Cross relaxation and energy transfer upconversion processes relevant to the functioning of 2 μm Tm³⁺-doped silica fibre lasers

We identify the cross relaxation (CR) and energy transfer upconversion (ETU) processes that are important to the operation of Tm³⁺-doped silica fibre lasers using the slope efficiency measured from a number of diode-pumped Tm³⁺-doped silica fibre lasers displayed as a function of Tm³⁺ concentration and Al³⁺:Tm³⁺ concentration ratio. These assessments are correlated with minimum energy mismatch between the initial and final states of each energy transfer process determined from the Stark level assignments relevant to a number of Tm ³⁺-doped crystals. The CR process ³H₄, ³H₆ → ³F₄, ³F ₄ is highly probable in silica because of the strong spectral overlap between the ³H₄ → ³F₄ fluorescence spectrum and ³H₆ → ³F ₄ absorption spectrum. The endothermic phonon-assisted CR process ³H₄, ³H₆ → ³H ₅, ³F₄, however, may have a non-negligible contribution to the total cross relaxation. The exothermic phonon-assisted ETU process ³F₄, ³F₄ → ³H₅, ³H₆ may be the major contributor to quenching of the lifetime of the ³F₄ multiplet particularly when the degree of clustering is large even though the ³F₄ → ³H₅ excited absorption band is outside the transparency range for silica glass. The endothermic phonon-assisted ETU process ³F₄, ³F ₄ → ³H₄, ³H₆ is also shown to have a non-negligible contribution to the quenching of the ³F₄ multiplet. These results have been combined to produce a Tm³⁺-doped silica fibre laser that produces a slope efficiency of ∼74%; the highest yet reported for a ∼2 μm fibre laser.