Influences of radiation trapping on spectroscopic properties of Er<sup>3+</sup>-doped fluorophosphate glasses

Meisong Liao; Lili Hu; Yongzheng Fang; Shiqing Xu; Liyan Zhang

doi:10.1364/JOSAB.24.001498

Journal of the Optical Society of America B
Vol. 24,
Issue 7,
pp. 1498-1504
(2007)
•https://doi.org/10.1364/JOSAB.24.001498

Influences of radiation trapping on spectroscopic properties of ${Er}^{3 +}$ -doped fluorophosphate glasses

Meisong Liao, Lili Hu, Yongzheng Fang, Shiqing Xu, and Liyan Zhang

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Meisong Liao, Lili Hu, Yongzheng Fang, Shiqing Xu, and Liyan Zhang, "Influences of radiation trapping on spectroscopic properties of Er³⁺-doped fluorophosphate glasses," J. Opt. Soc. Am. B 24, 1498-1504 (2007)

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Abstract

Fluorophosphate glasses with different contents of $Er F_{3}$ were prepared. Due to the radiation trapping of Er, concentration dependence of the fluorescence lifetime is subject to distortion, and the stimulated-emission cross section calculated by the Fuchtbauer–Ladenburg equation is underestimated. The influence of radiation trapping on the measured fluorescence lifetime and width are investigated quantitatively. By comparing the intensity ratio of the $1556 - 1532 nm$ peak in the fluorescence spectrum with that in the stimulated-emission cross-section spectrum obtained according to the McCumber theory, the distortion ratio of fluorescence spectrum due to radiation trapping is obtained. An empirical way to quantitatively evaluate the influences of radiation trapping on fluorescence lifetime and width is proposed.

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	$Ω_{2}$ $(\times 10^{- 20} {cm}^{2})$	$Ω_{4}$ $(\times 10^{- 20} {cm}^{2})$	$Ω_{6}$ $(\times 10^{- 20} {cm}^{2})$	$τ_{rad}$ (ms)	$σ_{abs}$ $(\times 10^{- 21} {cm}^{2})$	$σ_{emi}$ $(\times 10^{- 21} {cm}^{2})$
2Er4–30	4.36	2.01	1.14	9.18	6.74	7.41
5Er4–30	4.35	1.99	1.14	9.20	6.61	7.28
8Er4–30	4.35	1.97	1.13	9.23	6.52	7.17
12Er4–30	4.38	1.98	1.15	9.14	6.39	7.03
18Er4–30	4.35	1.96	1.15	9.17	6.30	6.93
26Er4–30	4.36	1.98	1.15	9.15	6.28	6.90

Sample	η ^a (%)	$τ_{mea}$ ^b (ms)	$ζ_{1}$ ^c (%)	FWHM^d (nm)	$ζ_{2}$ ^e (%)	$I_{f 1556} ∕ I_{f 1532}$ ^f	ζ ^g (%)
2Er4	98.47	9.04	0.44	51	0.00	0.621	$- 0.34$
2Er8	98.69	9.06	0.66	51	0.00	0.632	1.38
2Er13	99.46	9.13	1.42	52	1.92	0.634	1.64
2Er20	100.22	9.20	2.17	52	1.92	0.638	2.30
2Er30	101.96	9.36	3.85	53	3.77	0.651	4.17
5Er4	97.83	9.00	1.44	52	1.92	0.625	$- 0.41$
5Er8	98.91	9.10	2.53	52	1.92	0.631	0.48
5Er13	100.00	9.20	3.59	53	3.77	0.639	1.65
5Er20	101.09	9.30	4.62	53	3.77	0.646	2.84
5Er30	104.35	9.60	7.60	54	5.56	0.664	5.36
8Er4	96.22	8.90	0.90	59	1.69	0.654	0.09
8Er8	97.84	9.05	2.54	60	3.33	0.663	1.53
8Er13	100.54	9.30	5.16	62	6.45	0.684	4.51
8Er20	102.16	9.45	6.67	63	7.94	0.708	7.75
8Er30	109.19	10.10	12.67	64	9.38	0.725	9.96
12Er4	95.19	8.70	1.72	62	3.23	0.673	0.90
12Er8	96.94	8.86	3.50	63	4.76	0.688	3.12
12Er13	100.66	9.20	7.07	64	6.25	0.698	4.44
12Er20	105.03	9.60	10.94	66	9.09	0.757	11.92
12Er30	114.88	10.50	18.57	68	11.76	0.785	15.01
18Er4	86.80	7.96	2.01	62	1.61	0.698	3.82
18Er8	89.42	8.20	4.88	63	3.17	0.712	5.70
18Er13	93.78	8.60	9.30	64	4.69	0.719	6.72
18Er20	101.42	9.30	16.13	69	11.59	0.8	16.14
18Er30	110.58	10.14	23.08	75	18.67	0.867	22.57
26Er4	79.78	7.30	5.48	64	4.69	0.715	3.91
26Er8	84.15	7.70	10.39	66	7.58	0.737	6.80
26Er13	90.71	8.30	16.87	68	10.29	0.764	10.11
26Er20	99.45	9.10	24.18	76	19.74	0.865	20.58
26Er30	109.29	10.00	31.00	83	26.51	0.957	28.20

	$τ_{0}$ (ms)	${FWHM}_{0}$ (nm)	$I_{e 1556} ∕ I_{e 1532}$
2Er4–30	9.00	51	0.623
5Er4–30	8.87	51	0.627
8Er4–30	8.82	58	0.653
12Er4–30	8.55	60	0.667
18Er4–30	7.80	61	0.671
26Er4–30	6.90	61	0.687

	$Ω_{2}$ $(\times 10^{- 20} {cm}^{2})$	$Ω_{4}$ $(\times 10^{- 20} {cm}^{2})$	$Ω_{6}$ $(\times 10^{- 20} {cm}^{2})$	$τ_{rad}$ (ms)	$σ_{abs}$ $(\times 10^{- 21} {cm}^{2})$	$σ_{emi}$ $(\times 10^{- 21} {cm}^{2})$
2Er4–30	4.36	2.01	1.14	9.18	6.74	7.41
5Er4–30	4.35	1.99	1.14	9.20	6.61	7.28
8Er4–30	4.35	1.97	1.13	9.23	6.52	7.17
12Er4–30	4.38	1.98	1.15	9.14	6.39	7.03
18Er4–30	4.35	1.96	1.15	9.17	6.30	6.93
26Er4–30	4.36	1.98	1.15	9.15	6.28	6.90

Sample	η ^a (%)	$τ_{mea}$ ^b (ms)	$ζ_{1}$ ^c (%)	FWHM^d (nm)	$ζ_{2}$ ^e (%)	$I_{f 1556} ∕ I_{f 1532}$ ^f	ζ ^g (%)
2Er4	98.47	9.04	0.44	51	0.00	0.621	$- 0.34$
2Er8	98.69	9.06	0.66	51	0.00	0.632	1.38
2Er13	99.46	9.13	1.42	52	1.92	0.634	1.64
2Er20	100.22	9.20	2.17	52	1.92	0.638	2.30
2Er30	101.96	9.36	3.85	53	3.77	0.651	4.17
5Er4	97.83	9.00	1.44	52	1.92	0.625	$- 0.41$
5Er8	98.91	9.10	2.53	52	1.92	0.631	0.48
5Er13	100.00	9.20	3.59	53	3.77	0.639	1.65
5Er20	101.09	9.30	4.62	53	3.77	0.646	2.84
5Er30	104.35	9.60	7.60	54	5.56	0.664	5.36
8Er4	96.22	8.90	0.90	59	1.69	0.654	0.09
8Er8	97.84	9.05	2.54	60	3.33	0.663	1.53
8Er13	100.54	9.30	5.16	62	6.45	0.684	4.51
8Er20	102.16	9.45	6.67	63	7.94	0.708	7.75
8Er30	109.19	10.10	12.67	64	9.38	0.725	9.96
12Er4	95.19	8.70	1.72	62	3.23	0.673	0.90
12Er8	96.94	8.86	3.50	63	4.76	0.688	3.12
12Er13	100.66	9.20	7.07	64	6.25	0.698	4.44
12Er20	105.03	9.60	10.94	66	9.09	0.757	11.92
12Er30	114.88	10.50	18.57	68	11.76	0.785	15.01
18Er4	86.80	7.96	2.01	62	1.61	0.698	3.82
18Er8	89.42	8.20	4.88	63	3.17	0.712	5.70
18Er13	93.78	8.60	9.30	64	4.69	0.719	6.72
18Er20	101.42	9.30	16.13	69	11.59	0.8	16.14
18Er30	110.58	10.14	23.08	75	18.67	0.867	22.57
26Er4	79.78	7.30	5.48	64	4.69	0.715	3.91
26Er8	84.15	7.70	10.39	66	7.58	0.737	6.80
26Er13	90.71	8.30	16.87	68	10.29	0.764	10.11
26Er20	99.45	9.10	24.18	76	19.74	0.865	20.58
26Er30	109.29	10.00	31.00	83	26.51	0.957	28.20

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Equations (6)

Journal of the Optical Society of America B