Numerical and experimental investigation of mid-infrared laser action in resonantly pumped Pr3+ doped chalcogenide fibre
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Numerical modelling of a Pr3+-doped chalcogenide glass fibre laser is presented in this paper. The spectroscopic parameters are extracted from in-house prepared Pr3+ doped selenide-chalcogenide glass samples and used in the modelling. In this contribution, particular attention is paid to a novel resonant pumping scheme. The modelled laser performance is tested as a function of pump wavelength, fibre length, signal wavelength, fibre background loss and output coupler reflectivity. The modelling results show that the proposed resonant pumping scheme, which might be achieved in practice using a high power QCL pump, allows for a significant reduction in the laser threshold and an increase in the laser efficiency. A slope efficiency of 54% is calculated when the fibre losses are brought down to 1 dB/m.
KeywordsMid-infrared fibre laser Chalcogenide glass Mid-infrared Rare earth doped glass
High power mid-infrared fibre laser sources with emitting wavelengths covering the range stretching from 4 to 5.5 μm offer many applications in remote sensing, medicine and defence (Seddon 2011, 2013; Pollnau and Jackson 2008; Jackson 2012). However, in order to access these wavelengths, low phonon energy host materials are needed. Among the most promising host materials for this wavelength region are chalcogenide glasses (Seddon et al. 2010; Tao et al. 2015). Chalcogenide glasses possess good rare earth ion solubility, high refractive index and can be drawn into fibre. These characteristics make chalcogenide glasses an attractive host material for rare-earth ions (Seddon et al. 2010; Tao et al. 2015). Recent publications show that there is a particularly large interest in mid-infrared fluorescence from the (3F2,3H6) → 3H5 (~3.7–4.2 μm), and 3H5→3H4 (4.3–5.0 μm) transitions of Pr3+ doped selenide glass (Sakr et al. 2014; Sójka et al. 2014; Karaksina et al. 2016a, b; Shpotyuk et al. 2015; Chahal et al. 2016; Shaw et al. 2001). This is because Pr3+ ions in chalcogenide glass have a high pump absorption cross-section, and also because Pr3+ can be pumped with commercially available laser diodes. Despite this, a Pr3+ doped selenide chalcogenide glass fibre laser has not yet been realized. The first problem that stops this technology is the difficulty of manufacturing high purity rare earth doped chalcogenide glasses. Secondly, both the upper and lower laser manifolds possess long lifetimes in comparison to that of the ground state. This tends to cause self-terminating laser operation and makes achieving population inversion difficult. One possible solution to this latter obstacle can be cascading two laser transitions (Quimby et al. 2008). However, the practical realization of cascading is challenging, since it requires the fabrication of two pairs of wavelength-matched fibre gratings in the Pr3+ doped chalcogenide glass fibre. Additionally, significant pump power is required in order to achieve laser action for both transitions. Thus, a potentially better solution is to pump the laser resonantly using a QCL (quantum cascade laser). The low quantum defect of the resonantly pumped praseodymium ions potentially enables the fibre laser to achieve high wall-plug efficiency. Further, the resonant pumping reduces the thermal load due to a low quantum defect. This feature is particularly important for fibres fabricated from low glass transition temperatures like chalcogenide glasses. Currently, high power QCLs operating around 4.1 μm are commercially available (http://www.pranalytica.com; Rauter et al. 2013). Resonant pumping of the Pr3+ ions in low phonon laser crystals using QCLs was suggested in (Ferrier et al. 2009). However, in that study excited state absorption (ESA) was not included in the model which, as the authors themselves note, is a significant shortcoming.
In this contribution, we therefore have paid particular attention to the ESA processes, the inclusion of which is, as we show, essential for predictive modelling. Hence, we extract the ESA spectrum of the 3H5→(3F2,3H6) transition. Then using a complete set of experimentally extracted modelling parameters, including ESA emission and absorption cross-sections, we developed a numerical model of a resonantly pumped Pr3+ selenide fibre laser. Using the model, we study the influence of the ESA on the Pr3+ selenide fibre laser performance and identify the best pumping wavelength for obtaining mid-infrared lasing in a resonantly pumped Pr3+, doped selenide chalcogenide glass fibre laser. Finally, we comprehensively study the laser performance as a function of pump wavelength, fibre length, signal wavelength, fibre background loss, and output coupler reflectivity.
The paper is divided into five sections. After this introduction, Sect. 2 describes the experimental results, which confirm the presence of ESA when pumping resonantly. The procedure used to calculate the ESA cross-section is presented in Sect. 3. In Sect. 4, we develop a numerical model of the resonantly pumped Pr3+ doped chalcogenide glass fibre laser and perform a numerical study of the resonantly pumped fibre laser characteristics. Finally, some conclusions are drawn in Sect. 5.
2 Experimental proof of the presence of ESA
3 Calculation of ESA cross section
To evaluate numerically the effect of the ESA on the laser efficiency of the Pr3+ doped selenide fibre, the absorption cross-section related to the 3H5→(3F2,3H6) transition must be known. In this contribution, we estimated the ESA cross-sections using the Judd–Ofelt (J–O) theory, the McCumber method, and the Fuchtbauer–Ladenburg (F–L) equation (Gomes et al. 2010). The rates of spontaneous emission for (3F2,3H6) → 3H5, and 3H5→3H4 transitions were calculated using our Judd–Ofelt parameters for Pr3+ doped selenide glass: Ω2 = 8.156*10-20cm2, Ω4 = 8.08*10-20cm2, Ω6 = 5.70*10-20cm2, which were recalculated after removing Se–H contribution at 4.5 μm from absorption spectra. Taking into consideration the small energy difference between the levels 3F2 and 3H6 it may be assumed that both levels are in thermal equilibrium. Thus, using Boltzmann statistics, the total radiative rate from the combined pair of levels is given by (Caspary 2003; Quimby and Aitken 2003).
Radiative rates (electronic (Aed), and magnetic (Amd) dipole contribution) and radiative branching ratios (β) for 3F2→3H6, 3F2→3H5,3H6 → 3H5, 3F2→3H4, 3H6 → 3H4 and 3H5 → 3H4 transitions in Pr3+ selenide chalcogenide bulk glass as calculated using Judd–Ofelt theory
Calculated radiative lifetimes (τrad), non-radiative lifetime (τnr) (multi-phonon relaxations) and total lifetimes (τtot). The non-radiative lifetimes are estimated upon results presented in (Shaw et al. 2001)
Calculated radiative lifetime τrad/(ms)
Estimated non-radiative lifetime
Calculated total lifetime τtot/(ms)
According to the results presented in Tables 1 and 2, the (3F2,3H6) → 3H5, and 3H5→3H4 transitions have a similar strength. Thus, for 2 µm pumping, these transitions are self-terminating. This causes population bottlenecking as a result of the comparatively long lifetime of the (3F2,3H6) → 3H5 transition, and saturation of the laser output. The calculated ESA absorption cross-section is presented in Fig. 3. The maximum cross-section for ESA is equal to 0.90 × 10−24 m2 at λ = 3.76 μm.
4 Results and discussion
Pr3+ doped chalcogenide glass fibre laser modelling parameters
9.46 × 1024
Fibre core diameter
Fibre clad diameter
Fibre numerical aperture
Confinement factor for pump wavelength
Confinement factor for signal wavelength
Signal emission cross-section at 4.8 μm
1.14 × 10−24
The performance of resonantly pumped selenide chalcogenide glass fibre lasers doped with Pr3+ was comprehensively studied. Particular attention was paid to the role of excited state absorption (ESA), which has not been considered previously in the literature on mid-infrared transitions of Pr3+ in selenide chalcogenide glasses. ESA absorption cross section spectra were extracted using McCumber theory. The experimentally extracted parameters formed the basis for the numerical model used in this study. The numerical results showed that ESA had a major influence on the laser performance and that its effect could be reduced by selecting the pump wavelength so that σGSA > σESA. It was also shown that a resonant pumping scheme using a high power QCL is a better solution when compared with the best pumping scheme reported so far. The results obtained showed that resonant pumping allowed for a significant reduction in the laser threshold, and an increase of the laser efficiency. Furthermore, we showed that knowledge of the ESA spectral distribution is indispensable when selecting the optimal wavelength for resonant pumping.
This research has been partly supported by the European Commission through the framework Seven (FP7) project MINERVA (317803; www.minerva-project.eu). Also we acknowledge COST Action MP 1401 supported by the EU Framework Programme Horizon 2020. LS would like to acknowledge support by the Polish Ministry of Science and Higher Education under the project entitled “Iuventus Plus”, 2016–2018 (project no. IP0441/IP2/2015/73).
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