Effects of energy transfer among Er3+ ions on the fluorescence decay and lasing properties of heavily doped Er:Y3Al5O12

W. Q. Shi; M. Bass; M. Birnbaum

doi:10.1364/JOSAB.7.001456

Journal of the Optical Society of America B
Vol. 7,
Issue 8,
pp. 1456-1462
(1990)
•https://doi.org/10.1364/JOSAB.7.001456

Effects of energy transfer among Er³⁺ ions on the fluorescence decay and lasing properties of heavily doped Er:Y₃Al₅O₁₂

W. Q. Shi, M. Bass, and M. Birnbaum

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W. Q. Shi, M. Bass, and M. Birnbaum, "Effects of energy transfer among Er³⁺ ions on the fluorescence decay and lasing properties of heavily doped Er:Y₃Al₅O₁₂," J. Opt. Soc. Am. B 7, 1456-1462 (1990)

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Abstract

Nonexponential fluorescence decay has been observed from both ⁴I_11/2 and ⁴I_13/2 states of Er³⁺ ions in heavily doped Er: YAG at room temperature. Processes of cross relaxation that originate in these states are shown to be responsible. Rate equations that include cross-relaxation processes are written and numerically solved, to result in the determination of the cross-relaxation coefficients. It is found that these coefficients do not change with Er³⁺ concentration. The effects of the cross-relaxation processes of Er³⁺ ions on fluorescence decay and lasing properties are discussed.

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Concentration(at. %)	⁴I_13/2 (msec)^a	⁴I_13/2 (msec)^a	⁴S_3/2 (μsec)^b
1	0.102	8.56	14
16.7	0.105	13.74	1
33.3	0.094	9.58	0.5
40	0.096	7.14	0.32
50	0.093	4.19	0.2
60	0.097	1.95	–

Parameters	Values	Reference
C (16.7 at. %)	2.32 × 10²¹ cm⁻³	^a
C (33.3 at. %)	4.66 × 10²¹ cm⁻³	^a
C (50.0 at. %)	7.00 × 10²¹ cm⁻³	^a
τ₁	see Table 1	^a
τ₂	see Table 1	^a
τ₃	1.2 μsec^b	4
τ₄	see Table 1	4
W₄₃^mp	7.1 × 10⁴ sec^−1b	7
n₀W (16.7 at. %)	9.3 × 10⁵ sec⁻¹	7
n₀W (33.3 at. %)	19.3 × 10⁵ sec⁻¹	7
n₀W (50 at. %)	49.3 × 10⁵ sec⁻¹	7
W₀₄ (high pump)	2.45 ×10³ sec⁻¹ (E = 30 mJ)	–
W₀₄ (low pump)	2.45 × 10² sec⁻¹ (E = 3 mJ)	–

Concentration (at. %)	W₁ (cm³/sec)	W₂(cm₃/sec)	Reference
10	1.8 × 10⁻¹⁷	5.1 × 10⁻¹⁷	4
15	2.5 × 10⁻¹⁷	–	15
16.6	1.5 × 10⁻¹⁷	3.0 × 10⁻¹⁷	^a
33.3	4.0 × 10⁻¹⁷	3.0 × 10−17	^a
50	2.5 × 10⁻¹⁷	3.0 × 10⁻¹⁷	^a
50	25.0 × 10⁻¹⁷	–	15

Concentration(at. %)	⁴I_13/2 (msec)^a	⁴I_13/2 (msec)^a	⁴S_3/2 (μsec)^b
1	0.102	8.56	14
16.7	0.105	13.74	1
33.3	0.094	9.58	0.5
40	0.096	7.14	0.32
50	0.093	4.19	0.2
60	0.097	1.95	–

Parameters	Values	Reference
C (16.7 at. %)	2.32 × 10²¹ cm⁻³	^a
C (33.3 at. %)	4.66 × 10²¹ cm⁻³	^a
C (50.0 at. %)	7.00 × 10²¹ cm⁻³	^a
τ₁	see Table 1	^a
τ₂	see Table 1	^a
τ₃	1.2 μsec^b	4
τ₄	see Table 1	4
W₄₃^mp	7.1 × 10⁴ sec^−1b	7
n₀W (16.7 at. %)	9.3 × 10⁵ sec⁻¹	7
n₀W (33.3 at. %)	19.3 × 10⁵ sec⁻¹	7
n₀W (50 at. %)	49.3 × 10⁵ sec⁻¹	7
W₀₄ (high pump)	2.45 ×10³ sec⁻¹ (E = 30 mJ)	–
W₀₄ (low pump)	2.45 × 10² sec⁻¹ (E = 3 mJ)	–

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Equations (7)

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