Theoretical study of Dy<sup>3+</sup>,Na<sup>+</sup>: PbGa<sub>2</sub>S<sub>4</sub> mid-infrared laser based on experimental parameters

Abstract

Based on the absorption spectra of Dy<sup>3+</sup>, Na<sup>+</sup>:PbGa<sub>2</sub>S<sub>4</sub> crystal elements, as well as the theoretical calculation data obtained from Judd-Ofelt analysis, we have derived partial fluorescence absorption and emission cross sections. For energy levels that cannot be directly measured, we have employed the reciprocal method to calculate their respective absorption and emission cross-sections. Combing both experimental measurements and calculated data, a numerical simulation is conducted to investigate the experimental setup for generating a 4.3 μm mid-infrared laser through direct pumping of dysprosium and Dy<sup>3+</sup>, Na<sup>+</sup>:PbGa<sub>2</sub>S<sub>4</sub> crystals using 1.3 μm and 1.7 μm diode lasers pumping. The simulation calculates spatial distributions of laser power, gain coefficient, and absorption coefficient within the crystal. Furthermore, we analyze the effects of pumping power, crystal length, and output mirror reflectance on laser performance. The model introduces 2.9 μm laser oscillation and observes the change of output power before and after introduction. Our findings demonstrate that the incorporation of 2.9 μm laser oscillation effectively facilitates the population transfer from the <sup>6</sup>H<sub>13/2</sub> level to the ground state 6H15/2, thereby mitigating the self-terminating phenomenon during the transition between the <sup>6</sup>H<sub>11/2</sub> and <sup>6</sup>H<sub>13/2</sub> levels, consequently enhancing both output power and slope efficiency of the laser system. Numerical results indicate that maximum output powers for the 1.3 μm diode laser pumping are achieved at 103 mW with a pumping threshold of 12 mW and a slope efficiency of 2.8%, while for the 1.7μm diode laser pumping, they reach up to 315 mW with a pumping threshold of 46 mW and a slope efficiency of 8%. Additionally, the optimal crystal lengths are determined as 17 mm for the 1.3 μm diode laser pumping and 32 mm for the 1.7 μm diode laser pumping. Finally, the best reflectance value for the output mirror is 0.92. These numerical results have important guiding significance for crystal processing and the selection of optical path structure parameters.