Population inversion between the 3H 4 and the 3F 4 excited states of Tm 3+ investigated by means of numerical solutions of the rate equations system in Tm 3+-doped and Tm 3+, Ho 3+-codoped fluoride glasses

Abstract

Population inversion between the 3H 4 and the 3F 4 excited states of Tm 3+ ions responsible for the 1.5 μm emission in Tm 3+ singly doped (0.5%) and Tm 3+, Ho 3+-codoped fluoride (ZBLAN) glasses and its dependence on the Ho 3+ 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 3H 4 and the 3F 4 excited states of Tm 3+ was calculated to examine the beneficial effects on the gain associated with Ho 3+ codoping. The results have shown that Tm 3+ population inversion is reached only for high Ho 3+-codoping (⩾0.3 mol%). Highest population inversion (∼1.6×10 18 Tm 3+ 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 (∼2.5×10 17 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 Ho 3+-codoping maximizes the potential gain of Tm 3+-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.