Determination of cross-relaxation efficiency based on spectroscopy in thulium-doped rare-earth sesquioxides

Tm³⁺ doped cubic rare-earth sesquioxides have been recognized as excellent laser materials operating at ∼ 2 μm. Upon ³H₄ excitation by commercially available laser diode around 800 nm, a cross-relaxation (CR) process enables efficient Tm³⁺ laser originated from ³F₄→³H₆ transition. The CR process, (Tm1:³H₄, Tm2:³H₆) → (Tm1:³F₄, Tm2: ³F₄), cuts one excitation photon into two photons of 2 μm with quantum efficiency of 200%. As a result, efficient CR is needed. The CR efficiency is usually determined based on the emission lifetime of ³H₄. However, the CR between the nearest Tm³⁺ is too fast to emit, overrating the emission lifetime and underrating the CR efficiency. Here, we propose a spectroscopic method for determination of CR efficiency based on emission intensity ratio. Tm³⁺ doped cubic Y₂O₃, Lu₂O₃, Sc₂O₃, YScO₃, LuScO₃ and YLuO₃ sesquioxides are prepared by solid-state reaction. Near infrared emission spectra and decay curves are studied as a function of Tm³⁺ concentration. The relationship between CR efficiency and emission intensity ratio is established. Large Stark splittings of 1002 cm⁻¹ and 511 cm⁻¹ are observed for the ³H₆ ground state and the ³F₄ excited state of Tm³⁺, respectively in Sc₂O₃:Tm³⁺, leading to a long-wave emission at 2.15 μm. The comparison of these six samples reveals that Sc₂O₃: Tm³⁺ has the largest CR parameter and Lu₂O₃:Tm³⁺ has the highest quantum efficiency for populating the ³F₄ from the ³H₄ at the same Tm³⁺ concentration.