Modeling of Tm,Ho:YAG and Tm,Ho:YLF 2-μm lasers and calculation of extractable
energies

Didier Bruneau; Stéphane Delmonte; Jacques Pelon

doi:10.1364/AO.37.008406

Applied Optics
Vol. 37,
Issue 36,
pp. 8406-8419
(1998)
•https://doi.org/10.1364/AO.37.008406

Modeling of Tm,Ho:YAG and Tm,Ho:YLF 2-μm lasers and calculation of extractable energies

Didier Bruneau, Stéphane Delmonte, and Jacques Pelon

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Didier Bruneau, Stéphane Delmonte, and Jacques Pelon, "Modeling of Tm,Ho:YAG and Tm,Ho:YLF 2-μm lasers and calculation of extractable energies," Appl. Opt. 37, 8406-8419 (1998)

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Abstract

The development of a model for 2-μm laser operation in Tm,Ho:YAG and YLF crystals pumped in the near infrared is reported. This model, based on a simplified spectroscopic scheme, is fitted to a set of characterization experiments by means of three adjustable parameters. Results show that the excited-state populations are predicted with a relative accuracy of approximately 10% for a large range of pump levels. Using this model, we calculate the extractable energy on short-laser-pulse interactions for the two materials under different operation conditions. We study the sensitivity to pump duration and the optimization of dopant concentrations. We investigate the improvement of the extractable-energy efficiency with multiple-pulse operation. For double-pulse operation the improvement is approximately a factor of 1.5 and leads to overall extractable-energy efficiencies of 16% in YAG and 15% in YLF for an absorbed pump energy of 10 J cm^-3.

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Simulation Parameter	YAG	YLF
Tm concentration [Tm] (10²⁰ cm^-3)	8.2	7
Ho concentration [Ho] (10²⁰ cm^-3)	0.8	0.7
Pump wavelength λ_P (nm)	780	781
Efficient pump absorption cross section σ_P (10^-20 cm²)	0.7	0.93
Laser wavelength λ_L (nm)	2090	2065
Laser transition cross section σ_L (10^-20 cm²)	9.2	15
Population fraction in the lower laser level at 300 K, f _a	1.8 × 10^-2	2.4 × 10^-2
Population fraction in the upper laser level at 300 K, f _b	0.104	8.6 × 10^-2
Ratio of the ³ F ₄–⁵ I ₇ energy-transfer rates at 300 K, θ = q _HT/q _TH	9 × 10^-2	6.1 × 10^-2
³ F ₄ fluorescence lifetime (r _T)^-1 (ms)	11	8
⁵ I ₇ fluorescence lifetime (r _H)^-1 (ms)	15.6	16.1

Model Parameter	YAG	YLF
Pump quantum efficiency η_P	1.78	1.48
Excitation transfer coefficient q _TH (10^-17 cm³ s^-1)	31.7	7.44
Upconversion coefficient q _UC (10^-17 cm³ s^-1)	7.24	1.43

Relative Standard Deviations	YAG	YLF
σ(α_M) (%)	7.4	4.9
σ(τ_R) (%)	12.2	5.4
σ(τ_D) (%)	14.7	7.8

Crystala	Process	Rate Coefficient (10^-17 cm³ s^-1)	Ref.
6% Tm,0.5% Ho:YAG	³ F ₄ ⇒ ⁵ I ₇ excitation transfer	10	20
6% Tm,0.5% Ho:YAG	³ F ₄ ⇒ ⁵ I ₇ excitation transfer	20	10
5.9% Tm,0.33% Ho:YAG	³ F ₄ ⇒ ⁵ I ₇ excitation transfer	13	28
5.8% Tm,x% Ho:YAG	³ F ₄ ⇒ ⁵ I ₇ excitation transfer	14.6	22
5% Tm,x% Ho:YLF	³ F ₄ ⇒ ⁵ I ₇ excitation transfer	6.2	22
x% Tm,x% Ho:YLF	³ F ₄ ⇒ ⁵ I ₇ excitation transfer	6–8	11
6% Tm,0.36% Ho:YAG	⁵ I ₇–³ F ₄ upconversion	2.4	8
0.8%Cr,6% Tm,0.4% Ho:YAG	⁵ I ₇–³ F ₄ upconversion	14	23
6% Tm,0.5% Ho:YAG	⁵ I ₇–³ F ₄ upconversion	2.0	20
5.9% Tm,0.33% Ho:YAG	⁵ I ₇–³ F ₄ upconversion	8.0	28
5.5% Tm,x% Ho:YAG	⁵ I ₇–³ F ₄ upconversion	7.5	22
5% Tm,x% Ho:YLF	⁵ I ₇–³ F ₄ upconversion	1.0	22

Energy Distribution	YAG	YLF
Energy stored in Tm ³ F ₄ (J cm^-3)	3.1	2.7
Energy stored in Ho ⁵ I ₇ (J cm^-3)	2.2	2.55
Laser extractable energy (J cm^-3)	1.15	1.0

Crystal	Number of Extractions	Overall Extractable-Energy Efficiency ∑η_EX (%)	Extractable-Energy per Pulse E _EX/P (J cm^-3)	Gain on Each Pulse γ (cm^-1)
5% Tm,0.66% Ho:YAG	1	11.2	1.12	0.133
5% Tm,0.5% Ho:YAG	2	16.4	0.82	0.097
5% Tm,0.4% Ho:YAG	3	19.2	0.64	0.076
5% Tm,0.45% Ho:YLF	1	9.9	0.99	0.17
5% Tm,0.36% Ho:YLF	2	15.3	0.75	0.131
5% Tm,0.31% Ho:YLF	3	18.7	0.62	0.107

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Applied Optics