Quantum efficiency and excited-state relaxation dynamics in neodymium-doped phosphate laser glasses

J. A. Caird; A. J. Ramponi; P. R. Staver

doi:10.1364/JOSAB.8.001391

Quantum efficiency and excited-state relaxation dynamics in neodymium-doped phosphate laser glasses

J. A. Caird, A. J. Ramponi, and P. R. Staver

Journal of the Optical Society of America B
Vol. 8,
Issue 7,
pp. 1391-1403
(1991)
•https://doi.org/10.1364/JOSAB.8.001391

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J. A. Caird, A. J. Ramponi, and P. R. Staver, "Quantum efficiency and excited-state relaxation dynamics in neodymium-doped phosphate laser glasses," J. Opt. Soc. Am. B 8, 1391-1403 (1991)

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- Original Manuscript: July 18, 1990
- Published: July 1, 1991

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Abstract

Radiometrically calibrated spectroscopic techniques employing an integrating-sphere detection system have been used to determine the fluorescence quantum efficiencies for two commercially available Nd³⁺-doped phosphate laser glasses, LG-750 and LG-760. Quantum efficiencies and fluorescence lifetimes were measured for samples with various neodymium concentrations. It is shown that the effects of concentration quenching are accurately described when both resonant nonradiative excitation hopping (the Burshtein model) and annihilation by cross relaxation are accounted for by Förster–Dexter dipole–dipole energy-transfer theory. The Förster–Dexter critical range for nonradiative excitation hopping was found to be R_DD = 11 Å, while the critical range for cross relaxation was close to R_DA = 4 Å in these glasses. The quantum efficiency at low Nd³⁺ concentrations was (92 ± 5)%, implying a nonradiative relaxation rate of 210 ± 150 s⁻¹ for isolated ions. Improved values for the radiative lifetimes and the stimulated emission cross sections for these glasses were also deduced from the measurements.

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			LG-750		LG-760

Parameter	Symbol	Units	Theoretical^a	Experimental	Theoretical^b	Experimental
R → Z branching ratio	β_RZ	—	0.401	0.392 ± 0.01	—	0.386 ± 0.01
R → Y branching ratio	β_RY	—	0.500	0.507 ± 0.01	—	0.512 ± 0.01
R → X branching ratio	β_RX	—	0.095	—	—	—
R → W branching ratio	β_RW	—	0.005	—	—	—
Radiative decay rate	A_r	s⁻¹	2840	2425	2760	2560
Radiative lifetime	τ_r	μs	352	410 ± 20	362	390 ± 20
Peak emission cross section	σ^em	10⁻²⁰ cm²	4.0	3.44 ± 0.2	4.2	4.14 ± 0.3
Index of refraction	n	at 1050 nm	—	1.516	—	1.508

Glass	Concentration (wt. % Nd₂O₃)	Nd³⁺ Density (10²⁰ cm⁻³)	β_RZ′	β_RY′	fβ_RZ^a	η_f′	η_f	τ_f′ (μs)	τ_f(μs)
LG-750	0.2	0.19	0.389	0.510	0.005	0.906	0.906	377	375
	1.0	1.00	0.376	0.520	0.025	0.871	0.874	357	349
	2.0	1.96	0.369	0.526	0.036	0.752	0.759	333	324
	3.0	3.14	0.351	0.541	0.063	0.706	0.719	311	297
	4.0	4.06	0.337	0.553	0.083	0.611	0.631	283	268
	8.0	8.32	0.304	0.580	0.126	0.330	0.360	166	158
	12.0	12.77	0.270	0.608	0.166	0.159	0.185	83	80
LG-760	0.04b	0.04	0.390	0.509	0.000	0.817	0.817	317	317
	0.4	0.37	0.377	0.520	0.015	0.934	0.935	367	362
	3.0	2.72	0.353	0.539	0.050	0.743	0.753	310	298
	6.0	5.58	0.322	0.565	0.095	0.589	0.613	259	244

Glass Type	Nd³⁺-Ion Density (10²⁰ cm⁻³)	Quantum Efficiency η_f	Fluorescence Decay Rate W_f = τ_f⁻¹ (s⁻¹)	Radiative Decay Rate A_f = η_fW_f (s⁻¹)	Nonradiative Decay Rate W_nr = (1 − η_f)W_f (s⁻¹)
LG-750	0.19	0.906	2670	2420	250
	1.00	0.874	2870	2510	360
	1.96	0.759	3090	2350	740
	3.14	0.719	3370	2420	950
	4.06	0.631	3730	^a	1380
	8.32	0.360	6330	^a	4050
	12.77	0.185	12500	^a	10200
LG-760	0.04^b	0.817	3150	2570	580^b
	0.37	0.935	2760	2580	180
	2.72	0.753	3360	2530	830
	5.58	0.613	4100	^a	1590

Parameter	Symbol	Units	LG-750	LG-760
Donor–donor critical transfer range	R_DD	Å	11.14	11.37
Cross-relaxation critical range (donor–acceptor)	R_DA	Å	4.07	3.52 (fit)
Zero-concentration nonradiative rate	W₀	s⁻¹	216 ± 150 (fit)	209 ± 150 (fit)
Donor–donor microparameter	C_DD	10⁻³⁹ cm⁶ s⁻¹	4.62	5.55
Donor–acceptor microparameter	C_DA	10⁻⁴¹ cm⁶ s⁻¹	1.10	0.49

			LG-750		LG-760

Parameter	Symbol	Units	Theoretical^a	Experimental	Theoretical^b	Experimental
R → Z branching ratio	β_RZ	—	0.401	0.392 ± 0.01	—	0.386 ± 0.01
R → Y branching ratio	β_RY	—	0.500	0.507 ± 0.01	—	0.512 ± 0.01
R → X branching ratio	β_RX	—	0.095	—	—	—
R → W branching ratio	β_RW	—	0.005	—	—	—
Radiative decay rate	A_r	s⁻¹	2840	2425	2760	2560
Radiative lifetime	τ_r	μs	352	410 ± 20	362	390 ± 20
Peak emission cross section	σ^em	10⁻²⁰ cm²	4.0	3.44 ± 0.2	4.2	4.14 ± 0.3
Index of refraction	n	at 1050 nm	—	1.516	—	1.508

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