Numerical modelling of Tb3+ doped selenide-chalcogenide multimode fibre based spontaneous emission sources
A model is developed of a terbium (III) ion doped selenide chalcogenide glass fibre source that provides spontaneous emission within the mid-infrared (MIR) wavelength range. Three numerical algorithms are used to calculate the solution and compare their properties.
KeywordsFibre lasers Low phonon energy glasses Fibre laser modelling Mid-infrared light
There are many applications for mid-infrared (MIR) light sources in medicine, biology, environment monitoring, food security and defense. There are many types of light sources potentially available for MIR wavelength range, which include fibre lasers. A large effort has been invested into the development of MIR lanthanide doped fibre lasers. Many pumping schemes have been proposed for this purpose. So far, the success in this field of research is limited to operating wavelengths less than 4 μm. However, the spontaneous emission MIR light fibre sources recently realised using lanthanide ion doped multimode fibres have exceeded the 4 μm barrier and found applications in sensor technology (Starecki et al. 2015; Chahal et al. 2016). Such sources are potentially highly reliable, low cost, and robust. In this contribution using a numerical model we study the luminescence properties of selenide-chalcogenide glass fibres doped with terbium (III) ions applied as wide spectrum spontaneous emission MIR light sources covering the wavelength range stretching from 4 to 5.5 μm. Such a system was shown recently to offer a very simple pumping mechanism (Sojka et al. 2017).
For this purpose we fabricated selenide chalcogenide glass terbium doped multimode fibre and bulk samples and performed absorption and photoluminescence spectrum measurements. From the experimental results using Judd–Ofelt theory and McCumber and Fuchtbauer–Ladenburg theory we extracted the absorption and emission cross section spectra for the relevant transitions and the photoluminescence lifetimes. The details of this procedure are provided in (Sojka et al. 2017). Using an experimentally derived set of parameters we realised a lanthanide doped multimode fibre numerical model based on the rate equations’ approach. Using the model, numerical analysis was performed of the MIR spontaneous emission fibre source, whereby three methods were compared, which calculate numerically a solution of the set of ordinary differential equations. One of them consists in calculating the solution rigorously subject to the given boundary conditions while the other two are based upon an approximate approach, which relies on the assumption of the low intensity of the signal flux. The results show the limitations of the approximate approach.
Two approximate algorithms have been compared for analysis of spontaneous emission fibre sources based on decoupling the solution of the equation for the pump wave from the one for the signal wave. As a reference, a method was used that rigorously solves the boundary value problem using a numerical method. The results show that approximate methods predict correctly the shape of the dependence of the MIR output power on the pump power. Thus using the approximate techniques below lasing threshold results in a small but non-negligible calculation errors. Counter intuitively, the values of the relative error do not tend to zero at low pump power values but do so at large values of the pump power for the technique, which calculates an approximate solution fulfilling the boundary conditions.
This Project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 665778 (National Science Centre, Poland, Polonez Fellowship 2016/21/P/ST7/03666).
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