Journal of the Optical Society of America B