Modeling on a multi-level rate equation model and rovibrational relaxations of HBr-filled hollow-core fiber lasers

By utilizing the transitions between rovibrational energy levels of gas molecules, a large number of laser spectral lines can be output in the range from mid-infrared to far-infrared. However, research on its laser dynamics is still insufficient. Here, we propose a multi-level rate equation theoretical model using HBr-filled hollow-core fiber gas laser (HCFGL) as an example. Compared with traditional four-level or six-level gas laser models, our model includes 66 rovibrational energy levels involved in the main laser process and fully considers both vibrational and rotational relaxation processes. The calculated results show more accurate estimates of laser threshold and slope efficiency. By using the gradient descent algorithm, the problem of efficiently solving highly nonlinear equations has been solved. It reveals that the gain of the gas medium predominantly concentrates at the entry point, resulting in a significant thermal impact and a notable depletion of the population. Furthermore, the output behavior of various pump spectra exhibits a consistent correlation with the distribution of rotational levels within the corresponding vibrational state. This study not only provides guidance for the design of HCFGL but also a practical scheme for the theoretical modeling and simulation of gas laser dynamics.