Population inversion between the 3H4 and the 3F4 excited states of Tm3+ investigated by means of numerical solutions of the rate equations system in Tm3+-doped and Tm3+, Ho3+-codoped fluoride glasses

Population inversion between the 3H4 and the 3F4 excited states of Tm3+ ions responsible for the 1.5 μm emission in Tm3+ singly doped (0.5%) and Tm3+, Ho3+-codoped fluoride (ZBLAN) glasses and its dependence on the Ho3+ concentration (x=0.2–1%) was investigated by means of numerical solution of the rate equations system for continuous pumping at 797 nm. Mean lifetimes of donor and acceptor states were evaluated by using the integration method applied to the best fitting of fluorescence curves previously reported. Lifetime values were used to obtain the rate constants of all non-radiative energy-transfer processes involved and a complete set of rate equations better describing the observations was given. The rate equations were solved by numerical method and the population inversion between the 3H4 and the 3F4 excited states of Tm3+ was calculated to examine the beneficial effects on the gain associated with Ho3+ codoping. The results have shown that Tm3+ population inversion is reached only for high Ho3+-codoping (⩾0.3 mol%). Highest population inversion (∼1.6×1018 Tm3+ ions cm−3) was obtained in Tm(0.5%), Ho(1%)-codoped (ZBLAN) pumped by 2.8 kW cm−2. This population inversion density is ∼6.4 times higher than that one observed in Tm:Tb:GLKZ, Tm:Tb:Ge–Ga–As–S–CsBr and Tm:Ho:Ge–Ga–As–S–CsBr for a similar pumping condition (∼2.5×1017 cm−3). In addition, Tm(0.5%):Ho(1%):ZBLAN presents the highest population inversion that linearly increases with the pumping intensity; this behavior does not show saturation effect at least for the maximum intensity of 12 kW cm−2 employed. The use of 1 mol% of Ho3+-codoping maximizes the potential gain of Tm3+-doped (0.5%) ZBLAN to produce stimulated emission near 1.5 μm, making this material suitable for using it as fiber optical amplifier and/or fiber laser operating in 1.4–1.5 μm region of the spectrum.