Stochastic model of energy transfer processes among rare earth ions

P. Loiko; M. Pollnau

doi:10.1117/12.2307028

17 May 2018 Stochastic model of energy transfer processes among rare earth ions

P. Loiko, M. Pollnau

Proceedings Volume 10683, Fiber Lasers and Glass Photonics: Materials through Applications; 106831X (2018) https://doi.org/10.1117/12.2307028
Event: SPIE Photonics Europe, 2018, Strasbourg, France

Abstract

Energy-transfer processes strongly affect the performance of lanthanide-doped photonic devices. In this work, we introduce a simple stochastic model of energy-transfer processes and successfully apply it to the example of crossrelaxation (CR) and energy-transfer upconversion (ETU) in amorphous Al₂O₃:Tm³⁺ waveguides on silicon intended for lasers operating at ~2 μm. The stochastic model is based on the rate-equation formalism and considers two spectroscopically distinct ion classes, namely single ions and ions with neighbours (pairs and clusters), with the corresponding ion fractions being dependent on the doping concentration. We prove that a more accurate description of the luminescence properties of amorphous Al₂O₃:Tm³⁺ is obtained when accounting for the presence of these distinct ion classes. Based on the developed model, we derive microscopic CR and ETU parameters of CCR = 5.83×10^-38 cm⁶ s ^-1 , C_ETU1 = 0.93×10^-40 cm⁶ s ^-1 , and C_ETU2 = 7.81×10^-40 cm⁶ s ^-1 , and determine the laser quantum efficiency η_q of excitation of Tm³⁺ ions in the upper laser level. For the maximum Tm³⁺ concentration of 5.0×10²⁰ cm^-3 studied experimentally in this investigation, η_q reaches 1.73. Furthermore, the transition cross-sections at the pump and laser wavelengths are determined. For the ³H₆ → ³F₄transition, the maximum stimulated-emission cross-section is σ_e = 0.47 × 10^-20 cm² at 1808 nm.

Citation Download Citation

P. Loiko and M. Pollnau "Stochastic model of energy transfer processes among rare earth ions", Proc. SPIE 10683, Fiber Lasers and Glass Photonics: Materials through Applications, 106831X (17 May 2018); https://doi.org/10.1117/12.2307028

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